Análisis dimensional

135
(/)', -#)#$',. " .$#,2.'"+ #$ ( /)0$!-'# # #$ & #!'# #+0)'.'. %'*&+.',+#) -$%/*# $#'"'3* "+,,$%'# 1 /)$*. # &.-#.#" $#)-&! ." #"

description

Julio Palacios

Transcript of Análisis dimensional

Page 1: Análisis dimensional

(/)', -#)#$',." .$#,2.'"+ #$ ( /)0$!-'# # #$ & #!'#

#+0)'.'.%'*&+.',+#)

-$%/*# $#'"'3*

"+,,$%'# 1 /)$*. #

&.-#.#" $#)-&! ." #"

Page 2: Análisis dimensional

97J;:HqJ?9E :; B7 KD?L;HI?:7: :; C7:H?:

") .'&-&-$&(%)-&*)"'

I;=KD:7 ;:?9?rD

9EHH;=?:7 N 7KC;DJ7:7

%-+"-"!#"'+% I( 7(("$,&$

* 2 / -

Page 3: Análisis dimensional

;I +,*+&%$"$m @e\Y_FQ\QSY_c&CQTbYT&*2..

FbY^dUTY^ I`QY^

D(E HWdb(f3,2+'./:U`wcYd_\UWQ\3C( /(.-/'*2/-

JQ\\UbUcdY`_WbsVYS_cTU\Q ;TYd_bYQ\;c`QcQ'9Q\`U&I( 7( Hu_c H_cQc&+/( CQTbYT

#$%!" "

;cdU \YRb_XQbUce\dQT_TUc]UcebQT_(B_ aeU XQi U^t\ TUVe^TQ]U^'dQ\]U^dU eUf_ SQRbuQU^ e^ `Qb TUSQ`ude\_c(FUb_\Q ^_fUTQTUcdQ\&i cUXQ\\QdQ^U^ `eW^QS_^ \QcYTUQcTUSeQ^d_cQed_bUccU_Se`Q^ U^SeUcdY_^UcbU\QSY_^QTQcS_^ 7^s\YcYcTY]U^cY_^Q\i XQcdQS_^ \QcT_SdbY'^Qc VY\_cwVYSQcQSU`dQTQc`_b \Q ]Qi_buQ TU\_c VucYS_cS_^dU]`_bs^U_c&aeU XUZejWQT_Y]`bUcSY^TYR\UZecdYVYSQb]Yc QcUbd_cXQcdQ\Q cQSYUTQT&i TU]_cdbQbaeU&U^ d_T_c\_c SQ`ude\_cTU\Q <ucYSQ&U\^eUf_ ]td_T_QfU^dQZQQ\_c `bUS_^YjQT_c_b \_c dbQdQTYcdQc(

JbQc U^cQi_c2 bUSdYVYSQSY_^UcaeU XQ^ TebQT_]eSX_c Qv_c&SbU_XQRUbS_^cdbeYT_e^Q dU_buQS\QbQi cU^SY\\QTU\Qc ]QW^YdeTUcVucYSQc(CYS_^VYQ^jQcURQcQU^U\RU^U`\sSYd_TU]Y S_\UWQU\`b_VUc_bHYSQbT_

1 IQ^ @eQ^&aeU XQUhQ]Y^QT_]Y^eSY_cQ]U^dU]Y ]Q^ecSbYd_i ]U XQceWUbYT_QSUbdQTQc]_TYVYSQSY_^Uc(BUUh`bUc__b U\\_]Y S_bTYQ\WbQdYdeT(

BYcR_Q&VURbUb_*2..(

Page 4: Análisis dimensional

?DJHE:K99?rD

IU TURUQ\RQbw@UQ8QdYcdU<_ebYUb"*#U\XQRUbQ`\YSQT_Q\Qc]QW'^YdeTUcVucYSQcU\S_^SU`d_WU_]tdbYS_TUTY]U^cYwi& `_b U\\_&]UbUSUcUbS_^cYTUbQT_S_]_ U\`bUSebc_bTU\7^s\YcYcTY]U^cY_^Q\(;^ ce _RbQY^]_bdQ\&.9K?B:6 2>2<HD:AE656 <2 492<6EB$UcdQR\USUU\ S_^SU`d_TUTY']U^cYw^TU]_T_ dQ^S\Qb_i `bUSYc_aeU ^_ `_TU]_c bUcYcdYb\Q dU^dQ'SYwTUbU`b_TeSYb\_dUhdeQ\]U^dU3

n;c ^USUcQbY_XQSUb_dQbaeU SQTQ]QW^YdeT&Y^TUdUb]Y^QTQ_ 9E\\,'

dQ^dU&dYU^Ue^Q 5:=6>C:M>aeU \UUc`b_`YQ&i aeU \_c dtb]Y^_c TUe^QUSeQSYw^^_ `_TbuQ^cUbS_]`QbQT_ccY _ defYUcUU\]Yc]_ 6G@?>6>D656 5:=6>C:?>6CC

n;^ \Q dU_buQQ^Q\udYSQTU\SQ\_b&d_TQUSeQSYw^bU`bUcU^dQe^Q bU\Q'SYwU^dbU\Qc ]QW^YdeTUcS_UhYcdU^dUc\_^WYdeT&:' dYU]`_&8' dU]`UbQ'debQ&9' SQ`QSYTQTSQ\_buVY_Q`_b e^YTQTTUf_\e]U^& U4S_^TeSdYfYTQTce`UbVYSYQ\&1! i S_^TeSdYfYTQTdtb]YSQ&*" :YSXQbU\QSYw^^_ TU`U^TUTU\QU\USSYw^TU\Qe^YTQTTU\_^WYdeTaeU&_b ce `b_`YQ QdebQ\UjQ&UcS_^dY^WU^dU(p

>QSU_RcUbfQb\eUW_<_ebYUbaeU\Qc]UTYTQcTUe^Q ]Yc]Q SQ^dYTQTUcds^U^ bQjw^Y^fUbcQTU\Qc e^YTQTUcaeU cU U]`\UU^ `QbQ]UTYb\Q(K^ SQ]RY_U^\Q e^YTQTTU\_^WYdeT_ QVUSdQ^YQ\_c dYU]`_c^YQ\QcdU]`UbQdebQc&`Ub_ cuY^V\eiUc_RbU\Qc]UTYTQcTU1! U&i *" 8Qcs^T_cUU^\QTUVY^YSYw^TUUcd_cS_UVYSYU^dUc&TUTeSUU\SQ]RY_aeU Uh`UbY]U^dQ^SeQ^T_ cU Q\dUbQ\Q e^YTQTTU\_^WYdeTi& WU^UbQ\YjQ^T_U\ S_^SU`d_WU_]tdbYS_&TYSUaeU n\QTY]U^cYwTU U S_^ bU\QSYwQ \Q e^YTQTTU\_^WYdeTfQ\U' ,&\QTU* Uc' * N \Q TU1 Uc' +p(B\Q]Q QUcd_c x']Ub_c 6G@?>6>D6C5:=6>C:?>2<6CS_^ bU\QSYwQ \Q\_^WYdeT&i XQSUQ^s'\_WQcS_^cYTUbQSY_^UcS_^ bUc`USd_Q \Qc _dbQcT_c fQbYQR\Uc&dYU]`_ idU]`UbQdebQ&_RdU^YU^T_U\cYWeYU^dUSeQTb_3

Page 5: Análisis dimensional

B\Q]Q <_ebYUb\QQdU^SYw^c_RbU\QSYbSe^cdQ^SYQTUaeU U\QbWe]U^d_TUd_TQVe^SYwaeUVYWebUU^e^Q \Ui VYcYSQ&`_b UZU]`\_&e^Q Uh`_^U^SYQ\_ e^Q Ve^SYwdbYW_^_]tdbYSQ&XQTUdU^Ub e\_c d_T_c cec Uh`_^U^dUcTY]U^cY_^Q\Uc&`eUc cw\_QcuceSUTUbsaeU ce fQ\_b^e]tbYS_ cUQY^TU`U^'TYU^dUTU\Qc e^YTQTUcaeU cUU\YZQ^`QbQ]UTYb\_^WYdeTUc&dYU]`_c idU]`UbQdebQc(;^ UcdQQVYb]QSYw^bQTYSQ&cUWxfUbU]_c&d_T_ U\7^s\Y'cYcTY]U^cY_^Q\(

:U \Q `bUSUTU^dUUh`_cYSYwbUce\dQS\QbQ]U^dUaeU&QbQ<_ebYUb&\Q TY]U^cYw^&U^ cY^We\Qb&Uce^ QdbYRed_USe\YQbTUSQTQ]QW^YdeTiaeU \_c Uh`_^U^dUcTY]U^cY_^Q\Uc&\_ aeU QX_bQcU\\Q]Q^ TY]U^cY_^Uc&c_^ ]Q^YVUcdQSY_^UcTUTYSX_QdbYRed_(

BQcYTUQcTU<_ebYUbVeUb_Q`\YSQTQcS_^ WbQthYd_QVY^UcTU\ QcQT_cYW\__b HUi^_\Tc "+#&B_TWU",#&<Ydj=UbQ\T"-#&HyS[Ub".#&@UQ^c"/#&i& ]ei Uc`USYQ\]U^dU&`_b \_bT HQi\UYWX"0#(BQc Q`\YSQSY_^UcS_^cuc'dYUb_^&`bY]Ub_&U^\Q S_]`b_RQSYwTU\QX_]_WU^UYTQTTU\QcU_eQSY_'^Uc S_^ U\VYTUTUcSeRbYbUbb_bUcTUSs\Se\_ i& TUc`etc& _b Y^YSYQdYfQ`bY^SY`Q\]U^dUTU\_bT HQi\UYWX&cUQ`\YSwU\7^s\YcYcTY]U^cY_^Q\Q \QbUc_\eSYwTU`b_R\U]Qc Sei_ dbQdQ]YU^d_TYbUSd_`bUcU^dQTYVYSe\dQTUc]QdU]sdYSQcY^ce`UbQR\Uc(B_bT HQi\UYWXU]`\Uw `_b `bY]UbQfUj \Qc]QW^YdeTUcS_^ Uh`_^U^dUcTY]U^cu_^Q\Uc^e\_c U^\QCUSs^YSQTUV\eYT_ci&`_b U\\_&]UbUSUcUbS_^cYTUbQT_&TUc`etc TU<_ebYUb&S_]_ U\Ve^TQT_bTU\ 7^s\YcYcTY]U^cY_^Q\(9_^dbYReiUb_ UVYSQj]U^dUQ UcdUTUcQbb_\\_Y^YSYQ\\_c dbQRQZ_cTUHYQR_eSXY^c[iU^ HecYQ"1#i \_c TUF\Q^S[ "2#i;u^cdUY "*)# U^ 7\U]Q^YQ(

;\ Qv_ *2*- Q`QbUSYwU^D_bdUQ]tbYSQe^ dbQRQZ_TU8eS[Y^WXQ]"**#U^ U\ aeU cU TQe^Q bUW\QQbQQfUbYWeQbU\ ^x]Ub_ TU]_^_]Y_c TUUh`_^U^dUcTY]U^cY_^Q\Uc^e\_c aeU `eUTU^V_b]QbcUS_^ d_TQc\Qc]QW'^YdeTUcaeU Y^dUbfYU^U^U^U\VU^w]U^_aeU cUUcdeTYQ(JQ\Uc]_^_]Y_ccU TU^_]Y^Q^>N=6B?C0d i& `_b Uc_&TY_8bYTW]Q Q \Q SYdQTQbUW\QU\^_]RbU TUdU_bU]QTU`Y(

;^ bUQ\YTQT&<_ebYUbXQRuQiQ `bUfYcd_&cUWx^XU]_c fYcd_&aeUd_TQUSeQSYwVucYSQTURuQS_^cYcdYbU^e^ ]_^_]Y_ TUTY]U^cY_^Uc^e\QcYWeQ\QT_Qe^Q Ve^SYwSei_c QbWe]U^d_cdefYUcUdQ]RYt^TY]U^cY_^Uc^e\Qc&i U\\\Q]QT_ dU_bU]QTU`YUbQiQ U]`\UQT_dsSYdQ]U^dU&`Ub_S_^d_T_ bYW_b&`_b \_c <ucuS_cY^W\UcUcQ^dUc]U^SY_^QT_c&Uc`USYQ\]U^dU`_b@UQ^c(7TU]sc& cUWx XYj_^_dQbCtdbQ\ "*+#&U\ dU_bU]QU^ SeUcdYw^

G ** * 9 U

B_^WYdeT((((((((( * E E ' * " #JYU]`_ (((((((((( E * E %* %* EJU]`UbQdebQ((((( E E * %* ' * %*

XQRuQcYT_iQ U^e^SYQT__b LQcSXi "*,# U\Qv_ *12+&Qe^aeU cY^bUVU'bYbcUUh`bUcQ]U^dUQ\_c ]_^_]Y_c TUTY]U^cYw^e\Q( :U d_T_c]_T_c&U\ dbQRQZ_TU 8eS[Y^WXQ]def_ \Q V_bde^QTU QdbQUb\Q QdU^SYwTUVucYS_c&]QdU]sdYS_cUY^WU^YUb_cTU\]e^T_ U^dUb_&aeU \_ XQ^c_]UdYT_Q SbudYSQ]Y^eSY_cQ(

9_^cdQ U\ dU_bU]QTU`Y TUT_c `QbdUc(;^ \Q `bY]UbQcUdbQdQTUTU]_cdbQbaeU d_TQUSeQSYwVucYSQ4?=@<6D2$Ucd_Uc&aeU ceRcYcdQSeQ^T_cUSQ]RYQ QbRYdbQbYQ]U^dU\Qce^YTQTUcVe^TQ]U^dQ\Uc&`eUTUd_]Qb \QV_b]Q3

U^\QaeU \Qc0dYc_^ d_T_c\_c ]_^_]Y_c TUTY]U^cYw^e\Q&Y^TU`U^TYU^'dUcU^dbUcu&aeU `eUTU^V_b]QbcUS_^ \Qc]QW^YdeTUcaeU Y^dUbfYU^U^U^U\`b_R\U]Q( BQcUWe^TQQbdUQVYb]QaeU U\^x]Ub_ TUdQ\Uc]_^_]Y_cUcYWeQ\Q\Q TYVUbU^SYQ&0* >% 6! U^dbUU\^x]Ub_ d_dQ\TU]QW^YdeTUci U\TU\QcVe^TQ]U^dQ\Uc(

BQ`bY]UbQQbdUTU\dU_bU]QUc\QaeU ]sc XQ\\Q]QT_ \QQdU^SYw^TU\_c ]QdU]sdYS_c(FbY]Ub_&BUfY'9YfYdQ"*-# XYj_ _dQbaeU \QcUSeQSY_^UcX_]_Wt^UQcaeU cUUcdeTYQU^ \_c Sebc_cTU7^s\YcYc _ c_^ \QcaeU cU]Q^UZQ^U^ <ucYSQ&cY^_U^ =U_]UdbuQ&i edY\YjwU^ ce dbQdQT_TUCUSs'^YSQVe^SY_^UcaeU c_^ X_]_Wt^UQc&_b cU`QbQT_&S_^ bU\QSYwQ \_cTYfUbc_cWbe`_cTUfQbYQR\Uc&\Qc aeU bU`bUcU^dQ^\_^WYdeTUc&dYU]`_ci]QcQc(;cdU ]td_T_ `_TbuQcUbWU^UbQ\YjQT_Y^db_TeSYU^T_^eUf_c Wbe`_cTUX_]_WU^UYTQT&`Ub_Uc`bUVUbYR\UedY\YjQb\QdU_buQTU\QcVe^SY_^UcX_']_Wt^UQcWU^UbQ\YjQTQcTUcQbb_\\QTQ`_b ;XbU^VUcd'7VVQ^QccZUgQ"*.#(;cdQ dU_buQbUcU^dQWbQ^TUcTYVYSe\dQTUc&i aeYjs cUQtcdQ\Q bQjw^TUaeU \_c VucYS_c_ \U XQiQ^ `bUcdQT_\Q TURYTQQdU^SYw^(F_b V_bde^Q&WbQSYQcQ\ `b_VUc_bHYSQbT_IQ^ @eQ^ "*/#& _cUU]_c e^Q Uh`_cYSYw^S\QbQi cU^SY\\QTU\QcVe^SY_^UcX_]_Wt^UQcWU^UbQ\YjQTQc&S_]`\UdQTQS_^ Q\We^_cdU_bU]Qc(BQ`bY^SY`Q\S_^dbYReSYw^TUH( IQ^ @eQ S_^cYcdUU^ XQRUbTU]_cdbQT_aeU \_c cYcdU]QcTUTY]U^cY_^UcecQT_cU^ SQTQSQ`ude\_TU\Q <ucYSQV_b]Q^ Wbe`_cQRU\YQ^_cS_^ RQcUVY^YdQ&Q^s\_W_cQ \_c cYcdU]QcXY`UbS_]`\UZ_c&\_ SeQ\ `Ub]YdUcYcdU]QdYjQb\Qc dU_buQcVucYSQcS_]_ XYj_A?UY S_^ \Qc WU_]UdbuQcU^ ce VQ]_c_ `b_WbQ]QTU;b\Q^WU^&i bUce\dQ QcuU\UWQ^dU]U^dUS\QcYVYSQT_c\_c cYcdU]QcTUe^Y'TQTUci cec dbQ^cV_b]QSY_^Uc&dQ^d_SeQ^T_cUS_^cUbfQ\QRQcU&cUWxcUXQSuQXQcdQQX_bQ&S_]_ SeQ^T_cUSQ]RYQtcdQ(

9_^ ce iQ fYUZQXYcd_bYQ&S_^ ce edY\YTQT]Q^YVYUcdQ&aeU cUbUfU\Q&_cw\_U^ U\SQ]`_ TU\Q<ucYSQdUwbYSQ&cY^_U^ `b_R\U]Qc dtS^YS_c&U^\_cU^cQi_c S_^ ]_TU\_c bUTeSYT_cTU) QfY_^Uc&ReaeUc&i S_^cdbeSSY_^Uc

Page 6: Análisis dimensional

*+ 7DqB?I?I :?C;DI?ED7B?DJHE:K99?rD

XYTbse\YSQci&c_RbUd_T_&S_^ \QY^dUbfU^SYw^TU\_c VucYS_c]sc U]Y^U^'dUc&cUbuQTUUc`UbQbaeU U\7^s\YcYcTY]U^cY_^Q\UcdefYUcUiQ QcU^dQT_c_RbURQcUccw\YTQc&i aeU XeRYUcUe^Q^Y]YTQTQSUbSQTU\Q ]Q^UbQTUU]`\UQb\_(BUZ_cTU cUbQcu&\_c VucYS_ccU XQ\\Q TYfYTYT_cU^(Wbe`_cSeiQc _`Y^Y_^UcTYcSbU`QU^ \_ ]sc UcU^SYQ\4U^ U\S_^SU`d_]Yc]_ TUTY]U^cYw^(

:YbuQcUaeU Q\_c VucYS_c\UcXQ_SebbYT_\_ aeU Q\XUbbUb_TU\SeU^d_&QaeYU QVeUbjQTU]QbdY\\UQbcU\U_\fYTwU\_VYSY_(GeYjsU\_\fYT_S_]U^'jw SeQ^T_CQhgU\\ QdbYReiwQ SQTQ]QW^YdeT&1$ e^Q 7MB=E<25:=6>%C:?>2<)

7\We^_cQed_bUc&U]`UjQ^T_ `_b J_\]Q^ "*0#&QdbYReiUQ\_c cu]R_'\_c aeU VYWebQ^U^ \Q Vwb]e\QcTY]U^cY_^Q\UcSYUbd_cU^dYT_Uc_dtbYS_iQVYb]QaeU \Q nfUbTQTUbQUcU^SYQTU\Qc]QW^YdeTUc&TUcTUU\`e^d_ TUfYcdQVucYS_&UcdsbU`bUcU^dQTQ`_b ce bUc`USdYfQVwb]e\QTY]U^cY_^Q\p(;cdQ _`Y^YwUcY^c_cdU^YR\U&`_baeU&cUWx XU]_c XUSX_fUb U^ _db_dbQRQZ_"*2#&S_^TeSYbuQQ TUcQdY^_cdQ\UcS_]_ U\SbUUbaeU U\]_]U^d_TUe^ `Qb TUVeUbjQcUc\Q ]Yc]Q S_cQaeU e^ dbQRQZ__ aeU U\SQ\_b&iaeU e^ s^We\_ i \Q UcRU\dUjTUe^Q S_\e]^Q c_^ ]QW^YdeTUcTUYWeQ\u^T_\U(;^ ]_T_ Q\We^_ eUTU^ d_]QbcU\Qc USeQSY_^UcTY]U^cY_^Q\UcS_]_ cecdYdedYf_cTU \Qc TUVY^YSY_^Uc&`eUc S_^ U\\_ YW^_bQbuQ]_c\QTYVUbU^SYQU^dbU\Q U^UbWuQY^dUb^Q&aeU Uce^Q Ve^SYwTUUcdQT_&i U\SQ\_b_ U\dbQRQZ_&aeU^_ \_ c_^( . _db_dQ^d_SQRUTUSYbTU\QcVe^SY_^UcdUb]_TY^s]YSQc3U^UbWuQ\YRbU&U^dQ\`uQi U^dQ\`uQ\YRbUaeU&Q `UcQbTUdU^Ub\Q ]Yc]Q Vwb]e\QTY]U^cY_^Q\&c_^ S_cQcTYVUbU^dUc(

B_c Qed_bUc]_TUb^_c&cQ\f_ bQbQcUhSU`SY_^Uc&_ XQ^ _\fYTQT_U\S_^SU`d_S\scYS_TUTY]U^cYw^&_ `bUcSY^TUTU\YRUbQTQ]U^dUTU\]Yk]_&i S_]_ SQTQe^_ U^dYU^TU`_b TY]U^cYwS_cQTYVUbU^dU&cebWk T?I9K'cY_^UcQ`QcY_^QTQc&cY^`_cYRY\YTQTTUQSeUbT_U^dbU\_c S_^db]SQ^dUc(>U QaeuQ\We^_cR_d_^UcTU]eUcdbQ(

IUWx^F\Q^S[&ndQ^VQ\d_TUcU^dYT_UcXQR\QbTU\Q TY]U^cYwB62<TUe^Q ]QW^YdeTS_]_ TU\ _]RbU B62<TUe^ _RZUd_p(

HUYSXU^RQSX!)'" TYSU3n9QTQ]QW^YdeTVucYSQcUce`_^U T_dQTQTUe^Q TY]U^cYwaeU SQbQSdUbYjQce _eQ\YTQT(pJbQc UcdUS_^Qd_TUTUVY^Y'SYw i TUTUSYbaeU \Q fU\_SYTQTi \Q QSU\UbQSYw^i U\ SQ]`_ U\tSdbYS_TURU dU^UbTY]U^cY_^UcTuVUbU^dtc&TYSUaeU XQi QbRYdbQbYUTQTU^ \Q]Q^UbQTUnbUTeSYb\QTY]U^cYwTUe^Q ]QW^YdeTTQTQQ\QcTY]U^cY_^UcU\U]U^dQ\Uc3\_^WYdeT&]QcQ i dYU]`_ i aeU&_b Uc_&cUce`_^U QbRYdbQ'bYQ]U^dUaeU SQbUSUTUTY]U^cYw^&^_ cw\_SYUbd_cVQSd_bUc^e]tbYS_c&cY^_XQcdQVe^SY_^UcTUUcdQT_"`_b UZU]`\_&\QdU]`UbQdebQ#p(

IUWx^U\ `b_VUc_b:YUccU\cX_bcd"+*#&\_c cu]R_\_c TU\Qc Vwb]e\QcTY]U^cY_^Q\Ucn^_ c_^ e^YTQTUcUc`USYQ\Uc&cY^_dQ^cw\_bU`bUcU^dQ^dUc"-6@B::C6>D2>D6>#TUSQTQdY`_TU]QW^YdeT(((i Ucd_cbU`bUcU^dQ^dUcc(UTU^_]Y^Q^TY]U^cYwTU\Q ]QW^YdeTbUc`USdYfQp&D_ QSUbdQ]_cQ QTY'fY^Qb\_ aeU XQTUU^dU^TUbcU`_b bU`bUcU^dQ^dU&iUc_ aeU&U^\eWQbTUU]`\UQbU\f_SQR\_Q\U]s^&bUSebbU:YUccU\cX_bcdQe^ f_SQR\_b_]Q^SU&aeYjs S_^ \Q S_^fYSSYwTUcUbQcu]UZ_b S_]`bU^TYT_ _b cec S_]`Q'dbY_dQc(

9YUbdQ]U^dU&XQR\QbTU\Q UcU^SYQTU\Qc ]QW^YdeTUci fY^Se\Qb\QS_^ \Qc TY]U^cY_^UcUc S_cQaeU&_b ce SQbsSdUb]UdQVucYS_&XQRuQTUcUbbU`eTYQTQ_b \_c VucYS_cQTcSbYd_cQ\Q<Y\_c_VYQ_`UbQSY_^Q\_ BwWYSQ

U^\QaeU +(! +($ OOO c_^ \_c cu]R_\_c TU\Qc]QW^YdeTUcaeU V_b]Q^\QRQcU&i E"\6 zzz E"] c_^ \_c Uh`_^U^dUcTY]U^cY_^Q\UcTU 1&9Qiw U^ U\_\fYT_\Q TUVY^YSYw^aeU <_ebYUbXQRuQTQT_TUdQ\UcUh`_^U^dUci ceb'WYUb_^\Qc]sc fQbYQTQc_`Y^Y_^UcQSUbSQTU\_ aeU cYW^YVYSQ^\_c cu]R_\_c`b_fYcd_cTU Qbt^dUcYcbUSd_c"$#( K^Q _`Y^Yw]ei UhdU^TYTQ&aeU cUbU']_^dQ Q 9\Ub[ CQhgU\\&i TU\Q aeU XU]_c `QbdYSY`QT_]eSX_c VucYS_cTU ]Y WU^UbQSYw^&Uc aeU TYSX_ccu]R_\_c i& `_b dQ^d_&\Qc Vwb]e\QcTY]U^cY_^Q\UccUbUVYUbU^Q \Qc e^YTQTUc&i QcucUUcSbYRU&`_b UZU]`\_3

( ( S]+ - ( WUbW* $( ,)

cY^SQUbU^ \Q SeU^dQTUaeU ^_c fUbuQ]_cU^ e^ Q`bYUd_cYe^ Q\e]^_Y^aeYcYdYf_^_c `bUWe^dQcUSw]_ cUXQSUQbQ]e\dY`\YSQbe^ SU^du]Udb_SeQTbQT__b e^ WbQ]_i TYfYTYbU\ `b_TeSd_ `_b e^ cUWe^T_U\UfQT_Q\ SeQTbQT_(

"$# F_b bQbQUhSU`SYw^&U^ U\fYUZ_dbQdQT_TU<ucYSQTU\`b_VUc_b9Xg_\k)(^TU \Q K^YfUbcYTQTTU IQ^ FUdUbcRebW_"*1#&_RbQaeU W_jwTU WbQ^bUcdYWY_Q `bY^SY`Y_cTU cYW\_&i aeU ^_ cUSYdQiQ U^ `QbdUQ\We^Q&cU U^SeU^dbQk^QTUVY^YSYw^TU \Qc TY]U^cY_^UcaeU Ucds TU QSeUbT_S_^ \Qc YTUQcTU <_ebYUb&:YSUQcu3

nIY\Qe^YTQTTUbYfQTQ+ fQbuQb_`_bSY_^Q\]U^dUQ\Q`_dU^SYQ5 kU\Qe^u'TQTTU\_^WYdeT&Q \Q `_dU^SYQA TU\Q e^YTQTTU]QcQ i Q \Q `_dU^SYQB kU \Qe^YTQTTUdYU]`_&cUTYSUaeU \Q e^YTQT+ dYU^U\Q TY]U^cYw@ S_^ bU\QSYwQ\Q e^YTQTTU\_^WYdeT&\Q TY]U^cYwA S_^ bU\QSYwQ \Q e^YTQTTU]QcQ i \QTY]U^cYwB S_^ bU\QSYwQ \Q e^YTQTTUd(YU]`_(p (

9_]`\UdQ^T_ UcdQTUVY^YSYw^S_^ U\ S_^SU`d_TUe^YTQTUcS_XUbU^dUc&(c] U\SeQ\ ^_ dYU^UcU^dYT_XQR\QbTUbU\QSY_^UcTU`b_`_bSY_^Q\YTQTU^dbUe^YTQTUc&cU\\UWQUhQSdQ]U^dUQ \Q Y^dUb`bUdQSYw^TU\Qc TY]U^cY_^UcaeU TkbU]_k U^ U\SQ`ude\_L( 9_^fYU^UXQSUb_dQb aeU& eUcd_ aeU \Qc Vwb]e\QcTY]U^c\EkQ\Ucc_^ Q`\YSQR\UcQ\Qce^YTQTUcTUe^Q `QbUZQTUcYcdU]QcS_XUbU^dUc&SeQ\UcaK\UbQ&^_ Uc`b_`Y_ QdbYReYb\Q TY]U^cYwQ \Qce^YTQTUc&cY^_Q \Qc]QW]deTUc(

!#

Page 7: Análisis dimensional

(* 2>d<:B:B 5:=6>B:?>2<

VUYOZO\OYZGJKRIhXI[RUJK EOKTG'<G XKGIIOjTL[K OTOIOGJGVUX3XOJMbSGT "))#% W[OKTGLOXSGW[K0JGYJOSKTYOUTKYTUZOKTKTKTSUJU GRM[TUIGXfIZKXGHYUR[ZU%YOTUW[KNGTJK JKLOTOXYK%VXKIOYGSKTZK%G VGXZOXJKRVXUIKYUW[KYK[ZOROIKVGXGSKJOXRGSGMTOZ[JXKYVKIZO\Gc"$#'

@GXGYKXIUTYKI[KTZKIUTY[ JUIZXOTG%JKHOKXGJGX3XOJMSGTRGXKIKZGVGXGVGYGXJKRVXUIKYUJK SKJOJGGRGJOSKTYOjT%VKXUYKROSOZGG[ZORO`GXRGYJOSKTYOUTKYUHZKTOJGYVUXRUYSgZUJUYIRfYOIUY_%MXGIOGYG KYZGOTIUTYKI[KTIOG%KR2TfROYOYJOSKTYOUTGRTUVOKXJKKTY[YSGTUYZUJGY[\OXZ[GROJGJ'@KXUNGIKI[KYZOjTJK VXOTIOVOUKRTKMGXW[KG IGJGSGMTObZ[J IUXXKYVUTJG[TG JOSKTYOjTJKZKXSOTGJG%V[KYGLOXSGW[KaTU ZOKTKYKTZOJUNGHRGXJK RGYJOSKTYOUTKYJK [TG SGMTOZ[JSOKTZXGYTUYKNG_GKYZGHRKIOJUKRYOYZKSGJK [TOJGJKYKTW[KNGJK SKJOXYKc'5K KYZGVUYObIOjTVXK\OGXKY[RZGW[K%GRVRGTZKGXRUYVXUHRKSGYJK2TfROYOYJOSKTYOUTGR%KYZUKY%GRLUXSGXRGROYZGJK RGYSGMTOZ[JKYW[KOTZKX\OKTKTKTKRLKTjbSKTUIUTYOJKXGJU%_ KYIXOHOXY[YK^VUTKTZKYJOSKTYOUTGRKY%NGIKXG`UTGbSOKTZUYZGTIGY[hYZOIUY%Y[ZORKY$ GRGSHOIGJUY%W[KNGTJK JKYIUXG`UTGXG ZUJUKRW[KZXGZKJK OTOIOGXYKKTKYZGYI[KYZOUTKY%_ ZUJUKRRU%YKMkTZKTJXKSUYUIGYOjTJK \KX%VGXGUHZKTKXYUR[IOUTKYJKLOIOKTZKY%V[KYZUW[KTUXK\KRGTZUJGRGOTLUXSGIOjTW[KKR2TfROYOYJOSKTYOUTGRKYIGVG`JK Y[SOTOYZXGX'

<G ZKTJKTIOGJK 3XOJMSGTNGVXK\GRKIOJUKTZXKRUYLhYOIUYIUTZKSbVUXfTKUY'7X' A[YYU")*#%GRXKY[SOXRUYZXGHGPUYSfY XKIOKTZKY%GLOXSGW[K0JUYSUTUSOUYJK EGYIN_TUYUTOT\GXOGTZKYSfY W[KVGXGRUYIGSbHOUYJK[TOJGJKYW[KVKXZKTK`IGTGRGKYZX[IZ[XGKTW[KTUYIURUW[KSUYc_ KTZOKTJKVUXKYZX[IZ[XGI[GRW[OKXG!JKRGYSkRZOVRKYSGTKXGYJK GZXObH[OXJOSKTYOUTKYG RGYSGMTOZ[JKY'

4UT Y[ RUGHRKVXUVjYOZUJK K^V[XMGXKR2TfROYOYJOSKTYOUTGRJK KRKbSKTZUYSKZGLhYOIUY%TUNGTRUMXGJURUYRjMOIUbVUYOZO\OYZGYUZXUXKY[RZGJUW[KRGX[OTGIUSVRKZGJKRSOYSU'6T UZXUR[MGXTUYNKSUYUI[VGJU

"$# @GXGRUYVUYOZO\OYZGY%RGHGYKJKRIUTUIOSOKTZULhYOIUYUTRGYSKJOJGY'6YZUV[KJKGJSOZOXYKI[GTJU YKZXGZGJK JKYI[HXOXRK_KYK^VXKYGHRKYKTLUXSGSGZKSfZOIG%VKXUTU JK !SUJU GHYUR[ZU'8GRORKUV[JU JKXXOHGXZUJGRGLhYOIGGXOYZUZgROIGIUT YjRUUHYKX\GXW[KZUJUYRUYI[KXVUYIGKTKTKRGOXK$#/* IUT RGSOYSG\KRUIOJGJ%_ JKYI[HXOjRGRK_JK RGOTKXIOGNGIOKTJUTUZGXW[K[TG HURG%JKYV[gYJK XUJGXI[KYZGGHGPU%KYIGVG`JK XUJGXI[KYZGGXXOHGNGYZGGRIGT`GX$#/* Y[ GRZ[XGOTOIOGR%JK JUTJKXKY[RZGW[K%YORGI[KYZGGXXOHGYKXKKSVRG`GVUX[T VRGTUNUXO`UTZGR%$ YOTU N[HOKXKXU`GSOKTZUY%RGHURGXUJGXhGYOTIKYGX%V[KYT[TIG GRIGT`GXhGY[ TO\KRUXOMOTGR'4USU YK\K' 8GRORKUTUZ[\U W[KSKJOXTGJGVGXGKINGXRGYHGYKYJK RG=KIfTOIG'

8[OJU 3KIQ "#! \G SfY GRRfW[KRUYVUYOZO\OYZGY%V[KYVGXGgR%KLKTjSKTULhYOIUKYZUJGSKJOJGK^VKXOSKTZGRW[KV[KJK YKXK^VXKYGJGKT IKTZhSKZXUY%MXGSUY_ YKM[TJUYc'4UT KYZGJKLOTOIOjT%W[KKT XKGROJGJKY[TG GLOXSGIOjTMXGZ[OZG%RUW[K8GRORKUUHYKX\jJKYJKRGZUXXKJK @OYGTUYKXhGYOW[OKXG[T LKTjbSKTULhYOIU'

:>CA?5D44:e> (+

K^ZKTYGSKTZKJK JOINGJUIZXOTGLORUYjLOIG")+# KTXKRGIOjTIUTRG7hYOIGKTMKTKXG<2NUXGTUYROSOZGXKSUYGJKSUYZXGXW[KKR2TfROYOYJOSKTYOUbTGR%I[GTJU YKRRK\GTG Y[ K^ZXKSURGYIUTYKI[KTIOGYJK RG<jMOIGVUYObZO\OYZG%VOKXJKZUJGY[ KLOIGIOG'5OING<jMOIG%GL[KX`GJK W[KXKXYKXUVKbXGIOUTGR%YKNGNKINUOTUVKXGTZK"$#'

3[XTOYZUT3XU]T ")-# VGXZKJKRNKINU%YKiGRGJUVUX6JJOTMZUT").#%

JK W[KZUJGYRGYSKJOJGYJK VXKIOYOjTIUTYOYZKTKTRGUHYKX\GIOjTJKIUOTIOJKTIOGY%RUW[KRKRRK\GGJKLOTOXGRLhYOIUIUSU [T NUSHXKG W[OKTHGYZG[T UPUW[KTOYOW[OKXGTKIKYOZGVKXIOHOXRUYIURUXKY'9GIK TUZGX3[XTOYZUT3XU]T W[KKTZUJGSKJOJGNG_ W[KUHYKX\GXYOS[RZfTKGbSKTZKJUYIUOTIOJKTIOGY_%VUXZGTZU%ZUSGXKT IUTYOJKXGIOjTRG\KRUbIOJGJ JK VXUVGMGIOjTJK RGR[`%JK JUTJKXKY[RZGW[KYUTTKIKYGXOGY_Y[LOIOKTZKYJUYSGMTOZ[JKYL[TJGSKTZGRKY%W[KNGTJK YKXKRKYVGIOU_ KRZOKSVU%VXKIOYGSKTZK%_ XKL[KX`GY[ UVOTOjTIUT RGYOM[OKTZKIOZGJK RUXJ;KR\OT/a9G_ GRMUY[SGSKTZKOTZKXKYGTZKKTKRNKINUJK W[KVUJGSUYKYZGHRKIKX[T YOYZKSGSgZXOIUHGYGJUKT[TG [TOJGJJK RUTMOb'Z[J _ KT[TG [TOJGJ JK ZOKSVU'>U NG_KTKRRUTGJGT[K\U%V[KYKY_G IUTUIOJUJKYJKRUYZOKSVUYJK >K]ZUT%VKXUIUTYKX\GZUJUY[ OTZKXgY$ GIZ[GROJGJ'O

>U JOIKRUXJ;KR\OTKT W[g IUTYOYZKKYKaGRMUY[SGSKTZKOTZKXKbYGTZKc%VUXRUW[KNG_W[KJGXRK[T YKTZOJUXKIjTJOZU_%GRZUSGXRUIUSUL[TJGSKTZUVGXGKYZGHRKIKXKR2TfROYOYJOSKTYOUTGR%YKOTI[XXKKT RGSOYSGLGRZGW[KI[GTJU YKGZXOH[_KG RGLjXS[RGJOSKTYOUTGRUHZKTOJGGRGSGTKXGIRfYOIGRG\OXZ[JJKIUTZKTKXRG\KXJGJKXGKYKTIOGJKRGYSGMbTOZ[JKY'@KXU%RUVKUXJKRIGYU%KYW[K%GRS[ZORGXRGHGYKXKJ[IOKTJUGJUYKRTkSKXUJK SGMTOZ[JKYL[TJGSKTZGRKY%G[SKTZGKRTkSKXUJK SUTUbSOUYIUT K^VUTKTZKYJOSKTYOUTGRKYT[RUY%IUT RUW[KRGOTLUXSGIOjTW[KVXUVUXIOUTGKR2TfROYOYJOSKTYOUTGRYKNGIKSKTUYVXKIOYG'

"$# <G SKPUXIXhZOIGJK RGJUIZXOTGVUYOZO\OYZGL[KNKINGVUX@RGTIQKT[TGIUTLKXKTIOG%ZOZ[RGJG"&+*(*-, 1,% !#01.2*//&,/$)#'0 W[KYKKTI[KTZXGXKVXUbJ[IOJG KTY[ G[ZUHOUMXGLhG"),#'

a<GYUVOTOUTKYJK RUYVUYOZO\OYZGYTUV[KJKTYKXIUSHGZOJGYJKYJK[T R1[TZUJK \OYZGV[XGSKTZKRjMOIU'F%YOTKSHGXMU%[T K^GSKTJKZKTOJUJK%RGY:RROBS YXK\KRGW[KYUTOTGJKI[GJGY_ KYZgXORKY%VUXW[K:1XKYIOTJKTJK [TG IOXI[TYZGTIOGW[KZOKTKOSVUXZGTIOGJKIOYO\GVGXGKRVXUMXKYU4:KTZhLOIU'@UX [INU W[KGRGX KKKR@UYOZO\OYSUJK KYZGXK^KTZUJK VXKP[OIOUY%ZOKTKW[KVGXZOXJK [TG VXKS YGL[TJGSKTZGRYOTU W[OKXKJKMKTKXGXKT[T YUROVYOYSUOTOTZKROMOHRK'CGRVXKSOYGIUTYOYZKKT W[KZUJGSKJOJGLhYOIGV[KJKYKXXKVXUJ[IOJGJK ZGRSUJU W KKRXKY[RZGJUKYOTJKVKTJOKTZKJK RGVKXYUTGROJGJJKRUHYKX\GJUX%JKRR[MGX_ ZOKSbVUKTW[KYKKLKIZkGRGSKJOIOjT%_ JK I[GRW[OKXUZXGIOXI[TYZGTIOG'CUJU'K ZUXK\KRG%YOSVRKSKTZK%W[KKRLGIZUXJKIOYO\UVGXG'KRXKY[RZGJUJK RGSKJOIOjTKYZfL[KXGJKRUHYKX\GJUX_ W[K%KTIUTYKI[KT''! RGYSKJOJGYVRGTZKGTVXUHRKbSGY W[KOSVROIGTIUTK^OUTKYIG[YGRKYKT[TG XKGROJGJOTJKVKTJOKTZKJKRUHbYKX\GJUX'!#

Page 8: Análisis dimensional

!% ;HwFCLCL >CG?HLCIH;F

?b fYU`]XUX'`UfYXiWW]~bXY UVUgY\UWYeiY eiYXYbXYgdc^UXUgXYgig X]aYbg]cbYgU`[ibUg XY UgWcbghUbhYgX]aYbg]cbUXUg'dcf `c eiY Y`ZcfaUf VUgYgaih]`UXUg bc Yg b]b[ibU bcjYXUX*RU BY]gYbVYf[!),"ih]`]n~ Yb gig YghiX]cgXYGYWzb]WUcbXi`Uhcf]Uib g]ghYaUYb Y`eiY gY\UW|Ub][iU`YgU ( `U WcbghUbhYXYJ`UbW_'H%m `U jY`cW]XUXXY`U `inYbY`jUW|c'Wcb c eiY g~`c eiYXUibU aU[b]hiX Yb`UVUgY'U`cb[]hiX*

; biYghfc acXc XYjYf' g] Y`;bz`]g]g X]aYbg]cbU \U XYgYfj]f dUfUU`[c' YgdfYW]gceiY Yl]ghUib aWabS[Oc\md]Q]%XYacXc eiY UWUXUaU[b])hiX WcffYgdcbXUibU Z~fai`U X]aYbg]cbU dYfZYWhUaYbhYXYhYfa]bUXU'diYg g~`c WcbYghUWcbX]W]~bdcXfYacg YghUfgY[ifcg XYeiY gYfzWcffYWhU`Ugc`iW]~bcVhYb]XUU`Ud`]WUfY`hYcfYaUXYd] U ib dfcV`YaU XYV]XU)aYbhYd`UbhYUXc*

?b hfUVU^cgUbhYf]cfYg!*'" \Yacg hfUhUXcXYYghUV`YWYfY`g]ghYaUib|jcWc* >YgXYiY[c' Ygib dfcd~g]hc eiY bc diYXY`c[fUfgYWcbY`gc`cfUW]cW]b]cm' diYghc eiY `UF~[]WUdcg]h]j]ghU\U ZfUWUgUXcYbY`YadY}c'dfcWYXYfYWiff]fU`cg a{hcXcg XY`U eiY BY]gYbVYf[#.,$ ``UaU ;maWQOOPab`OQbO%YghcYg'`U@|g]WUYb eiY gYWfYYYb`Udcg]V]`]XUXXYZcfai`Uf`YmYgdUfU`cg dfcWYgcgbUhifU`YgXYaUbYfUdfYW]gUm g]ad`Y' `YmYgeiYbc XYf]jUbX]fYWhUaYbhYXY UgaYX]XUg'g]bc eiY \Ub g]XcYghUV`YW]XUgdcf UVghfUWW]~b* *

MfUhUfYacgYb YghYhfUVU^cXYXYgUffc``UfibU hYcf|UXY`;bz`]g]gX]aYbg]cbU`VUgUXUYb \YW\cgY`YjUXcgU `U WUhY[cf|UXYdcghi`UXcg'meiY fYgi`hUbgYfYb b•aYfc XYXcg*?` df]aYfc gYfYZ]YfYU `U|bXc`YXY`UgYWiUW]cbYgZ|g]WUg6Y`gY[ibXc UhU}YU`g][b]Z]WUXcXY`UgWcbghUbhYgib]jYfgU`Yg'mdYfa]hYW`Ug]Z]WUf`UgYb]bY`iX]V`Ygm gidYfZ`iUg*

HiYghfcg dcghi`UXcgVUghUbdUfUWfYUfib g]ghYaUX]aYbg]cbU ib|)jcWc' m gi jU`]XYnXYVYfzWcadfcVUfgYdcf j|U YldYf]aYbhU`'YghcYg'Yb dfcV`YaUgXY;bz`]g]g X]aYbg]cbU`WimUgc`iW]~bWcad`YhUgYUWcbc)W]XU*;` dfcWYXYfUg|'bcg `]VfUacgXY UghfUVUg]adiYghUgdcf `U@]`cgc)Z|UcdYfUW]cbU`*HiYghfUhYcf|UYghz\YW\UdUfUZ|g]WcgeiY' UibeiY gYUbhiYfhcgmXU`hcb]UbcgWcac Y`Ygh]`]nUXcdcf ?XX]b[hcb' bc fYbibW]UbU`igc XYhcXUggig ZUWi`hUXYgaYbhU`Ygm' YbhfYY``Ug'U `UXYWfYUfYbhYgUVghfUWhcg*BUV`UfYacg'diYg' XY`UgaU[b]hiXYg Z|g]WUg'hU`YgWcac `UZiYfnU'UaUgU'`UYbYf[|U'YhW*'Wcac XYYbhYgUVghfUWhcgeiY ]bhYfj]YbYbYb`cg X]jYfgcgZYb~aYbcgWcbWiUbh|Ugc WUbh]XUXYgeiY jUf|Ub Yb WUXUWUgcdUfh]Wi`Uf'm eiY Yl]ghYbUibeiY bUX]YUga]XU*

Oi`bYfUacg XY`]VYfUXUaYbhY`cg dfYWYdhcgXY`U @]`cgcZ|UcdYfUW]c)bU`' dUfU`U WiU bc Yl]ghYbg]bc `UgaYX]XUg'dYfc bcg aUbhYbYacgXYb)hfc XY`U ViYbUXcWhf]bUdcg]h]j]ghU'diYg bcg ZibXUacg Yb \YW\cgmgcaYhYacg biYghfcgfYgi`hUXcgU`UWcadfcVUW]~bYldYf]aYbhU`*?` \YW\c

CHMKI>N==CyH,2

YbeiY bcg VUgUac , * ** g Yg UYQCghYb=CUXY Y YgZ| *X]UbhYYWiUW]cbYgWimUYghfi h ZS R LC=UgeiY gYZcfai`Ub aY)X] *' WifU acS gYfhU`eiY d ]hY * *

aYbg]cb UWUXUaU[b]hiX > i| Yfa] UhbViCfibU' * YUe fYgi`hUeiY Y`;b "C|g] X]YghUgiVcfX]bUXcU`UghYcf|UgZ"** * * U LCL aYbg]cbU`

XY Uga]gaUg* CLC=Ug'bc h]YbYYQCghYbW]U]bXYdYbX]YbhY

>YgXYbiYghfc dibhc XYj]ghU Y`;bz`]U] X] *fzWhYfa]ghYf]cgceiY WcgU *" , U*LCLCaYbgCIbUWUfYWYXY YU)

' WifCIgU'YUhbVimYb, "Z]YghUbYbYj]hUfhcXU]bZ`iYbW]UaYh Z|g] H cg eiY aUg WY`caUb|'Z|g]Wc<f]X[aUb ibc XY`c U CLC=U*UXUaYbcg eiY Y`Ya]bYbhY

' g WUadYcbYgXY`U @]` 77Wcbg]XYfUXcWcac `Uazl]aU U h ]X X * cgc `U cdYfUW]cbU`'m"* i cb U YbWiYghCIbYgXY;b "`]gu *

g]cbU`'UZ]faUYb gi fYW]YbhYU h" i` XC" U CLX|aYb*fC=I Y U :\QhQZ] SRW 7j" '

eiY X]W\cUbz`]g]gg]fjY #aUfUYhUV` * D hO \bO\hQO #,+$ &&? L YWYf=CYfhUg`] 8? &

Yb`UZcfaU XYWiU`ei]YffY`Uc|c ]V` ]a] UW]cbWgbYWYgUf]Ug' * cb JILC YYbhfYUg * V` X *

ZCLC=I9$m Yghc'sUib WiUbXcgYU* ]V` jUpU Yg Yib LCghYaUX bbdcg] Y XUfibU ]bZ *'

A YhU``UXUXY UgYWiUW]cbYgZibXUaYbhU`Y * cfaU=CIb dfYW]gUXY\U``UfgYU gc`iW]~bv>]WY Z]b g UdUfhCfXY UgWiU`Yg\UVf|UX]aYbg] *' Yb eiY sY`ZibXUaY hc X , ;b" **aYbg|cbU^ gY\U``UYb Y`fYei]g]hc XC* b Y z`]g|ghiXYgfY`Uh]jUg9$* Y gYbh]XcUVgc`ihcXY`UgaU[b])

L] `UgUZ]faUW]cbYgXY<f]X aUb 7 &bU`dYfCb]h]f|U\UWYfdfYj|g| [ iYpYbW]YfhUg'Y`;bz`]g]g X]aYbg]c)

ZibXUaYbhU`Ygbcg gcb X5ppp555p5gUp`pg9opcVfYpYb~aYbcgWimUgYmYgA XY UhYcf|UA gi YghiX]cXYVYf| * g Uf]UYbW]aUXY`U YldYf]YbW]U

*" Yf]UWcffYgdcbXYfU, G hUZ"*cda]~b' Uib WiUbXcbc hYb * * * U Y CLC=U*HiYghfUg]Wcg'Yg ighUaYbhYUWcbhf[UU5bcgdfYDNC=CILWcbhfUcg a{hcXcg aYhUZZ)

bUc

;HwFCLCL >CG?HLCIH;F' ) -

Page 9: Análisis dimensional

J;KM? JKCG?K;

0=7.,6/7<8; ./5 ,7U53;3; .36/7;387,5

Page 10: Análisis dimensional

=;J|MNFI ,

:/;=6/7 ./ 5, </8:V, ./ 5, 28681/7/3.,../ 0=7-387/; > ./ /-=,-387/; #%$

#" 5?N DPJAGKJCNFKIKEWJC?NECJCM?HGS?B?N"

LYX]WYeiY ibU ZibW]~bfYU`'V & V"U4%YYY%U\$ XY\ jUf]UV`YgfYU`YgYgV][]Ul\SO WiUbXc'U` ai`h]d`]WUf`UgjUf]UV`Ygdcf gYbXcgZUWhcfYgfYU`Yg'p`" *€€ ' h\% ]bXYdYbX]YbhYgc `][UXcg' U ZibW]~beiYXUai`h]d`])WUXUdcf ibU ZibW]~bXY{ghcg']bXYdYbX]YbhYXY UgjUf]UV`YgQ` *** K\%

eiY gY `UaU ZUWhcfXY\cac[YbY]XUX'c gYUWiUbXc5

="W4<K/ YYY%WM<M#. =J#pC" *** ' WM#f #Q`"! <M# >)%)?

dUfUhcXcg`cg g]ghYaUgXYjU`cfYgfYU`Yg'p`" €€€ ' h\% ]bXYdYbX]YbhYgc`][UXcgdcf W]YfhUgfY`UW]cbYgeiY gY``UaUb SQcOQW]\SaRS Q]\RWQWn\'FUZibW]~bgY `UaU]bWcbX]W]cbU`c WcbX]W]cbU`aYbhY\cac[{bYU gY[•b eiY`cg ZUWhcfYgp`9 €€€ ' h\ gYUbc bc ]bXYdYbX]YbhYg*

?g Yj]XYbhYeiY hcXc acbca]c' UP!%''' %UW %YgZibW]~b]bWcbX]W]c)bU`aYbhY\cac[{bYU A eiY gi ZUWhcfXY\cac[YbY]XUXYgWP!%''' %h\'

?` fYW|dfcWcYghUaV]{bW]Yfhcg] `UZibW]~bgYgidcbY Wcbh]biU*GS]`S[O ,*+ G]RO Tc\QWn\ Q]\bW\cO W\Q]\RWQW]\OZ[S\bSV][]Ul\SO

Sac\ []\][W]'

p%$ >UfYacg Yb YghYWUd|hi`c`c Yghf]WhUaYbhYbYWYgUf]cdUfUbiYghfc dfc)d~g]hc' hcazbXc`c XY``]Vfc XYK]WUfXcLUb DiUb #,1$' XcbXYYbWcbhfUfzY``YWhcfY` XYgUffc``cWcad`YhcXY`U hYcf|Um `UgXYacghfUW]cbYgeiY ca]h]acg*Fcg `YWhcfYgU ei]YbYgg~`c ]bhYfYgYY` UgdYWhcZ|g]WcXY`;bz`]g]g X]aYbg]cbU`'diYXYb dfYgW]bX]fXY`cg hYcfYaUg*FYg VV79iUWcb`UgXYZ]b]W]cbYgXYZibW]c)bYgmYWiUW]cbYg\cac[{bYUg*

Page 11: Análisis dimensional

"" ;HwFCLCL >CG?HLCIH;F,* K?LNG?H >? F; M?IKx; >? F; BIGIA?H?C>;>

"#

FU \cac[YbY]XUX]bWcbX]W]cbU`XYhYfa]bUWcad`YhUaYbhYU ZcfaUXYhcXUZibW]~bWcbh]biU'gU`jc`cgYldcbYbhYgeiY Z][ifUbYbY acbca]c*Hc cWiffY c a]gac WiUbXcU\cac[YbY]XUXYgWcbX]W]cbU`'dYfc' g] `UgYWiUW]cbYgXYWcbX]W]~bgcb acbca]cg' gYWiad`YY`g][i]YbhYhYcfYaU*

GS]`S[O -*t FWc\O Tc\QWn\Q]\bW\cOSa Q]\RWQW]\OZ[S\bSV][]Ul\SOf ZOaSQcOQW]\SaRS Q]\RWQWn\a]\ Se^`SaW]\Sa []\][WOa3

VOP`k RS aS`3

#

Qf&` e\&Z$ 4 #b. a & ("&<Qe`a "R " *** Wl

` Wl Wlf` 414(? E EE < `bQ

,`` €€€ <` , >

+ C @OaTc\QW]\Sa V][]Ul\SOa US\S`OZWgOROaa]\ ZOao\WQOaGS]`S[O ' ZOI ZR R ZOac[O RS aca

RSTW\W[OU\WbcRSaRS [O\S`O _cS d_cO O fO^bOa O`O R jR R' R S\RWS\bSRSZaWabS[O S c\h O Sa'QO\bWRORSaaSOh\ S^ ]X * Xc A XYacghfUXcdcf K* LUbDiUb #,1$'

h aU \U LC c YbibW]Y * *?ghY YcfY ** \ X iad`]f `UgXYZ]b]W]cbYgWiUbh]hUh]jUg

Y]a cbY Y`fYeag`hc eiY Ub Y Y *d gYUUd`]WUV`YY`Ubz`]g]gX|aYbg]cbY`)

dUfUeiY"L # Q8 M#%

_cS RSXO\: LOQb]`SaW\RS^S\RWS\bSa%VOP`k RS aS`3

2

= 8Q`) ,

KYW|dfcWUaYbhY'WiU`ei]YfUeiY gYU U ZibW]~b"R' YghUYldfYgfcbXYZ]bYibU ZibW]~b\cac[{bYU Wcb`Ug YWiUW]cbYgXY\cac[YbY]XUXdfYWYXYbhYg*

$" /AP?AGKJCNFKIKEWJC?N"

LYX]WYeiY ibU YWiUW]~b'=#KZ" ''' %e\$ . 7% YbhfYMjUf]UV`YgfYU`Yg'Yg\cac[{bYU WiUbXcgiVg]ghYU` ai`h]d`]WUf`UgjUf]UV`Ygdcf gYbXcgZUWhcfYg'YgXYW]f'WiUbXc5

FU YWiUW]~bgY``UaU WcbX]W]cbU`c ]bWcbX]W]cbU`aYbhY\cac[{bYUgY[•b eiY `cg ZUWhcfYg-(/ &&&$ 4\ gYUbhcXcgUfV]hfUf]cgc Ygh{b][UXcg*' GS]`S[O .*t p] c\O SQcOQWn\%K\ 8 T#eZ%''' %K\&Z$%_cS RSTW\Sc\OdO`WOPZS8)*\] Tc\QWn\Q]\bW\cORS ZOa SabO\bSa%Sa Q]\RWQW]\OZ[S\bSV][]&Ul\SO%f ZOaSQcOSW]\SaRS Q]\RWQWn\a]\ []\][W]a3

"Q 8 \&`$

Page 12: Análisis dimensional

=;J|MNFI CC

58; /7</; ./ 5, 0X;3-,

#" 8@NCMQ?@HCN"

LYcdYfUYb @|g]WUWcbYbhYgeiY gYWUfUWhYf]nUbdcf U`[•b YZYWhccVgYfjUV`Y*FU XYgWf]dW]~bXYhU YZYWhcWcbgh]himY`URSTW\WQWn\QcOZWbObW&dOc S^Wabl[WQOXYYbhYYbWiYgh]~b'diYg YgUbhYf]cfY]bXYdYbX]YbhYXYhcXU YmZ|g]WU*?ghU XYZ]b]W]~bbc XYVYca]h]fgY U bc gYfeiY gYhfUhYXYWcgUghcaUXUgXY` Yb[iU^YWcff]YbhYm WimcgYbh]XcgYUdYfZYWhU)aYbhYW`Ufc'Wcac giWYXYWcb UgX]ghUbW]Ug'`UgXifUW]cbYgm`UghYadY)fUhifUg*FUgXYZ]b]W]cbYgYd]gh{a]WUgg]fjYb dUfUgUVYfXYei{ gY\UV`Um dUfU fYWcbcWYfWUXUcVgYfjUV`Yg]YadfY eiY hcdYacg Wcb{`* Jcf\UVYfdfYgW]bX]XcGUlkY`` XY`U XYZ]b]W]~bYd]gh{a]WUXY`cg jYWhcfYgXYWUadcY`YWhfcaU[b{h]Wcgif[]Yfcb WcbZig]cbYgXY UgeiY bc YghUacghcXUj|UYbhYfUaYbhY]VfYg*

$" 5KNCJOCNAKIL?M?@HCN"

>Y Xcg cVgYfjUV`Yg"0# m "1# gYX]WYeiY gcb WcadUfUV`YgYbhfYg|WiUbXcYl]ghYibU XYZ]b]W]~bcdYfUW]cbUmib]jYfgU`XY UfUn~b5

"0#&.M"1# %

XcbXY\ Ygib b•aYfc eiY ]bX]WUeiY "0# Yg\ jYWYgaUmcf eiY "1#%YghcYg5

"0# . M"1#'

Page 13: Análisis dimensional

"% ;HwFCLCL >CG?HLCIH;F

?` UX^Yh]jcscdYfUW]cbU`vg][b]Z]WUeiY gY\Ub XYXYgWf]V]f`cg UdUfUhcgih]`]nUXcgYb`UWcadUfUW]~b'Ug|Wcac `UgcdYfUW]cbYgUfYU`]nUf*?` fY)ei]g]hc XYsib]jYfgU`]XUX]Yl][YeiY `UfUn~b\U``UXUgYU]bXYdYbX]YbhYXY`UbUhifU`YnUXYcg WiYfdcgih]`]nUXcgYb`UWcbghfiWW]~bXYcg UdUfUhcg*

>Y `cg Xc`cfYgdiYXYXYW]fgYeiY ibcg gcb aUmcfYgeiY chfcg' dYfcbc gcb WcadUfUV`YgdcfeiY hcXUj|Ubc gY\U ]bjYbhUXcib UdUfUhceiYdYfa]hUUjYf][iUf WizbhUgjYWYgib Xc`cf YgaUmcf eiY chfc Xc`cf*Fca]gac cWiffY'dcf U\cfU' Wcb`U XifYnU'Wcb`cg [fUXcgXYa]YXc' XYVY``YnU'XYV]YbYghUf'YhW*

FU Yl][YbW]UXYeiY `UfUn~bYbhfYcVgYfjUV`YggYUXYZ]b]XUcdYfUY]c)bU`aYbhYYghzXYUWiYfXcWcb`cg df]bW]d]cgXY`U F~[]WUdcg]h]j]ghU*?` fYei]g]hcXYib]jYfgU`]XUXYgbiYjc mYlhfU}cUX]W\U~[]WU#%$*

NbU jYn XYZ]b]XU`UfUn~bYbhfYcVgYfjUV`YgeiYXUXYZ]b]XU`U][iU`)XUXm`UgiaU' diYg XY

gYXYXiWY5g]bC 8 ,'

A

#p$ ;` ]adp5aYf `U WcbX]W]~bXYeiY `UfUn~b YbhfY UgWUbh]XUXYggYU]bXY)dYbXpYphYXY`aghfiaYf6hhc dUfh]Wi`Ufih]`]nUXc' d]YfXYbhcXU]adcfhUbW]U`UgXYZ]b]W]cbYgaYfUb5YbhYagpfiaYbhU`Yg*>YgXYbiYghfc fYU`]gac ]b[Ybic' `U fU)n~b YbhfY*XcgWUbp`XUXYgYl]ghYUbhYgY]bXYdYbX]YbhYaYbhYXYeiY gYWcadUfYb*Jcf Y``ch*]YbYgYbh]XcpYW]feiY `UA]fU`XUYgW]Yfhcb•aYfc XYjYWYgazg U`hUeiYY` aphfc' UibeiY bUX]Y\UmU\YW\c `U WcadUfUW]~b'm' WiUbXc{ghUgYfYU`]nU'\UVfU eiY WcbhfUghUfdfYj]UaYbhY`cg ]bghfiaYbhcg XYaYX]XU U Z]b XYYghUfgY[ifcg XYeiY *bc ]bZ`imYbgig dUfh]Wi`Uf]XUXYgXYWcbgVf)iWW]~b*H]b[•b Z|g]WcgYXUfzdcf gUh]gZYW\cWcbgig UdUfUhcgg]b \UVYf`cgWcbhfUghUXc\UghUWcbjYb)WYfgYXYeiY WcbXiWYbU fYgi`hUXcgeiY YghzbXYUWiYfXcWcb`U XYZ]b]W]~bib])jYfgU` XY`U fUn~b pbhfY*UgWUbh]XUXYgeiY hfUhUXYaYX]f*

JUfU5 cg cpYfUWCIbU\ghUg'YbhfY`cg eiY aYfYWYW]hUfgYU <Yddc FYj] #..$'`UgaYp`XUgZZg]WUgbc gcb azg eiY b•aYfcg cVhYb]XcgYZYWhiUbXcXYhYfa]bUXUgcdYfUY]cbYg*JUfU Y``cgbc YpbYWYgUf]cYghUV`YWYf`cg Wf]hYf]cgXY][iU`XUXAXYpiaU ? &?g giaUaYbhY Wif]cgU'U YghYfYgdYWhc'`U X]gWig]~bYbhUV`UXUYb Y`DVWZ]a]^VWQOWA *"UOgWhS%YbpfY*>]b[`Y #./$ m >U`nY` #.0$*?ghY•`h]ac YgfYU`]ghU'A WfYYYb pUYl]ghYbW]UI:DYh`5'UXY`Ug'aU[b]hiXYg m XY`Ugib]XUXYg*>]b[`Y'eiY Yg Zif`VpXc cdYfUW]cbU`]ghU'fYd`]WUXYgdYWh]jUaYbhYeiY Ygc Yg ]aU[])b'UfgYU WUbh]XUXZhp`=UWcfbcib VcXf]c #1bcT>?XY eiY gYdiYXYhcaUf UfV]hfU)f`UaYb'hY'ibU dcfW]~b m ``UaUf`U ib]XUX* FU X]gWig]~bUXei]YfYWUfUWhYfYg\iacf|gh*]Wcg' m >U`nY` dfcdcbY eiY gY``UaY ;fW\]VU`XUW]YfhUib]XUXXYWUf[UY`{Whf]WUdf'cdpYghUdcf p]b[`Y' U `c eiY {ghYUWWYXYWcbhU`XYeiY gYhcaY YbWiYbhUY`g][i]YbhYWcbgY^c5sbc YgZcfncgc eiY dUfUYZYWhiUfibU aYX]XUZ|g]WU\UmU eiY dcbYfgYWUVYnUUVU^cp9*?b Z]b' >U`nY```c[fU Y` [c`dY Z]bU`WcbYghYUf[iapbhc5 Nb dphcf' dUfUfYj]gUfgi fYVU}c'WiYbhUUgWUVYnUg'a]YbhfUgeiYgi Ua][c Y`WUfb]WYfcD69fYZ]YfYWcbhUfUgdUhUg*LYf|U]b•h]` hfUhUfXYdcbYf`YXYUWiYfXcWcbY`dUghcf'LCUXYazgXYWUfb]WYfc'ZiYgYX]gW|di`cXY dfcZYgcf>]b[`Y*

b* FIL ?HM?L >? F; @xLC=;-2

D aYbhY `U XYZ]b]W]~bXY`U fUn~b YbhfYXcg cVgYfjUV`YgKYWdfcWU ' * *

h"ha"XUdcf `UXYZ]b]W]~bXY UC[iU`XUXm XY UgiaU LCgYdiYXYgYfgig ,

,, NQRSKADNDEDITIQIBIKIDAD'?b YZYWhc6gYUb"0# m "0N# XcgYbhYg

)WiadYY O ' 3D X ( h XL YZ]YWhcgWUfUWhYf|gh]WcggYUbXY,4iU a c Y' Ygc Yg' Y

hU`YgeiY gi *"][iU` XYZ]b]W]~bYd]gh{Cb]WU*FUgXYZ]b]=`pbYgXp`U`piU`XUXmXYUgiaU

8?8 Y`Y[]fib biYjc YbhY!0" XYC[iU`aXc`Y eiY `cg XUXcg'bcg dYfa, ]fUb "* *XY hU` acXc eiY' U` fYdfcXiW]f`cm giaUf`c fYChYfUXUaYbhYWcbg][c

a]gac' `UgYWiUW]cbYg5

"0# . "0!# # "0!# $"0N# . "0!# # "0!# $

5 \ 4 "0!#5 MN4 "0!#

*gYUbgUh]gZYW\UgWcbhcXU UdfYW]g]~beiY gYXYgYY*?bhcbWYgXY

"0# . M"0!#-

UYXYXiWY5"0# \%%%.%%$"0N# MN

XcbXYM mMNgcb b•aYfcg YbhYfcg*

5.* GU[b]hiXYgR WUbh]XUXYg*

>Y ib Wcb^ibhcXYcVgYfjUV`Yg"0 c$ #;`$ ***' WcadUfUV`YgYbhfYg|XcgUXcg'X]fYacgeiY gcb CAMRIDADEQXYibU a]gaU LAGMIRSD#%$* *

FU U`hifUXYib YX]Z]W]c`UX]ghUbW]UYbhfYXcgdibhcg m`UUad`]hiXXY`UgcgW]`UW]cbYgXYib cgp],UXcf]bYU`'gcb WUbh]XUXYgXYUaU[b]hiX``UaUXUKNMGIRSD'?` X|Um`UXifUW]~bXYUgcgW]`UW]cbYgXYib d{bXpc"LcbWUbh]XUXYgXYRIELON'?` dYgcXYib WiYfdcm Y`YgZiYfncbYWYgUfCI

dUfUXcV`UfibU VUffUgcb WUbh]XUXYgXYZiYfnU*?ldiYghUg `Ug WcgUgXYYghYacXc' `Ug aU[b]hiXYg gcb WcbWYdppg

UVghfUWhcgU`cg eiY gY `Y[UUdUfh]fXY UgWUbh]XUXYg*?ghUcfXYbUW`Ib"=cffYgdcbXYU`dfcWYgcbUhifU`Yb eiY gYdUfhYXY c WcbWfYhc'eiY gcbCUgWUbh]XUXYg'dUfU `Y[UfU`c UVghfUWhc'eiY gcb `UgaU[b]hiXYg*

FU X]gh]bW]~bYbhfYaU[b]hiXYg m WUbh]XUXYgYgbYWYgUf]UWiUbXc*gYhfUhUXYdfYW]gUf`Ug ]XYUg*JYfc Yg Wcff]YbhYYb @|g]WUhcaUf `c

#%$ ?b hcXcg`cg ]X]caUg' WcbYlWYdW]~bXY ggdUZ]cA XY ]b[`{g' Y`jcWUV`caU[b]hiX g~`c gYYad`YUWcbgi g][b]Z]WUXc'Ughfcb~a`=769*?g XYbchUf' UXYazg')eiY Yb YgdU}c`Y ]b[`{g' `cg h{fa]bcg aU[f*"uu"Xm WUbh]XUXcghzb hfUghfcWUXcg'diYg WUbh]XUXgYhfUXiWYdcf [OU\WbcRS m aU[b]hiX dcf _cO\bhbf'

Page 14: Análisis dimensional

"' ;HwFCLCL >CG?HLCIH;F b* FIL ?HM?L >? F; @xLC=; "(

[YbYfU dcf `c dUfh]Wi`Ufm' dcf Ygc' giY`Y\UV`UfgYXY aU[b]hiXYg mfUfUjYn XYWUbh]XUXYg'Uib Yb`cg WUgcgYb eiY Y`jcWUV`ccdcfhibc Yg*YghY•`h]ac*

&" /H AMGOCMGKBCGEP?HB?B"

?` Wf]hYf]cXY][iU`XUXjU ]bjc`iWfUXc Yb Y` WcbWYdhcc XYZ]b]W]~bYd]gh{a]WUXYWUXUaU[b]hiX' diYg YgcVj]c UXa]h]f eiY ibU aU[b]hiXgYaUb]Z]YghUWcb][iU` WiUbh|UYbXcg WUgcgX]gh]bhcgWiUbXcgig YZYWhcg*gcb ][iU`Yg*LYX]fz' dcf Y^Yad`c' eiY Xcg WiYfdcgh]YbYb][iU` hYadYfU)hifU WiUbXcib hYfa~aYhfc WiU`ei]YfUaUfWU c a]gac U`gYfdiYghc YbWcbhUWhc'df]aYfc Wcbibc mXYgdi{gWcbchfc*

?j]XYbhYaYbhY'Y`Wf]hYf]cXY][iU`XUXYg]bhf|bgYWc'YghcYg'gYYghU)cV`YWYg]b bYWYg]XUXXYfYWiff]fU `U aYX]XUXYchfUgaU[b]hiXYg*;g|'dUfU XYW]X]fg] Xcg jY\|Wi`cg aUfW\Ub Wcb ][iU` jY`cW]XUX'VUghUfz*cVgYfjUfg]gYWcbgYfjUWcbghUbhYgi X]ghUbW]U'mbc gYfzdfYW]gcaYX]f b]YgdUW]cgb] h]Yadcg*#" ' pp c)

$ /%

B

WiYfdcgeiY g]fjYb XYgcdcfhYU `cg giaUbXcg* FU giaU XY`UgaUgUgXYjUf]cg WiYfdcggYcVh]YbYg]b azg eiY fYib]Xcg YbY`d`Uh]``cXYibUVU`UbnU*=f]hYf]cUbz`c[c' gigh]himYbXc U VU`UbnUdcf Ufh]Z]W]cgUXYWiU)Xcg'diYXYgY[i]fgYdUfU`UgX]ZYfYbhYgZcfaUg XYYbYf[|U#gU`jc`UdchYb)W]U`$' dUfU`UgWUf[UgY`{Whf]WUgm dUfU`cg dc`cg aU[b{h]Wcg*

Jcf gYbW]``UeiY dUfYnWUYghUeiY \Yacg ``UaUXcgiaU dcf UWiai`U)W]~b'dUfUXUXUdcf ViYbUYgdfYW]gcWcadfcVUf Yb WUXUWUgceiY gYWiad`Yb `cg fYei]g]hcg ZcfaU`YgXY`U giaU* ?``c fYei]YfYeiY Yl]ghU`U WcffYgdcbX]YbhYZSf RS Q]\aS`dOQWn\%eiY bcg UgY[ifYeiY `U giaU bcWUaV]UWiU`ei]YfUeiY gYU U aUbYfU XY^ibhUf `cg WiYfdcgYb eiY gY\U``Yb`UgWUbh]XUXYgeiY gYhfUhUXYgiaUf* AfUW]UgU X]W\UYmeiYXUbWiad`]XUg UgWcbX]W]cbYgXYWcbaihUV]`]XUX'ib]Zcfa]XUX' UgcW]UV]`]XUXm Yl]ghYbW]UXY`WYfc*FU `cb[]hiX' Y` zfYUm Y` jc`iaYb gcb hUaV]{baU[b]hiXYg UX]h]jUg'mdUfUXYZ]b]fUgiaU YbWUXUibU XYY``Ug\Um eiYdcghi`Uf `U Yl]ghYbW]UXYWiYfdcgf|[]Xcg*

V$ Fc[O dSQb]`WOZ'?g Ud`]WUV`YU `UgaU[b]hiXYg X]f][]XUgUd`]WU)XUgYbib a]gac dibhc* MUYgY`WUgcXY UgZiYfnUgmXY UgaU[b]hiXYgeiY WUVYWcbg]XYfUfYb WUXUdibhc XYib WUadcY`YWhfcaU[b{h]Wc*FUUiaU Yb YghYWUgcgYVUgUYb Y`dcghi`UXc XYeiY `Ug aU[b]hiXYg YbWiYgh]~bgYWcadcfhUb Wcac jYWhcfYg'YghcYg' `YgYgUd`]WUV`Y`U fY[`UXY dc`|[cbc m cWiffYeiY' dUfUhcXcg`cg YZYWhcgWcbg]XYfUXcg'`UfYgi`)hUbhYYgYei]jU`YbhYU`Wcb^ibhcXY UgWcadcbYbhYg*

Y$ @ObS[^S`Obc`O' LYdiYXYdfYgW]bX]fXY UXYZ]b]W]~bYd]gh{a]WUXY`UhYadYfUhifUdcfeiY YghYjcWUV`cYl]ghYYbhcXcg`cg ]X]caUg' mY``cVUghUdUfU gUVYfXYei{ gYhfUhU*L]b YaVUf[c' h]YbYU hYadYfUhifUib WUfzWhYfYgdYW]U`'diYg bc cWiffYeiY XY`U fYib]~b XYXcg WiYfdcgfYgi`hYibU hYadYfUhifUeiY diYXUhcaUfgY Wcac `U giaU XY`UgeiYhYb|UWUXUibc dcf gYdUfUXc'b] gYWcbW]VY`UYl]ghYbW]UXYXcghYadYfU)hifUg Yb ib a]gac dibhc* >Y Uei| eiY bc g]fjU b]b[ibc XY`cg Wf]hY)f]cg A# m B#%dYfc bc dcf YgcXY^UXYgYf`U hYadYfUhifUibU aU[b]hiXZ|g]WU'diYg Y`gY[ibXc df]bW]d]cdYfa]hYXYZ]b]fUfUn~b YbhfYXcghYa)dYfUhifUgdcf j|U cdYfUhcf]Um ib]jYfgU`*

'" 5? BCDGJGAGYJBCNPI?"

JUfU `cg aUhYazh]Wcg#%$' U giaU YgibU cdYfUW]~bWiU`ei]YfUaY)X]UbhYUWiU WcbWUXUXcgcV^YhcggYWcbghfimYib hYfWYfc'm eiY Wia)d`Y`cg fYei]g]hcgXYib]Zcfa]XUX' UgcW]UV]`]XUX'Yl]ghYbW]UXY a~Xi`c A

WcbaihUV]`]XUXYbU`[ibcg WUgcg*?b chfc `i[Uf #-0$\]W]acg jYf eiY YghY*•`h]ac fYei]g]hc bc gYWiad`Y g]YadfYYb`UgiaU Z|g]WU'diYg YbfY`Uh])j]XUXcWiffYeiY `UgiaU XYjY`cW]XUXYgbc YgWcbaihUh]jU*?b WUaV]c'hcXcg`cg Z|g]WcgYghUfzbWcbZcfaYgYb eiY' dUfUYghUV`YWYf`UgiaU' \UXY\UVYfib Q`WbS`W]RS S_cWdOZS\QWO%gY[•b Y`WiU`' cg giaUbXcg' dUfUY`"*YZYWhcWUfUWhYf|gh]WcXY`U aU[b]hiX Yb WiYgh]~b'\Ub XYdcXYf gYfgig)h]hi]Xcgdcf `UgiaU*

?lUa]bYacg U\cfU `Ug W]fWibghUbW]UgeiY \Ub XYWcbWiff]fYb `U*eiY dcXYacg ``UaUf giaU dcf Yei]jU`YbW]U*;bhY hcXc' diYghc eiY `U*giaU gY\U XYWUfUWhYf]nUfdcf XYhYfa]bUXcYZYWhccVgYfjUV`YYb U`[•bWiYfdc' gYfz dfYW]gceiY `cg giaUbXcg diYXUb fYib]fgY Yb Y`a]gac cuYl]ghUbmUYb {`*=UVY'diYg' X]gh]b[i]f Xcg W`UgYgXYgiaU5

U$ Fc[O ^]` OQc[cZOQWn\%?g Ud`]WUV`YU `Ug[OU\WbcRSaORWbWdOa%Ug| ``UaUXUgdcfeiY `U giaU diYXYXYZ]b]fgYdcf g]ad`Y fYib]~b XY`cg*

(" =JGB?BCNR ICBGB?N"

;X~dhYgYdUfUWUXUaU[b]hiX ibU WUbh]XUXXYhYfa]bUXU'"0]$ . :0%

m X{gY`YY`bcaVfY XYc\WROR'@cfaUbXc `UgfUncbYg

#%$ ?bWcbhfUfz Y``YWhcfibU Yldcg]W]~bm Wf|h]WUXY`UghYcf|UgaUhYfbz**h]WUgXY UaYX]XUYbY`hfUVU^cXYJ] m =U``Y^U#.1$*

"P Y

'`'h+* N 0 '!!! $ TTT 0

Page 15: Análisis dimensional

"0# . 0!%H"6

ff* FIL ?HM?L >? F; @xLC=;* %#.+ ;HwFCLCL >CG?HLCIH;*F

gYdiYXY\UWYfWcffYgdcbXYfU WUXUWUbh]XUX"0#% XY`U aU[b]hiX Yb*WiYgh]~b'ib b•aYfc' 6% eiY gY``UaU [SRWROXY UWUbh]XUX#6$ Wcb U*ib]XUXH6'

;` WUaV]Uf`Uib]XUX:6 dcf chfU' :! 6% fYgi`hUfzchfUaYX]XUXY"0#,

:Z Q]QWS\bSRS ZOa[SRWROaRS c\O [Wa[O QO\bWRORSa WUcOZO ZOW\dS`aO'RS ZO`Ogn\ S\b`S ZOac\WRORSa'

>YgXYbiYghfc dibhc XYj]ghU' eiY YgY`XY fYU`]gac]b[Ybic' `Ug*WUbh]XUXYgWcbgh]himYbY`XUhcdf]aUf]c' diYg Yl]ghYbWcbUbhYf]cf]XUXU`Ugib]XUXYg*?ghUg•`h]aUg gcb WcgUgWcbjYbW]cbU`Yg'a]YbhfUgeiY `Ug*WUbh]XUXYggcb W\dO`WO\bSaWcbfY`UW]~bU `cg WUaV]cgXYib]XUXm' YbYghYgYbh]Xc'diYXYXYW]fgYXYY``UgeiY h]YbYbfYU`]XUXcV^Yh]jU*

dUfUbUXUXYib]XUXYgb] XYaYX]XUg*MUcWiffYWcbhcXUgUgaU[b]hi)XYgaYbW]cbUXUgYb Y`UdUfhUXcUbhYf]cf*

BUmchfUgaU[b]hiXYg' eiY ``UaUfYacgaSQc\RO`WOa#%$c Q][^cSabOa%Yb`UgeiY bc Yl]ghYUgiaU dcf Yei]jU`YbW]Ub] gYdiYXYXYZ]b]f`UfUn~bYbhfYgig WUbh]XUXYgg]b fYWiff]fU `U aYX]XUXYchfUgaU[b]hiXYg*?^Yad`cg XYaU[b]hiXYggYWibXUf]Uggcb `UjY`cW]XUX'`UUWY`YfUW]~b'`UXYbg]XUX'Y`|adYhi' `U]adi`g]~b' Y`hfUVU^c'UZfYWiYbW]Um hcXUgUgWcbghUbhYgWUfUWhYf|gh]WUgXYcg WiYfdcg*?ghUgaU[b]hiXYgbc fYei]YfYbXYZ]b]W]~bYd]gh{a]WU'diYg gi WcbWYdhcXYf]jUXYibU dfYgWf]dW]~bcZ~fai`U WcbeiY gYYgdYW]Z]WUb`UgcdYfUW]cbYgeiY gY\Ub XYfYU`]nUfWcb`UgaYX]XUgXYchfUgaU[b]hiXYg dUfUcVhYbYfU aYX]XUXY`UaU[b]hiX YbWiYgh]~b*?ldfYg]cbYghU`YgWcac5

J Ta4[

=%%d

#YbhfYaYX]XUg$

mgYh]YbY'Yj]XYbhYaYbhY'

0 H"6)

0! :0

FU XYZ]b]W]~bXY UfUn~bYbhfYWUbh]XUXYgXYibU aU[b]hiX' c `UXY`U giaU' \U XYYghUV`YWYfgYYb WUXUWUgcdUfh]Wi`Uf'm U YghYfYgdYWhcWUVYX]gh]b[i]f Xcg W`UgYgXYaU[b]hiXYg*?b ibUg' eiY ``UaUfYacg^`W[O`WOac aW[^ZSa #%$' X]W\UXYZ]b]W]~bdiYXYZcfai`UfgY g]b \UV`Uf

\Ub XYWcbg]XYfUfgYWcac ]XYbh]XUXYgYb`UgeiY Y`df]aYf a]YaVfc bcYgg]bc ibU YldfYg]~bUVfYj]UXUXY gY[ibXc*Jcf YgcfYgi`hUUXYWiUXcXYW]feiY YghUgaU[b]hiXYg`c gcb ^]` RSTW\WQWn\%m Wcbj]YbYdcbYf`c XYaUb]Z]YghcYb WUXUWUgc*?b `UZfUgYs`UjY`cW]XUXYg'^]` RSTW\WQWn\%Y`WcW]YbhYXYX]j]X]f`U X]ghUbW]UfYWcff]XUdcf `U XifUW]~bv'U `cWiW]~bgiVfUmUXU]bX]WUeiY bc gYhfUhUXYib \YW\cWcadfcVUV`YYldYf]aYb)hU`aYbhY'g]bc eiY gY``UaU jY`cW]XUXU`fYgi`hUXcXYYZYWhiUf`U cdY)fUW]~b]bX]WUXU*

?b `UZ~fai`U XYXYZ]b]W]~bXY UgaU[b]hiXYggYWibXUf]UgYghzWcb)hYb]XcY`Wf]hYf]cXYgiaU' eiY bc gYdcghi`U' g]bc eiY XYf]jUXYX]W\UZ~fai`U*

JcXf|U dfYgW]bX]fgYXY`UgaU[b]hiXYg gYWibXUf]UgfYYad`UnzbXc`Ugdcf gig XYZ]b]W]cbYg'dYfc Wcbj]YbYWcbgYfjUf`UgdcfeiY g]ad`]Z]WUbWcb)g]XYfUV`YaYbhYY``Yb[iU^Y*

>Y ib acXc [YbYfU`'g] @9/ e*% YYY gcb `UgaYX]XUgXYW]YfhUgaU[b])hiXYgWcYl]ghYbhYgYbib a]gac WiYfdc'hU`YgWcac gi jc`iaYb' gi aUgU'gi X]ghUbW]UUib cf][Yb' `UZiYfnUU eiY YghzgcaYh]Xc'YhW*'gYdiYXYbhcaUf YghUgaYX]XUgWcacUf[iaYbhc XYibU ZibW]~bWiU`ei]YfUmYgWf]V]f5

)" 6?EJGO=BCNLMGI?MG?N" NCAPJB?MG?N"

#%$ c XYVYbWcbZibX]fgYUg aU[b]hiXYg eiY \Yacg ``UaUXc df]aUf]UgWcb`UgZibXUaYbhU`Yg'c gYUWcb`UgeiY UfV]hfUf]UaYbhYgYY`]^UbdUfUZcfaUf`UVUgYXY g]ghYaUX]aYbg]cbU`*?` gYfdf]aUf]U c bc YgibU WiU`]XUX]b\YfYbhYU WUXUaU[b]hiX' a]YbhfUg eiY WiU`ei]YfaU[b]hiX' UibeiY bc gYUdf]aUf]U'diYXYhcaUfgY Wcac ZibXUaYbhU`*

FU [YbYfU`]XUXXY`cg UihcfYg' dcf bc XYW]fhcXcg' gidcbYb hzW]hUaYbhYeip `U VUpppU XYZcfaUfgYdfYW]gUaYbhYWcbaU[b]hiXYg df]aUf]Ug* JUfU `cg`~[]Wc)dcg]V]j]ghUgg~`c gYf|Ubdf]aUf]Ug `U `cb[]hiX m Y`h]Yadc' diYg hcXUg UgXYazg aU[fihiXYg \Ub XYaYX]fgYcVgYfjUbXcWc]bW]XYbW]Ug*?ghU YgchfUfUn~bdcf `UeiY Y`;bz`]g]g X]aYbg]cbU`'Yb gig aUbcg' d]YfXYhcXUgi YZ]WUW]U*

H: gYWcbZibXUhUadcWcbiYghfUW`Ug]Z]WUW]~bWcb UXYKiggY``YbYlhYbg]jUg#Wcb piU*`XUXm giaU$ Y ]bhYbg]jUg#Wcb][iU`XUXm XYg][iU`XUXgc`UaYbhY$*?ghUg •`h]aUg' dcf bc Yl]gh]f dUfU Y``UgU XYZ]b]W]~bXY`U fUn~b YbhfYWUbh])XUXYg'bc h]YbYbWUV]XUYb `UghYcf|UgZ|g]WUg*MU cWiffY' dcf Y^Yad`c' Wcb`UXifYnU*

=iUbXc gYdfYgW]bXYXY`fYei]g]hc XYib]jYfgU`]XUXYb `U XYZ]b]W]~bXY`UfUn~b YbhfpWUbh]XUXYg'bc \Um acXc XYX]gh]b[i]f YbhfYaU[b]hiXYg df]aUf]UgmgYWibXUf]Ug*Jcf Ygc'dUfU<f]X[aUb #--$' `UZiYfnU' UjY`cW]XUXm`UXYbg]XUXdiYXYbgYfdf]aUf]Ug c gYWibXUf]Ug'gY[•b Wcac gYXYZ]bUb*

f . F"UT U+% ppp $ #YbhfYaYX]XUg$*

#%$ Jcf `Ua]gaU fUn~b eiY cV`][UUX]gh]b[i]f YbhfY UgaU[b]hiXYg df]aU)f]Ugm `UgZibXUaYbhU`Yg'bc gYXYVYbWcbZibX]f UggYWibXUf]Ugc WcadiYghUgWcb UgeiY hcXcg`cg UihcfYg``UaUb aU[b]hiXYg XYf]jUXUg'YghcYg'Wcb`UgeiYbc Z][ifUb Yb`UVUgYXYg]ghYaUX]aYbg]cbU`*?` WUfzWhYfXYgYWibXUf]UYg]b\Y)fYbhYU `U aU[b]hiX' a]YbhfUg eiY `c XYgYf XYf]jUXUYg WcgUWcbjYbW]cbU`*

Page 16: Análisis dimensional

#" ;HwFCLCL >CG?HLCIH;F

;` jUf]Uf `UgaYX]XUgQ`" K+% ppp jUf]Ufz hUaV]{bY`jU`cf bia{f]Wc' f%XYF' ?ghc bcg Uihcf]nUUWcbg]XYfUfV Wcac `UaYX]XUXY UWiUbh|U"V#%

WcbeiY W]YfhUaU[b]hiX Yl]ghYYbY`WiYfdcYbWiYgh]~b*HUXU]a]hU O ^`W]`W Udcg]V]`]XUXXYXYZ]b]faU[b]hiXYgWcadiYghUg

aYX]UbhYZibW]cbYgWiU`Ygei]YfUXYchfUgdfYj]UaYbhYXYZ]b]XUg*MUbg~`c f][Y `UfUn~bXYih]`]XUX'eiY giY`YYldfYgUfgYX]W]YbXceiY `UaU[)b]hiX Yb WiYgh]~b\U XYhYbYfaS\bWR]TmaWQ]%c' `c eiY Yg`c a]gac' \UbXYgYfgigWYdh]V`YgXYibU fYdfYgYbhUW]~baYbhU`*Jcf Y^Yad`c' WcbY`gYbh]XcXY Uj]ghUdUfU^in[Uf XYhUaU}c' mWcbY`aigWi`Uf dUfUUdfY)W]UfY` dYgc' hYbYacg Y`YaYbhcgVUghUbhYgdUfU Y`UVcfUfY` WcbWYdhcWiU`]hUh]jcXYXYbg]XUX'eiY ``YjU]bjc`iWfUXUgUgfY`UW]cbYgXY][iU` mXYaUmcf c aYbcf* JYfc `U XYZ]b]W]~bWiUbh]hUh]jUbc diYXY`c[fUfgYdcfeiY ZU`hUY`Wf]hYf]cXYYei]jU`YbW]UdUfU UgiaU m'dcf Ygc'gYfYei]Y)fY `UYWiUW]~bXYXYZ]b]W]~b*

OYfYacg azg UXY`UbhYeiY' dUfU dcXYf Uhf]Vi]f ibU X]aYbg]~b UWUXUaU[b]hiX WcadiYghU'YgdfYW]gceiY Ygh{bXYZ]b]XUgaYX]UbhYZib)W]cbYgWcbX]W]cbU`aYbhY\cac[{bYUg* JYfc \Um aU[b]hiXYg' Wcac gcb`UWcbghUbhYei|a]WU mY` =% WimUih]`]XUXYgaUb]Z]YghUUdYgUfXYeiYgi XYZ]b]W]~bbc Wiad`Y `U WcbX]W]~bXY\cac[YbY]XUXWcbX]W]cbU`*

LYf|UWcbjYb]YbhYWcbgYfjUfY` g][bc XY]XYbh]XUXYb `UgZ~fai`UgXYXYZ]b]W]~bXY UgaU[b]hiXYg gYWibXUf]Ug'dYfc Yb hcXcg`cg `]VfcggYgigh]himYdcf Y`XY][iU`XUX'Wcb c eiY gYWcbZibXYbWcb UgYWiUW]cbYgeiY g]fjYb dUfUYldfYgUfUg YmYgZ|g]WUg*=cbj]YbY' g]b YaVUf[c' X]gh]b)[i]f W`UfUaYbhYYbhfYYmYgmXYZ]b]W]cbYg*FUgdf]aYfUggcb gigWYdh]V`YgXYWcadfcVUW]~bYldYf]aYbhU`6Yb`UggY[ibXUgbc h]YbYgYbh]XchU`Wca)dfcVUW]~b'diYg gYhfUhUXY]XYbh]XUXYg*Jcf Ygcbc YgWcffYWhc'UibeiYgYUZfYWiYbhY'Wcbg]XYfUf`U`YmXYHYkhcb Wcac ibU XYZ]b]W]~bm XYW]feiY `UZiYfnUSa Y`dfcXiWhcXY UaUgUdcf `UUWY`YfUW]~b*

*" 6CBGB?NBGMCAO?NC GJBGMCAO?N"

L] bc gYWcbcW]YfUb`Ug`YmYgZ|g]WUg'`UaYX]W]~bXYhcXUaU[b]hiX df]aUf]U\UVf|U XYYZYWhiUfgY'dfYW]gUaYbhY'U dUfh]f XY`cg dcghi`UXcg Yb eiY gYVUgUY`Wf]hYf]cXY][iU`XUXm XYgiaU* R `UaYX]W]~bXY`UgaU[b]hiXYg gYWibXUf]Ug\UVf|U XYYZYWhiUfgY'dfYW]gUaYbhY'U dUfh]f XYgi fYgdYWh]jUZ~fai`U XYXYZ])b]W]~b'YghcYg' a]X]YbXc `UgaU[b]hiXYg df]aUf]Ug eiY Yb Y``UZ][ifUb* JUfUaYX]f Yb [fUacg' dcf Y^Yad`c' `UaUgU ]bYfW]UXYib WiYfdc' hYbXf|Uacg eiYfYib]f hUbhcg[fUacg mZfUWW]cbYgXY[fUac Wcac ZiYgYbbYWYgUf]cgdUfUZcfaUfib WiYfdc eiY' gcaYh]Xc U ibU ZiYfnUWiU`ei]YfU'UXei]f]YgYY` a]gac acj])a]Ybhc eiY Y`WiYfdcYb WiYgh]~bVU^c`U UWW]~bXY`U a]gaU ZiYfnU*?ghU aY)X]XUXY`UaUgU' Yb eiY bc gYfYWiffYU b]b[ibU `YmZ|g]WU#gU`jc`cg dcghi`UXcgXYYl]ghYbW]UXY`UaUgU Wcac aU[b]hiX Z|g]WU$gYf|UibU [SRWRORW`SQbO'

``* FIL ?HM?L >? F; @xLC=; ..

FUg aYX]W]cbYgX]fYWhUggYfYU`]nUbfUf|g]aUg jYWYg'm Yb gi `i[Uf gYfYWiffYU `Ug]bX]fYWhUg'eiY gYVUgUbYb U`[ibU `YmZ|g]WU'm XYUei| eiY \UmUaiW\UgaUbYfUgXYaYX]f WUbh]XUXYgXYibU a]gaU aU[b]hiX* FUg aUgUg' dcf Y^Yad`c'gYa]XYb WcbVU`UbnUg'WcbVzgWi`UgXYX]jYfgcgh]dcg' WcbfcaUbUg' WcbfYgcfhYg'YhW{hYfU'`c eiY dfiYVU eiY hcXUaU[b]hiX Yg igWYdh]V`YXYjUf]UX|g]aUgXYZ])b]W]cbYg]bghfiaYbhU`Yg'Wcb`c eiY {ghUgd]YfXYbhcXUgi ]adcfhUbW]U' U WiU`fYWUYgcVfYY`fYei]g]hc XYib]jYfgU`]XUX'YghcYg'gcVfY`U WcbX]W]~bXYeiY Y`fYgi`hUXcXY`UgaYX]W]cbYggYU]bXYdYbX]YbhY'bc g~`c XY`cg WiYfdcgih]`]nUXcgYb`UWcbghfiWW]~bXY cg UdUfUhcg'g]bc hUaV]{b XY a{hcXc ]bX]fYWhcih]`]nUXc*FU WcbWcfXUbW]UYbhfY cg fYgi`hUXcgcVhYb]XcgU`Yad`YUf`cg X]jYfgcga{hcXcg?"L ibU WcadfcVUW]~bXY`UjU`]XYnXY`Ug`YmYgZ|g]WUgYb eiY gYZibXUb' m gYf|Uaim X]Z|W]XYYld`]WUfg] `UgWUbh]XUXYgbc hij]YfUb ibU Yl]ghYbW]UfYU`']bXY)dYbX]YbhYXYgi XYZ]b]W]~b]bghfiaYbhU` m XY cdYfUXcfeiY `Uga]XY*

;*pwFCghL 8=3/+4;387,5" ! L

Page 17: Análisis dimensional

=;J|MNFI !

9:36/: 98;<=5,.8

#" 5? J?OPM?HCS?BCH?NHCRCNDPJB?ICJO?HCNBCH?0XNGA?"

McXUhYcf|UZ|g]WUgYVUgUYb W]Yfhcb•aYfc XYZSfSa Tc\RO[S\bOZSaXY`UgeiY' dcf `cg a{hcXcg XY`U F~[]WUaUhYazh]WU'gYXYXiWYb`UgZSfSa RS`WdOROa'?g XYbchUf eiY `U X]gh]bW]~bYbhfYibU m chfUYgdYW]YXY YmYgYg'\UghUW]Yfhcdibhc' WcbjYbW]cbU`'diYg \UmW]YfhU`]VYfhUXYb`UY`YWW]~bXYUg YmYg']bXYdYbX]YbhYgYbhfYg|' gcVfYUgeiY gYZibXUibUhYcf|UXYhYfa]bUXU*

MfUhYacgXYUjYf][iUf Y`gYbh]XcXY`U `YmZibXUaYbhUXY`U GY)Wzb]WU5

NbU cd]b]~b aim YlhYbX]XUYgeiY YghUYWiUW]~bg]fjY dUfUdfYW]gUfY`WcbWYdhcXYZiYfnU'XYZ]b]{bXc`UWcac Y`dfcXiWhcXY UaUgUXYWiYfdcYb eiY UWh•Udcf `U UWY`YfUW]~beiY `Y ]adf]aY #%$*?ghU cd]b]~b Yg]bUXa]g]V`YdcfeiY XY[fUXUY` WcbWYdhcXYZiYfnUWcbj]fh]{bXc`UYbaU[b]hiX gYWibXUf]U'mdcfeiY `U`YmXYU]bYfW]UeiYXUf|Ug]bWcbhYb]Xcdcf bc UZ]faUfbUXUeiY diYXUgYfW]Yfhcc ZU`gc*

#%$ Id]bU <i``cc_ #.2$ eiY `U gY[ibXU `YmXYHYkhcb g]fjY dUfU XYZ]b]f`UaUgU5>Y gYfUg|' `UaYX]c]~b XYaUgUg\UVf|U XYYZYchiUfgYWcadUfUbXc UUWY`YfUW]~beiY UXei]YfYY` ciYfdc Yb ciYgh]~b dcf `U UWW]~bXYibU ZiYfnU'Wcb`U eiY YghUa]gaU ZiYfnUWcaib]WUf|UU`_]`c[fUac dUhf~b' WcgUeiY gYf|U'c]YfhUaYbhY'ibU bcjYXUX*Gim UcYfhUXUaYbhYcV^YhUEYYbUb#.3$' eiY UbhYgXYHYkhcb YfUccbcc]XU`UZiYfnUdcf ei]YbYgfYgc`j|Ub dfcV`YaUgXY?ghzh]cU'eiY `UaUgU gYaYX|U Yb`cg aYfcUXcgXYgXYcg h]Yadcg azg fYachcg' m eiY XY`U UWY`YfUW]~bhYb|UmUccbcc]a]Ybhc AU`]`Yc*KYgiaY EYYbUbgig ccaYbhUf]cgX]c]YbXceiY s`UgY[ibXU`YmXYHYkhcb' `c a]gac eiY Y` df]aYf df]bc]d]c XYMYfacX]bza]cU' YgU`[c azg eiY ibU XY}b]W]~bv*

Page 18: Análisis dimensional

#% ;HwFCLCL >CG?HLCIH;F

; biYghfc acXc XYjYf' `U aUbYfU WcffYWhUXYYbibW]UfU `YmXYHYkhcb Wcbg]ghYYb WcaYbnUfdcf XYZ]b]fWiUbh]hUh]jUaYbhY`UaUgU' `UZiYfnUm `UUWY`YfUW]~b'Wcac aU[b]hiXYg df]aUf]Ug`UgXcgdf]aYfUg mWcac aU[b]hiX gYWibXUf]U`UhYfWYfU'm`iY[c UZ]faUfeiY `UUWY`YfUW]~bXYib a~j]` YgX]fYWhUaYbhYdfcdcfW]cbUU`UZiYfnUeiY gcVfY{` UWh•UmYghzYbfUn~b]bjYfgUXYgi aUgU*L]aV~`]WUaYbhY5

#T$ "! "L# "A# #YbhfYWUbh]XUXYg$'

XcbXYY`g][bc "! g][b]Z]WUsdfcdcfW]cbUAX'?ghU aUbYfUXYWcbg]XYfUf`Ug`YmYgZ|g]WUgdcbY XYaUb]Z]Yghcgi

WUfzWhYfib]jYfgU`' YghcYg'Y`\YW\c XYeiY diYXUbgYfYbibW]UXUgg]b\UWYffYZYfYbW]UU b]b[•b g]ghYaUdUfh]Wi`UfXYib]XUXYg'diYg VUghUUXYZ]b]W]~bXY UfUn~bYbhfYWUbh]XUXYg*

HiYghfcdf]aYf dcghi`UXcgYVUgUYbib \YW\ceiY WiU`ei]YfUdiYXYWcadfcVUf'diYg UZ]faUeiY ^cSRS\ SaQ]US`aSZOaZSfSa Tc\RO[S\bOZSa RS[]R] _cS Q]\aWabO\S\ `SZOQW]\SaRS ^`]^]`QW]\OZWRORS\b`S ^]bS\QWOaRSbS`&[W\OROaRS ZOaQO\bWRORSa_cS W\bS`dWS\S\S\ SZTS\n[S\] Q]\aWRS`OR]'

>Y ib acXc [YbYfU`'WiU`ei]YfYmZ|g]WUZibXUaYbhUdiYXYZcfai)`UfgYXY Ug][i]YbhYaUbYfU5

#YbhfYWUbh]XUXYg$' S,',T

XcbXYcg YldcbYbhYg!49/ EEE $ !4; gcb b•aYfcg Z]^cg']bXYdYbX]YbhYgXY UbUhifU`YnUXY cg WiYfdcgeiY ]bhYfj]YbYbYb Y`ZYb~aYbc*

=cbj]YbY\UWYfbchUfeiY biYghfUUZ]faUW]~bYgib dcghi`UXcVUgUXcYb \YW\cg'mbc `UWcbgYWiYbW]UXYU`[•b df]bW]d]caYhUZ|g]Wc*HUXUgYcdcbY' `~[]WUaYbhY'U eiY `UgWcgUgcWiff]YgYbXYchfUaUbYfU'mViYbUdfiYVU XYY``cYg`c eiY giWYXYWcb`U acXYfbU KYc`c[|U #.4$ WimUgYWiUW]cbYgZibXUaYbhU`Yg'gY[•b dUfYWY'gcb fY`UW]cbYgYbhfYacbca]cgWcbYldcbYbhYgeiY' Yb`i[Uf XYgYfb•aYfcg WcbghUbhYg'jUf|Ub gY[•b gYUY`WiYfdceiY gYWcbg]XYfY*L] YghYZiYfYY`WUgcYb`cg XYazg WUd|hi`cgXY`U @|g]WU'biYghfc "dcghi`UXcgYf|UZU`gc'm Y` ;bz`]g]g X]aYbg]cbU`WUYf|Udcf gi VUgY*>YgXYiY[c' bc YgUd`]WUV`YU`cg dfcV`YaUgXYKYc)`c[|U' WiUbXcaYbcg Yb gi ZcfaU UWhiU`*

FUg`YmYgXYf]jUXUgbc g]YadfYUXcdhUbUZcfaU S,',T*Jcf Y^Yad`c'Y`dYf|cXc XYcgW]`UW]~bXY d{bXi`c g]ad`Y YghzXUXcdcf `U YWiUW]~b5

#YbhfYaYX]XUg$'

XcbXY)"(# YgibU ZibW]~bbc acbca]U XY Uf[iaYbhc Y*

```* JKCG?K JILMNF;>I #&

-* FUg YWiUW]cbYgXY`U @|g]WU*

?b `cg `]Vfcg XY@|g]WUeiY dfcWYXYbaYh~X]WUaYbhY'Y`YbibW]UXcjYfVU`XYWUXUYmZ|g]WUjU gY[i]Xc XYibU YWiUW]~bU`[{Vf]WUeiY gYWcbg]XYfUWcb UYldfYg]~bWUVUm Wcad`YhUXYX]W\UYm*;ib WiUbXcbc gYX][UYldfYgUaYbhY'U gigh]hiW]~bXY g][bc XYdfcdcfW]cbU`]XUXdcf Y`XY][iU`XUX]bX]WUeiY gY\Ub gigh]hi]Xc`UgWUbh]XUXYgdcf gigaYX]XUg*;Xa]h]fYacg' diYg' eiY ZOaSQcOQW]\SaTmaWQOa`SZOQW]\O\ZOa[SRWROaRS ZOaQO\bWRORSa_cS S\ SZZOaW\bS`dWS\S\#%$*

LYU'dcf Y^Yad`c' Udf]aYfU`YmXYHYkhcb6 UZiYfnUYgX]fYWhUaYbhYdfcdcfW]cbU U `UaUgUm U `UUWY`YfUW]~b*?b YghYYbibW]UXcbc diYXYgigh]hi]fgY'g]b azg b] azg' `U fY`UW]~bXYdfcdcfW]cbU`]XUXdcf `U XY][iU`XUXYbhfYWUbh]XUXYg'diYg bc h]YbYgYbh]Xc]baYX]UhcY`XYW]f'dcfY^Yad`c'eiY Y`dYgcXYib WiYfdcYbib `i[Uf XYhYfa]bUXcgYUZO[Wa[OQ]aOeiY Y dfcXiWhcXYUQO\bWRORXYaUgUdcf `UQO\bWRORXYUWY`YfUW]~beiY UXei]f]f|Ug]WUmYgY`]VfYaYbhY*L~`cYbY`WUgcYbeiY `U`YmfY`UW]cbYWUbh]XUXYgXYibU a]gaU aU[b]hiX WUVYgigh]hi]f `UdfcdcfW]cbU`]XUXdcf `U][iU`XUX*;g| cWiffYWcbY`df]bW]d]cXY U][iU`XUXXY UUWW]~bm XY UfYUWW]~b#%%$*

.* =cbghUbhYgWUfUWhYf|gh]WUgA WcbghUbhYgib]jYfgU`Yg*

;` dUgUfXY`U fY`UW]~bXYdfcdcfW]cbU`]XUXYbhfYWUbh]XUXYgU `UYWiUW]~bYbhfYaYX]XUg'gYfzdfYW]gc'Yb [YbYfU`']bhfcXiW]fib ZUWhcfXYdfcdcfW]cbU`]XUX'2%WcbWimcUil]`]c gYdcXfz gigh]hi]f `UYldfYg]~b

#YbhfYWUbh]XUXYg$

#%$ LY diYXY' Wcb XYZ]b]W]cbYgUXYWiUXUg'XUf gYbh]XcU `Ug YWiUW]cbYgYphfYaU[b]hippg* ?ghc Yg`c eiY \U \YW\c K* LUb DiUb #,1' dz[* ,-+$' aY)X]UbhYUXYpa=`~b Xp aU[b]hiXYg WcYl]ghYbhYg'm Ug| \U `c[fUXc WfYUfgi hYcf|UXY`UgaU[b]hiXYg Z|g]WUg*=cac YghYa{hcXc fYei]YfY YgdYWi`UW]cbYgYlWYg]jU)aYbpY UVghfUWhUg'bcg \U dUfYW]XcWcbjYb]YbhYbc XUf U `Ug YWiUW]cbYgchfcgYbh]XceiY Y` XYfY`UW]cbYgYbhfYaYX]XUg'YghcYg' b•aYfcg* Jcf chfU dUfhY'XYacgpfUfYacg*Yb Y`WUd|hi`cCO' r 2' eiY Y`Wcbg]XYfUfeiY `UgYWiUW]cbYgXY`U @Zg]WUfY`UW]cbUbWUbh]XUXYgbc X]fYWhUaYbhYWcadUfUV`YgWcbXiWYU ibUVgifXc* "

*#%%$ ?` Y*bibW]UXcjYf 59UXY`UYWiUW]~bF . [O% gYf|U5Yb hcXc dibhc aU)hYf]U`' U \3SRbRORS ZOQO\bWRORXYZiYfnUeiY gcVfY{` UWh•UYg][iU` U`U[SRWRORS ZOQO%%3%bbRORXYaUgU XY dibhc ai`h]d`]WUXUdcf `U [SRWRORS ZOQO\bWRORXYUWY`pfU=`Wpa*FU aUWpUWcb*UfYdYh]W]~bXY`U ZfUgYgiVfUmUXUWcbjYfh]f|UY` `Yb)[iUDYZ|LC=IYb WUbh]`YC`5U]bgcdcfhUV`YmdYXUbhYgWU'dcf `c eiY gYgidf]aY aimUWYfhpXUaYbhY'YbhYbX]{bXcgYeiY ib a]gac bcaVfY g]fjY dUfU XYg][bUf`UaU[fihiX Wcac YbhYUVghfUWhcm `UgaYX]XUgXYgig WUbh]XUXYgYb WUXUWUgcdUfh]Wi`Uf*

Page 19: Análisis dimensional

.3 ;HwFCLCL >CG?HLCIH;F

dcf `UYWiUW]~b

#YbhfYaYX]XUg$* S.',T

?` jU`cf bia{f]Wc XY2 gYcVhYbXfzaYX]UbhYUZ~fai`U

2 . &&&&&&&!f"&&&&&& S.'-T

eiY Yl][YWcbcWYf`cg YldcbYbhYgY``"€€€ ' SZ\ maYX]f Ybib WUgcdUfh]Wi)`Uf`UgWiUbh|UgXYf%Q` €€€ ' <M' ?` jU`cf cVhYb]XcXYdYbXYfz'Yb[YbYfU`'XY Ugib]XUXYgeiY gYih]`]WYb*

FU YWiUW]~bS.'-T diYXYWcbg]XYfUfgYWcac `UZ~fai`U XYXYZ]b]W]~bXY2%eiY UXei]YfYWcbY``c`UWiU`]XUXXYaU[b]hiX gYWibXUf]U*

;` aYX]f 2 diYXYbdfYgYbhUfgYXcg WUgcg5A# FU aYX]XUXY2 XYdYbXYXY`U bUhifU`YnUXY`WiYfdc*LYX]WY

YbhcbWYgeiY 8 YgibU Q]\abO\bSQO`OQbS`mabWQO%c Sa^SQmTWQO'

?^Yad`cg5FU `YmXYBcc_Y Ud`]WUXUU ib U`UaVfYXY`cb[]hiX Km gYWW]~bO%

gcaYh]XcU ibU ZiYfnUb'gYYldfYgUUg|5

#T$ "! "A# #OZ$"K#

#YbhfYWUbh]XUXYg$

m' U`dUgUfU`UYWiUW]~bYbhfYaYX]XUgfYgi`hU5

T 8 : OOZK !

XcbXY3 YgY`a~Xi`: XY5 cib[' aU[b]hiX gYWibXUf]UXYZ]b]XUdcf `U]XYbh]XUX

:5@& OOZ"

m gi aYX]XUfYgi`hUXYdYbXYfXY`U bUhifU`YnUXY`U`UaVfYm XY`Ugib]XUXYgeiY gYUXcdhYbdUfUaYX]f `U`cb[]hiX' Y`zfYUm`UZiYfnU*

Jcf gi dfcd]U bUhifU`YnU'UgWcbghUbhYgYgdYW|Z]WUggcb ]bY`iX]V`Yg'dcfeiY `U YWiUW]~bS.',T bc h]YbYjU`]XYn[YbYfU g]b `U dfYgYbW]UXY`ZUWhcf2' LYdiYXYbY`Y[]f Ugib]XUXYgXYacXc eiY fYgi`hYS . ( dUfU

MC`* JKCG?K JILMNF;>I #(

ib WiYfdcdUfh]Wi`Uf'dYfc gYfz8 8,8( WiUbXcgYUd`]eiY`UYWiUW]~bUchfc WiYfdcWiU`ei]YfU*

B# JiYXY giWYXYfeiY Y`jU`cf XY ZUWhcfXYdfcdcfW]cbU`]XUXgYU]bXYdYbX]YbhYXY UbUhifU`YnUXY WiYfdc*6 b]ROSQcOQW/\Tc\RO[S\bOZ_cS aS Q]\aS`dOW\dO`WOPZSQcO\R] QO[PWOZO\Obc`OZSgORSZQcS`^] Q]\ _cSaS ]^S`O Q]``Sa^]\RS c\O Q]\abO\bSc\WdS`aOZ'

?^Yad`cg5

`*c 8]\abO\bS RS ZOU`OdWbOQW/\'

;ib WiUbXcbc g]YadfYgYX][UYldfYgUaYbhY'`Ug YmYgXYU[fUj]hU)W]~bgcb Xcg' U gUVYf5

Fcg WiYfdcggYUhfUYbYbfUn~bX]fYWhUXYgig aUgUg[fUj]hUhcf]UgmYbfUn~b]bjYfgUXY WiUXfUXcXYgi X]ghUbW]U5

#T$ "! #[U$ #[" U$'"D#*

FU aUgU ]bYfW]UYgdfcdcfW]cbU U `UaUgU [fUj]hUhcf]U5

;` dUgUfXYYghUgYldfYg]cbYgU`UgfYgdYWh]jUgYWiUW]cbYgYbhfYaYX])XUgfYgi`hUbgYbXUgWcbghUbhYgib]jYfgU`Yg'eiY diYXYbhcaUf jU`cfYgWiU`Ygei]YfUgY[•b gYUbUgib]XUXYgeiY gYUXcdhYbdUfU`U X]ghUbW]U'`UZiYfnUm dUfUUaVUgYgdYW]YgXYaUgU*JYfc' Y`][]YbXcWcbjYb]YbhY)aYbhY`Ugib]XUXYg'dcf Y^Yad`cih]`]nUbXcY`g]ghYaUWY[Yg]aU`'cWiffY

eiY `Udf]aYfU jU`Y,' R `UgY[ibXUYgdO3T5 [U["U

R+

XY UgeiY gYXYXiWY5

FU WcbghUbhY< gYXYbca]bUWcbghUbhYXY U[fUj]hUW]~b*

+'( :_cWdOZS\bS[SQk\WQ] RSZ QOZ]`'

?bhfY Y`WU`cf'8% UVgcfV]Xcdcf ib g]ghYaUYb ibU hfUbgZcfaUW]~bW|W`]WU'm Y`hfUVU^cdfcXiW]Xc' ;% Yl]ghYU YWiUW]~b5

J5?E%

Page 20: Análisis dimensional

$ ;HwFCLCL >CG?HLCIH;F

XcbXY5 YgY`Yei]jU`YbhYaYWzb]WcXY`WU`cf'WimcjU`cf g~`c XYdYbXYXY Ugib]XUXYgWcbeiY gYa]XUb J m8'

,') 8]\abO\bS RS 6d]UOR`]'

?b hcXcWiYfdc'Y`b•aYfc XYac`Yg' \%YgdfcdcfW]cbUU`b•aYfc' 6XYac`{Wi`Ug5

XcbXYB0 Yg`U WcbghUbhYXY;jc[UXfc' WimcjU`cf g~`c XYdYbXYXY`Uib]XUXeiY gYUXcdhYdUfUaYX]f aUgUg*

-') 8]\abO\bS RS 7]Zbg[O\\'

?b hcXcg]ghYaUZcfaUXcdcf [fUb b•aYfc XYY`YaYbhcg'UYbYf[|U'?'eiY' dcf h{fa]bc aYX]c' WcffYgdcbXYU WUXU[fUXc XY`]VYfhUX'Ygdfc)dcfW]cbUU`UhYadYfUhifUUVgc`ihU1*

? 8 p J+'-

XcbXYJ Yg UWcbghUbhYXY<c`hnaUbb' eiY g~`cXYdYbXYXYUgib]XUXYgWcbeiY gYa]XUb `UYbYf[|Um`UhYadYfUhifU*

.'i 8]\abO\bS RS DZO\QY'

?b hcXcdfcWYgcdYf]~X]WcXYZfYWiYbW]Uj' `UYbYf[|Ug~`cdiYXYYldY)f]aYbhUf WUaV]cgeiY gYUba•`h]d`cg YbhYfcgXY

`,Y . _j'

XcbXYY Yg UWcbghUbhYXYJ`UbW_*

/'i ISZ]QWRORRS ZOZcg'

; hcXc UiaYbhc XYYbYf[|UWcffYgdcbXYib UiaYbhc XYaUgU #]bYfW]U`$XUXcdcf5

XcbXYYYgibU WcbghUbhYib]jYfgU` eiY' Wcbib g]ghYaUWcbjYb]YbhYXYib]XUXYg'Y`WY[Yg]aUdcf Y^Yad`c' Wc]bW]XYWcb UjY`cW]XUXXY U`inYbY`jUW|c*

0'i 8]\abO\bSa RSZdOQm]'

;`[ibUg WcbghUbhYgYgdYW|Z]WUgWcbgYfjUbib jU`cf Z]b]hcWiUbXcgYa]XYb YbY jUW|c*NbU XYY``UgYg UjY`cW]XUXXYU`in' XYeiY mU\Yacg

fb* JKCG?K JILMNF;>I /,

\UV`UXc*FUgchfUgXcgLcb`UdYfaYUV]`]XUXY`{Whf]WU'6<$ m`UdYfaYUV])`]XUXaU[b{h]WU'SFc' WimUgYWiUW]cbYgXYXYZ]b]W]~bgcb5

9 . Yc?6

;aVUg dYfaYUV]`]XUXYggcb' XYgXYiY[c' WcbghUbhYgWUfUWhYf|gh]WUgXYWUXUgighUbW]U'dYfc`cg jU`cfYg'Y5cR SFc' eiY hcaUb YbY jUW|cgYgiY`Yb]bW`i]fYbhfYUgWcbghUbhYgib]jYfgU`Yg*

1'i 8]\abO\bS RW\k[WQO'

FU df]aYfU `YmXYHYkhcb UXa]hYib ZUWhcfXYdfcdcfW]cbU`]XUX5

2.@4&[O"

eiY bc \U fYW]V]XcbcaVfY b] g|aVc`c* Li jU`cf XYdYbXY'YlW`ig]jUaYbhY'XYUgib]XUXYgeiY gYY`]^UbdUfUaYX]f`UZiYfnU'UaUgUm`UUWY`YfUW]~b*

2'i 8]\abO\bS SZSQb`][OU\lbWQO'

?b j]fhiX XY`U `YmXYFUd`UWY'hcXc Y`YaYbhcXYWcff]YbhYYghzgcaYh]XcUibU ZiYfnUeiY YgdfcdcfW]cbUU`U]bhYbg]XUX'*%U`U`cb[])hiX' X`' mU `UdfcmYWW]~bXYjYWhcfaU[b{h]Wc1 gcVfYY`d`UbcbcfaU`URZ' =cb `UbchUW]~bXY Wz`Wi`cjYWhcf]U`5

XZ8 fZRZ(M<'

XcbXYm Yg`U WcbghUbhYY`YWhfcaU[b{h]WU'eiY XYdYbXYhUbg~`c XY`Ugib]XUXYgeiY gYY`]^UbUfV]hfUf]UaYbhYdUfUaYX]f `UgaU[b]hiXYg eiYZ][ifUb Yb YghUYWiUW]~b*

Cb`OaQ]\abO\bSac\WdS`aOZSa'

=iU`ei]Yf acbca]c ZcfaUXc WcbWcbghUbhYgib]jYfgU`YggYfz ibUbiYjU WcbghUbhYib]jYfgU`*;`[ibUg h]YbYbbcaVfY' Wcac `UgXYP]Yb'LhYZUb'`UWcbghUbhYXY cg [UgYg'9 8 J60% mY` ZUfUXUm'eiY YgY`dfc)XiWhcXY UWcbghUbhYXY; jc[UXfc dcf `UWUf[UXYY`YWhf~b*

Page 21: Análisis dimensional

=;J|MNFI CO

L?A =7.8 98;<=5,.8

,* Id]b]cbYg UWYfWUXY`UgWcbghUbhYgib]jYfgU`Yg*

FUg WcbghUbhYgib]jYfgU`Ygh]YbYbib WUfzWhYfXYgWcbWYfhUbhY*;dU)fYcYbYb`Ug YmYgg]b \UVYfg]XcXYZ]b]XUgdfYj]UaYbhY'b] WiU`]hUh]jUb]WiUbh]hUh]jUaYbhY*Hc gcb Uhf]VihcgXYWUXUWiYfdc'jUf]UV`YgXYibcg*Uchfcg' `c WiU\UWYeiY bc gYUbaU[b]hiXYg' diYg gYdfYgYbhUbg]YadfY)Ycb][iU` WiUbh|U'm XYW]feiY Yb chfcg ib]jYfgcg diX]YfUbhYbYfchfcjU`cf Yg WcbjYfh]f U @|g]WUYb ibU aU`U GYhUZ|g]WU*=cac bc Yl]ghYY]bcib Y^Yad`UfXYWUXUibU' \UVf|UbXYgYf'g]ZiYgYbaU[b]hiXYg' ib]XU))XYgXYg| a]gaUg' mgi jU`cf gYf|Ug]YadfYY`b•aYfc ,* Hc gcb b•aYfcgZ]^cg'dcfeiY gi jU`cf XYdYbXYXY`Ug ib]XUXYgeiY gY UXcdhYbdUfUaYX]f `UgWUbh]XUXYgeiY WcbWiffYbWcbY``UgYb`UgfYgdYWh]jUgYWiUW]cbYg*@]bU`aYbhY'gi Yl]ghYbW]UYg'YbW]YfhcacXc' dfYWUf]U'diYg `UeiY \YacgC`UaUXcWcbghUbhYX]bza]WUbc gYYbWiYbhfUYb b]b[•b `]Vfc XY@|g]WU6)YYei]jU`YbhYaYWzb]WcXY WU`cf'eiY cWidUVUYlhYbgcgWUd|hi`cgYb`cg``|VfcgXYWca]YbncXYg][`c' \U XYgUdUfYW]XchchU`aYbhYYb `cg `]Vfcg)acXYfbcg6 UgWcbghUbhYgXY jUW|c' ?I 5 Z`,q' eiY bc gYYbWiYbhfUbYb`cg"hfUhUXcgW`zg]Wcg'Yad]YnUbU UdUfYWYfYb `cg WcbhYadcfzbYcg6Wcb`U*UXcdc]~b XY`g]ghYaUXYA]cf[] ZYbYWY`U WcbghUbhYY`YWhfcaU[b{h]WU')eiY dcf ]bhYfjYb]fWcbjUf]cg YldcbYbhYgYb`UgZ~fai`Ug XYY`YWhfcaU[)"bYh]gac' `Ug WcbjYfh|UYb jYfXUXYfcgfcadYWUVYnUg*

RU \Yacg \UV`UXcYb `U ]bhfcXiWW]~bXY`U hYbXYbW]UU fYXiW]fY`b•aYfc XYWcbghUbhYgib]jYfgU`Yg*Fc azg gYbW]``cgYf|U\UWYfhUV`U"fUgUWcbhcXUgY``Ug'dYfc Wcac bc gYX]gdcbYXYgiZ]W]YbhYgib]XUXYg*UfV|hfUf]Ug'WUXUUihcf gidf]aY `UgeiY aYbcg `YU[fUXUbm UdUfYWYb

Page 22: Análisis dimensional

'' DP* M@BOH?I JIMNOF<?I<H{FDMDM?DG@HMDIH<F '(

X[`Xi`f kiXYXafj\e cfj hl\' Zfe kXcf ZlXcgf[X [\ ZfejkXek\j' j\ gi\k\e[\)[Xi Z`\ikf j\ek`[f \jfk•i`Zf X [\k\id`eX[Xj c\p\j ]€j`ZXj*

Hf ]XckXe\Zc•Zk`Zfjhl\ fg`eXe hl\ j\ gl\[\e lk`c`qXicXjZfejkXek\j*le`m\ijXc\j X df[f [\ Zfdf[`e\j gXiX Xki`Yl`i X Xc^leX dX^e`kl[ cX*[`d\ej`‚e hl\ d~j Zfem\e^X*Ai* Lljjf #.0$' gfi \a\dgcf' X]`idX hl\)kXe j‚cf \jk~ [\k\id`eX[X cX[`d\ej`‚e [\c gif[lZkf FU$gfi cf hl\ cX*k\dg\iXkliX' \' gf[i~ k\e\i leX [`d\ej`‚e ZlXchl`\iX Zfe kXc[\ Xki`)Yl`i XcXZfejkXek\ le`m\ijXc F cX[`d\ej`‚e X[\ZlX[X*

HX[X `dgfikXi€X \jkX [`jZi\gXeZ`X [\ Zi`k\i`fj X ef j\i gfihl\ \cgcXek\f [\ ZlXchl`\i gifYc\dX [\ <e~c`j`j [`d\ej`feXc i\hl`\i\ [\Z`[`i)gi\m`Xd\ek\ hl• ZfejkXek\j le`m\ijXc\j _Xe [\ Zfej\imXij\ p Zl~c\j gl\)[\e jlgi`d`ij\* @cd`jdf k\fi\dX [\ g` i\jlckX \ek\iXd\ek\ `eƒk`cj`e kXc[\Z`j`‚e* @j ]fiqfjf' gfi kXekf' j\ekXi efidXj hl\ g\id`kXe Xm\i`^lXi)hl• ZfejkXek\j le`m\ijXc\j jfe `dgi\jZ`e[`Yc\j p Zl~c\j jfe jlg\i]clXj*@e cXg\jhl`jX [\ \jkXj efidXj Xe[Xdfj [\j[\ _XZ\dlZ_fj X•fj #-5$ p'\e [`m\ijfj kiXYXafj'_\dfj [X[f cXj hl\ gXi\Z\e Zfe[lZ`i Xci\jlckX[f'Xg\k\Z`[f' p' hl\ \e jl ]fidX [\]`e`k`mX' XgXi\Z\e Zfe[\ejX[Xj \e \cgfjklcX[f hl\ \eleZ`Xi\dfj d~j X[\cXek\*

--8* 9 _m "S 9 ZfejkXek\ [\ JcXeZb 9 2'2.0 R -,)*. \i^ R j$

-c8* 9 S+(Z$]d #\ 9 m\cfZ`[X[ [\ )") clq 9 .'55332 R -,-, Zd+j$

9 9 4!_: #8", 9 ZfejkXek\ [`\c•Zki`ZX[\c mXZ€f9 - l* [\ B`Ii^`$/23ky -,5

8 9 l3 _= #u7!f 9 g\id\XY`c`[X[ dX^e•k`ZX [\c mXZ€f9 03k*-,)3 l* [\B`fi^`$

M# FXj hl\ i\cXZ`feXe d~j [\ [fj dX^e`kl[\j6

A*jd9 6X%&& "6 9 ZfejkXek\ [`e~d`ZX$Td+

LW9 pc[c+U= #p9 ZfejkXek\ \c\ZkifdX^e•k`ZX$

) - #\ 9!". VP \U

"@2 eƒd\if [\ dfc•ZlcXj7 ^ 2 eƒd\if [\ dfc\j7 @4 29 2',..3/ R -,*+ dfc•ZlcXjadfc)^ 9 ZfejkXek\ [\)<mf^X[if$ #%$

9 ZfejkXek\ [\ =fckqdXee 9 -'/4,1 R -,)-2 \i^$5/

@eki\ cXj ZfejkXek\j [\c ^ilgf L# [\jkXZX \c \hl`mXc\ek\ d\ZXdZf[\c ZXcfi<%hl\ i\cXZ`feX[fj dX^e`kl[\j' \c ZXcfip \c kiXYXafhl\' Zfdf)\j jXY`[f' ef jfe ]leZ`fe\j [\ \jkX[f* <dYXj j\ i\]`\i\e X kiXej]fidX)f`fe\j' p cX\ZlXZ`‚e hl\ cXjc`^X\ogi\jX hl\' j` Xc]`eXc[\ cXkiXej]fidX)Z`‚e' i\ZfYiX \c j`jk\dX jl \jkX[f `e`Z`Xc'\c ZXcfiXYjfiY`[f j\ _X kiXej)]fidX[f kfkXcd\ek\ \e kiXYXaf*@jkX\ZlXZ`‚e' gfi Zfej`^l`\ek\' \ogi\jX"hl\ XdYXj dX^e`kl[\j' j` Y`\e jfe \g`jk•d€ZXd\ek\ [`]\i\ek\j' gl\j jlj\]\Zkfj ZXiXZk\i€jk`Zfjjfe [`jk`ekfj' gl\[\e kiXej]fidXij\ leX \e fkiX'p \c ki~ej`kf \jk~ i\^`[f gfi le gi`eZ`g`f [\ Zfej\imXZ`‚e*

FXj i\jkXek\j \ZlXZ`fe\j [\c ^ilgf L# k`\e\e le iXj^f Zfdƒe* L\cX)Z`feXe ]QW^YdeTUcY^cU`QbQR\Uc#%$'\jkf \j' dX^e`kl[\j kXc\j hl\ cXgi\)j\ef`X [\ leX [\ \ccXj\e le fYa\kf cc\mXZfej`^f cXgi\j\eZ`X [\ cXfkiX"\e \c d`jdf fYa\kf' [\ kXcdf[f hl\' X ZlXek€Xj ^lXc\j [\ cXgi`d\iX'Zfii\jgfe[\e ZlXek€Xj ^lXc\j [\ cXj\^le[X* <j€ fZlii\ hl\6

*') H_T_ SeUb`_aeU dU^WQe^ WbQ]_TU]QcQ Y^UbdU$`_cUUJ!/&$/&0&!&*)&&1&5

e^YTQTUcSUWUcY]Q\UcTU ]QcQ WbQfYdQd_bYQ'FX le`[X[ [\ dXjX ^iXm`kX)kfi`X ef k`\e\ efdYi\* @j cXdXjX hl\ \a\iZ\ cX]l\iqX [\ leX [`eX jfYi\fkiX `^lXc ZfcfZX[XX le Z\ek€d\kif [\ [`jkXeZ`X*

+'m 9_^TU XQhQe^ ]Q\&WbQ]_XQ TU XQRUbB4 2 2',..34*-,./ ]_&\USe\Qc'

,') 9_^TU bUY^U\Q dU]`UbQdebQ\ 9 c, ?$ XQ TUXQRUbWbQ^^s]Ub_TU`QbdqSe\QcSehQ U^UbWqQ]UTYQ`_b WbQT_TU\YRUbdQTfQ\WQ,'251 -,)-2 \i^*

.* GX^e`kl[\j `ej\gXiXYc\j*

M` \oXd`eXdfj cX c`jkX [\ cXj \ZlXZ`fe\j ]le[Xd\ekXc\j \e hl\)`ek\im`\e\e ZfejkXek\j le`m\ijXc\j' fYj\imXi\dfj hl\ gl\[\e ZcXj€]`)ZXij\ \e [fj ^ilgfj' X jXY\i6

L# FXj hl\ i\cXZ`feXe [fj dX^e`kl[\j6

]W 9 J<]d "< 9 ZfejkXek\ [\ cX iXm`kXZ`‚e9 2'23 < -,)4" [`e 7. Zd. $

K 9 >E "> 9 \hl`mXc\ek\ d\Z~e`Zf [\c ZXcfi9 0'-4 t$ZXc

#%$ L* MXeElXt #-2'*g~^* -,1$ ccXdXUaeYfQ\U^dUcXcXjdX^e`kl[\j `ej\gX)iXYc\j*tfdf \e E ]jD>X\o`jk\ pX \c ZfeZ\gkf [\ \hl`mXc\eZ`XXgc`ZX[fXcZXcfip;)c kiXYXE*fhl\' >`\ikXd\ek\' ef jfe `ej\gXiXYc\j' efj _X gXi\Z`[f Zfem\e`\ek\`ekif[lZ`i cXel\mX [\efd`eXZ`2e gXiX \m`kXiZfe]lj`fe\j*

t$ @jk\ mXcftZ;ii\jgfe[\ X cXel\mX \jZXcX[\ dXjXj dfc\ZlcXi\j i\cXk`)mXj cXjXO[X6\e \c elZc`[f -.,* @jkX\jZXcX_Xj`[f X[fgkX[X\c X•f -52, \e IkkXnX*gfi X e`‚e Dek\ieXZ`feXc[\ A€j`ZX*

Page 23: Análisis dimensional

02 DP* M@BOH?I JIMNOF<?I<H{FDMDM?DG@HMDIH<F '*

-') H_TQ `QbdqSe\QaeU dU^WQ\Q U^UbWqQ]USo^YSQ TU - \i^ \\UfQQc_&SYQT_e^ VU^r]U^_ `UbYrTYS_TUVbUSeU^SYQf 2 -,.3+2'2.0 _\iq*

.') @QU^UbWqQTUe^ UbWY_\\UfQS_^cYW_e^Q ]QcQ TU-+5" -,., ^iXdfj*/') :^ SeQ\aeYUb e^d_ TU\ fQSq_ T_^TU XQhQe^ SQ]`_ U\pSdbYS_TU

Y^dU^cYTQTe^ ^UeYd_^\S_e\_]R XQh e^ `_TUb U\USdbYiQ^dU"Y^TeSSYr^# aeUfQ\U 7 2 *(,/*dn -,5 Zflc+d""*

0') :^ d_T_ `e^d_ TU\ fQSq_ U^ aeU cUQ8 2 ) ]YbYQWQecc$XQh e^`_TUb Y]Q^QT_b aeU fQ\U : 9 -,3+0-k Xdgad*

@ekfeZ\j' j` j\ _XZ\ le \og\i`d\ekf \e \c hl\ 8 9 ,9 *** 9 -'_XYi~[\ j\i6

$! 0JQJ@F>AKABHOBDQJAKLKOPQH>AK!

cf hl\ gil\YX hl\ cXle`[X[ E4 ef gl\[\ j\i XiY`kiXi`X'j`ef hl\ _XYi~*[\ j\i' gi\Z`jXd\ek\' 0-k m\Z\j d\efi hl\ "4#'

M\X[f [+$ ttt \c j`jk\dX [\ Zf\]`Z`\ek\j eld•i`Zfj X[fgkX[fj Zfe)m\eZ`feXcd\ek\ gXiX jljk`kl`i cXj ZfejkXek\j le`m\ijXc\j jlg\i]clXj \ecXj \ZlXZ`fe\j ]le[Xd\ekXc\j* FXj le`[X[\j ZfdgXk`Yc\j Zfe [`Z_fjZf\]`Z`\ek\j ]fidXe le cYcdU]QS_XUbU^dU#0,$ Zfe cfj d`jdfj* ?\j[\cl\^f' cf d~j j\eZ`ccf j\i~ _XZ\i [l 9 [+$ 9 ***9 -' S jlgfe[i\dfj hl\\j Xj€d`\ekiXj ef j\ X[m`\ikXcf ZfekiXi`f*

Nf[X \ZlXZ`‚e ]le[Xd\ekXc \e cXhl\ j\ _X jlgi`d`[f cXi\jg\Zk`mXZfejkXek\ le`m\ijXc [\]`e\ leX le`[X[ #ef leX dX^e`kl[$ \e ]leZ`‚e[\ cXji\jkXek\j*

<c \jZi`Y`i cXj\ZlXZ`fe\j' ef \j gi\Z`jf d\eZ`feXi cXjle`[X[\j gfihl\j\ jfYi\ek`\e[\ hl\ _Xe [\ lk`c`qXij\ gi\Z`jXd\ek\ j`jk\dXj Zf_\i\ek\j*

Ffj j`jk\dXj Z\ek€d\kif)^iXdf)j\^le[f)[`eX p d\kif)b`cf^iXdf)j\)^le[f)e\nkfe jfe Zf_\i\ek\j Zfe cX\ZlXZ`‚e6

G_^ Y^U\eTYR\Uc\Qc S_^cdQ^dUce^YfUbcQ\UcaeU bU\QSY_^Q T_c ]QW^Y&deTUcY^cU`QbQR\Uc$h ce`UbV\eQcd_TQc\Qc TU]oc'

M\^ƒe \jkf' p k\e`\e[f \e Zl\ekX hl\' \e m`ikl[ [\ cXc\p [\ GXon\cc'\j S+ 2 -+†fTE*f' j‚cf hl\[Xe \e cXj\ZlXZ`fe\j ]le[Xd\ekXc\j [\ cXA€j`ZXXZklXcj\`j ZfejkXek\j le`m\ijXc\j' hl\ jfe6 <$ B4% [$ X3\ S S9!

BiXZ`XjX \jk\ gfjklcX[f j\ gl\[\ \eleZ`Xi \c k\fi\dX [\ g` [\ ledf[f gi\Z`jf* Ml aljk`]`ZXZ`‚eZfej`jk`i~ \e gifYXi hl\' Zfe jl Xlo`c`f' j\fYk`\e\ cXjfclZ`‚e Zfii\ZkX\e kf[fj cfj gifYc\dXj \e hl\ j\X ZfefZ`[X*cXjfclZ`‚e \oXZkX*

%! :FOPBI>OABQJFA>ABO@KEBNBJPBO!

T0'-V

@e i`^fi' XcgXjXi[\ cXji\cXZ`fe\j [\ gifgfiZ`feXc`[X[ \eki\ ZXek`[X)[\j X cXj \ZlXZ`fe\j \eki\ d\[`[Xj' [\Y`\iX \jg\Z`]`ZXij\ \c j`jk\dX [\le`[X[\j X[fgkX[f gXiX kXcgifg‚j`kf* J\if' j` j\ ZfejlckX ZlXchl`\ic`Yif [\ A€j`ZX'j\ m\i~ hl\ j\ \jZi`Y\e cXj\ZlXZ`fe\j ]le[Xd\ekXc\j p j\)[\jXiifccXe cXjk\fi€Xj j`e _XYcXigXiXeX[X [\ le`[X[\j* NXej‚cf \e cXjXgc`ZXZ`fe\jXgifYc\dXj gi~Zk`Zfj \j gi\Z`jf [\Z`i Zl~c\j jfe cXjle`[X)[\j hl\ j\ lk`c`qXe*

FXj le`[X[\j [\ cXjdX^e`kl[\j j\Zle[Xi`Xj hl\[Xe `dgl\jkXj gfi jlj]‚idlcXj [\ [\]`e`Z`‚e' g\if _Xp XiY`kiXi`\[X[Zfdgc\kX \e cX\c\ZZ`‚e [\le`[X[\j [\ cXjdX^e`kl[\j gi`dXi`Xj X Zfe[`Z`‚e [\ Zfej\imXi \e ZX[X*\ZlXZ`‚e ]le[Xd\ekXc cXZfii\jgfe[`\ek\ ZfejkXek\le`m\ijXc*J\if j` •jkX\j jlg\i]clX' ZXY\Xki`Yl`ic\XiY`kiXi`Xd\ek\le mXcfield•i`Zf ]`af' Zfe cX*Zfej`^l`\ek\ i\jki`ZZ`‚e \e cXc`Y\ikX[[\ \c\ZZ`‚e [\ le`[X[\j* <j€' \e KG@%

\ZlXZ`‚e [\ cX]fidX6

d\[`Xek\ cXZlXchl\[X [\]`e`[X cX[`eX p \c e\nkfe' i\jg\Zk`mXd\ek\'\e ]leZ`‚e [\ cXji\jkXek\j le`[X[\j*

@e ZXdY`f' \c j`jk\dX k•Ze`Zf' d\kif)b`cf^iXdf)j\^le[f)b`cfgfe[`f'\e \c hl\ cXel\mX le`[X[ [\ ]l\iqX j\ [\]`e\ Zfdf \c g\jf [\ le b`cf^iX)df [\ dXjX `e\ik\' ef \j Zf_\i\ek\ Zfe cX\ZlXZ`‚e gi\Z\[\ek\' gl\jZfdf - bg 9 5'4- H' cX\ZlXZ`‚e \eki\ d\[`[Xj' \ogi\jXe[f cXjle`[X[\j'j\ Zfem`\ik\ \e6

Q"V #2 ?)? A.j "D^d$

g 54- Td+ :* !%

p XgXi\Z\ \c S_UVYSYU^dU`QbocYd_$5'4-' hl\ gifZ\[\ [\ ef _XY\i ljX[f lej`jk\dX Zf_\i\ek\ Zfe cX\ZlXZ`‚e [X[X*

7\ edY\YiQbcYcdU]QcS_XUbU^dUcTUcQ`QbUSU\_c S_UVYSYU^dUc`QbocYd_c'@jk~^\e\iXc`qX[XcXfg`e`‚e [\ hl\ cXjc\p\j ]€j`ZXj[\]`e\e dX^e`kl)

[\j* FX \ZlXZ`‚e T0'-V'gfi \a\dgcf' \j Zfej`[\iX[X Zfdf cX[\]`e`Z`‚efg\iXZ`feXc [\ cX]l\iqX #m•Xj\'gfi \a\dgcf' \c Xik€Zlcf[\ ?`e^c\$ #/0$'j\ gl\[\ [Xi X cXZfejkXek\ V%j` \j jlg\i]clX' \c mXcfi-*d$ gfi \a\dgcf*

Page 24: Análisis dimensional

'+ <H{FDMDM??SD@HMcIH<F

ef i\gXiXe[f \e hl\ cXk\fi€X[\ cXi\cXk`m`[X[_XXck\iX[f[`Z_X\ZlXZ`‚ej`e hl\ gfi \ccf _XpXj`[f gi\Z`jf df[`]`ZXi cX[\]`e`Z`‚e [\ cX]l\iqXZfdf dX^e`kl[ gi`dXi`X' gl\j jlYj`jk\e `eXck\iX[fj cfj Zi`k\i`fj [\`^lXc[X[ p [\ jldX* ?\j[\ el\jkif glekf [\ m`jkX'cXjttlXZ`fe\j ]le[X)d\ekXc\j ef [\]`e\e dX^e`kl[\j' g\if [\ ZX[X\ZlXZ`‚e j\ [\[lZ\ cXle`[X[ Zf_\i\ek\ [\ leX dX^e`kl[ j`e d~j hl\ `dgfe\i cXZfe[`Z`‚e[\ hl\ ef XgXi\qZXle Zf\]`Z`\ek\ gXi~j`kf*

M\X'\e ^\e\iXc' leX \ZlXZ`‚e hl\ ef i\hl`\iX cXgi\j\eZ`X [\ le ]XZkfi

[\ gifgfiZ`feXc`[X[6h 9 Rtc ………gk^' I-%+J

@jkX\ZlXZ`‚e ]`aXcXle`[X[ [\ "`# \e ZlXekf j\ _XpXe\c\^`[f cXjle`[X)[\j [\ #Rc$' *** ' "_^#$ gl\j j\i~ h 9 - ZlXe[f \c j\^le[f d`\dYif mXc)^X -* J\if gf[i~ \c\^`ij\ XiY`kiXi`Xd\ek\cXle`[X[ [\ "`# X Zfe[`Z`‚e[\ `ekif[lZ`i le ]XZkfi[\ gifgfiZ`feXc`[X[' C2

T0'/V

Zlpf mXcfi'[X[Xj cXjle`[X[\j [\ Rc: ………' G^$ [\g\e[\i~ [\ cXle`[X[XiY`kiXi`XZfe hl\ j\ d`[X "`#'

>fdf j\ m\' cX`ekif[lZZ`‚e [\ leX ZfejkXek\ le`m\ijXc jlg\i]clX\hl`mXc\ X cXgi\j\eZ`X [\ le Zf\]`Z`\ek\ gXi~j`kf' hl\ g\id`k\ lk`c`qXile`[X[\j ZlXc\jhl`\iX gXiXcXdX^e`kl[ "`#' ?\ cXZfdgXiXZ`‚e [\ T0'.V

p T0'/V'i\jlckX6h! le`[X[ Zf_\i\ek\

!" " h le`[X[ XiY`kiXi`X

@QcS_^cdQ^dUce^YfUbcQ\Ucce`UbV\eQcc_^ S_UVYSYU^dUc`_boUYd_c'Jfi \a\dgcf' \e \c j`jk\dX Z\^\j`dXc cX\ZlXZ`‚e T0'-V\o`^\ hl\ cX

le`[X[ [\ ]l\iqX j\X cX[`eX*J\if' j` \e \c d`jdf j`jk\dX j\ hl`\i\ d\[`icX]l\iqX \e gfe[`fj #le gfe[`f 9 g\jf [\ le ^iXdf$' _XYi\dfj [\ `e)kif[lZ`i cXZfejkXek\ [`e~d`ZX' p j\i~6

!"- [`eX

- gfe[`f

))))

,+$

@cef [`jk`e^l`i ZcXiXd\ek\cXjZfejkXek\j le`m\ijXc\j `e\cl[`Yc\j [\cXj jlg\i]clXj j\ [\Y\ gifYXYc\d\ek\ X _XY\i kfdX[f Zfdf [\]`e`Z`‚e[\ leXj p fkiXj \c ZXi~Zk\iZfdƒe [\ [\g\e[\i \oZclj`mXd\ek\ [\ cXjle`[X[\j [\ d\[`[X*

DP* M@BOH?I JIMNOF<?I ',

L\jld`\e[f cf hl\ gi\Z\[\' [`i\dfj hl\ e^ cYcdU]QTUe^YTQTUcUcS_XUbU^dUS_^ e^ cYcdU]QTU USeQSY_^UcSeQ^T_ pcdQcc_^ cQdYcVUSXQc$U^SQTQSQc_`QbdYSe\Qb$Q\ cecdYdeYb\_c cq]R_\_c `_b cec bUc`USdYfQc]UTYTQc'

NiXj cXi^Xj [\c`Y\iXZ`fe\j' cXOe`‚e Dek\ieXZ`feXc[\ A€j`ZX'\e le ]fcc\kfk`klcX[f Gh]R_\c$ I^Ydc Q^T B_]U^S\QdebU Y^ DXhcYSc$ glYc`ZX[f \c X•f -52-'i\Zfd`\e[X cX j`^l`\ek\ [\]`e`Z`‚e6

wOe cYcdU]QS_XUbU^dUTU e^YTQTUc \j le j`jk\dX YXjX[f \e Z`\ikf eƒd\if [\le`[X[\j Y~j`ZXj' [\c hl\ j\ [\i`mXe kf[Xj cXj [\d~j le`[X[\j gfi dlck`gc`ZX)Z`‚e f [`m`j`‚e' j`e `ekif[lZ`i ]XZkfi\j eld•i`Zfj*z

< gfZf hl\ j\ d\[`k\' j\ ZX\\e cXZl\ekX [\ hl\ \jkX [\]`e`Z`‚e \j `ej\im`Yc\gfihl\ ZfekiXm`\e\ cXj efidXj [\ cXYl\eX ]`cfjf]€X fg\iXZ`feXc hl\ [\Y\ i\^`i\e A€j`ZX*HX[`\ jXY\ hl• j`^e`]`ZXdlck`gc`ZXi f [`m`[`i cXj le`[X[\j leXj gfifkiXj* M\ gi\k\e[\' gfi \a\dgcf' hl\ cX \ogi\j`‚e

- [`e 2 ^ *Zd+j.

[\]`e\ cXle`[X[ [\ ]l\iqX \e ]leZ`‚e [\ cXjle`[X[\j Y~j`ZXj[\c j`jk\dX Z\^\j`)dXc' g\if Zfdf ef j\ [`Z\ cf hl\ _Xp hl\ _XZ\i gXiXdlck`gc`ZXi \c ^iXdf gfi \cZ\ek€d\kif' e` Z‚df [`m`[`i \c i\jlckX[f gfi \c ZlX[iX[f [\ le j\^le[f' ef j\jXY\ Z‚df fYk\e\i cX[`eX*

@jkX[\j[`Z_X[X [\]`e`Z`‚e' alekXd\ek\ Zfe cX`[\X [\ hl\ cfj j€dYfcfj hl\]`^liXe \e cXj \ZlXZ`fe\j gl\[\e i\gi\j\ekXi ZXek`[X[\j' \j i\jgfejXYc\ [\ hl\ef _XpXj`[f gfj`Yc\ cc\^Xi X le XZl\i[f XZ\iZX[\ Zl~c\j _Xe [\ j\i cXj le`[X)[\j \c\ZkifdX^e•k`ZXj \e \c j`jk\dX [\ B`fi^` iXZ`feXc`qX[f*

&! ->OB ABQJ @KJGQJPKABI>DJFPQABO!

M\XleX k\fi€X ]€j`ZXZlpXj \ZlXZ`fe\j ]le[Xd\ekXc\j' [\ XZl\i[fZfe el\jkif gi`d\i gfjklcX[f' j\ \ogi\jXe d\[`Xek\ i\cXZ`fe\j [\ gif)gfiZ`feXc`[X[ \eki\ dfefd`fj Zfe \ogfe\ek\j ]`afj' `e[\g\e[`\ek\j [\cXeXkliXc\qX[\ cfj Zl\igfj Zfe hl\ j\ fg\iX* <c gXjXiXcXj\ZlXZ`fe\j\eki\ d\[`[Xj' XgXi\Z\i~e Zfdf ]XZkfi\j [\ gifgfiZ`feXc`[X[ cXj Zfej)kXek\j \jg\Z€]`ZXjp cXj ZfejkXek\j le`m\ijXc\j' p j\ gf[i~ \jZi`Y`i6

[fe[\ cfj \ogfe\ek\j @c: ………' @m j\i~e elcfj f `^lXc\j X - j\^ƒe hl\ cXi\jg\Zk`mXZfejkXek\ j\X jlg\i]clX f `e\cl[`Yc\' ZfjX hl\ hl\[X [\k\id`)eX[X j`e XdY`^„\[X[ gfi el\jkif j\^le[f gfjklcX[f*

,6U43:3: /<306:376,4! %

Page 25: Análisis dimensional

1, <H{FDMDM?DG@HMDIH<F DP* M@BOH?I JIMNOF<?I 1-

M`Y`\e \o`jk\ leX [`]\i\eZ`X \j\eZ`Xc \eki\ cXjmXi`XYc\jL\! ttt $ Lc p

- kXek\j I I j\ Jl\[\ gXiXle`]`ZXi cXefkXZ`‚e' i\gi\j\e)Xj Zfej O%''' % m' '

kXi\jkXj ƒck`dXj Zfe cfj d`jdfj j€dYfcfj hl\ cXjgi`d\iXj' Zfe cf hl\ \cj`jk\dX ]le[Xd\ekXc [\ \ZlXZ`fe\j gf[i~ \jZi`Y`ij\ Xj€6

f Y`\e' gl\jkf hl\ j\ kiXkX[\ eƒd\ifj6

5G cf^ NO $ ''' $ 5OG cf^ k^ 2 cf^ [l

T1'2V

T1'.V

5;O cf^ NO $ ''' $ 5LG cf^ k^ 2 cf^ [f'

FX gfj`Y`c`[X[ [\ ]fidXi j`jk\dXj Zf_\i\ek\j hl\[X jlg\[`kX[X X cXZfdgXk`Y`c`[X[[\ cXj\ZlXZ`fe\j T1'2V\e cXjhl\ cXj@`aMcXjVe jfe [Xkfjp cXj t€ jfe cXj`eZ‚^e`kXj*FX `eZfdgXk`Y`c`[X[' j` cX_lY`\i\' j\ i\d\[`X)i€X`ekif[lZ`\e[f el\mXj ZfejkXek\j le`m\ijXc\j* M`Xc^leX[\ \jkXj Zfej)kXek\j ef ]l\i\ cXiXq‚e \eki\ ZXek`[X[\j [\ dX^e`kl[\j `ej\gXiXYc\j'hl\[Xi€X `emXc`[X[f el\jkif gfjklcX[f*

M`X \j cXZXiXZk\i€jk`ZX[\ cXdXki`q ]fidX[X Zfe cfj Zf\]`Z`\ek\j @€a'

_XYi~ ] 2 ^ & X ]XZkfi\j t€ XiY`kiXi`fj' cf hl\ j`^e`]`ZX hl\ gl\[\e\c\^`ij\ X ZXgi`Z_f cXj le`[X[\j [\ fkiXj kXekXjdX^e`kl[\j' j\^ƒe i\)jlckX [\ T1'/V*>X[X Zfealekf [\ dX^e`kl[\j ZlpXj le`[X[\j j\ \c`^\eXiY`kiXi`Xd\ek\ ]fidXe leX RQcUp jl eƒd\if' ] 2 ^ & X$ \j cX]e\dY&`\YSYTQT[\ cXd`jdX*

>lXe[f j\ gXjX [\ le j`jk\dX Zf_\i\ek\ X fkif kXdY`•e Zf_\i\ek\'kf[fj cfj Zf\]`Z`\ek\j gXi~j`kfj j\ _XZ\e `^lXc\j X lef' p cXj Zfe[`Z`f)e\j T1'1V'hl\ c`^XecXj el\mXj le`[X[\j Zfe cXjgi`d`k`mXj' j\i~e6

t@6cc ………t@6ke 2 -4 ^

T1'-V''''''''''''''

@e \jk\ j`jk\dX [\ \ZlXZ`fe\j j\ jlgfe\ hl\ cXjd\[`[Xj Rc: *…*' L'^

_Xe j`[f fYk\e`[Xj d\[`Xek\ le j`jk\dX [\ le`[X[\j Zf_\i\ek\j Zft [`)Z_Xj\ZlXZ`fe\j* M j\ _lY`\j\e \c\^`[f le`[X[\j ef Zf_\i\ek\j' _lY`\j\eXgXi\Z`[f Zf\]`Z`\ek\j gXi~j`kfj' \Ul$''' $ \U^$\e cXj\ZlXZ`fe\j \o\ekXj [\]XZkfi [\ gifgfiZ`feXc`[X[' p _lY`\j\ i\jlckX[f6

0- 0- \UR+c ………L>^ 2 -

j`\e[f \Uq2 - \e cXj \ZlXZ`fe\j gifm`jkXj [\ ZfejkXek\ `e\cl[`Yc\*NiXk\dfj X_fiX[\ ]fidXi le el\mf j`jk\dX [\ le`[X[\j' E! - ***' E! ^

hl\ j\X Zf_\i\ek\ Zfe T1'-V*FXj el\mXj d\[`[Xj \jkXi~e i\cXZ`feX[Xj

Zfe cXj Xek`^lXj d\[`Xek\ cXj ]‚idlcXj6

t9t9tu' ***'t9 I!^ 5k^ M.$,Og!l Il g!^ I^

T1'3V

T1'1V

@e i\jld\e6 `QbQ V_b]Qb e^ cYcdU]QTU e^YTQTUc$S_XUbU^dUS_^ e^cYcdU]Q TU USeQSY_^Uc$eUTU^ U\UWYbcUQbRYdbQbYQ]U^dUdQ^dQce^YTQTUcS_]_ Y^TYSQ\Q TYVUbU^SYQ$d 9 e ) _' U^dbUU\ ^s]Ub_ TU ]QW^YdeTUch\Q SQbQSdUbqcdYSQTU \Q ]QdbYi M_b]QTQS_^ \_c Ug`_^U^dUcS_^ aeU TYSXQc]QW^YdeTUcVYWebQ U^ \Qc USeQSY_^UcTQTQc'

AXckXZfej`[\iXi X_fiX cXj\ZlXZ`fe\j [\ [\]`e`Z`‚e [\ cXjdX^e`kl[\jj\Zle[Xi`Xj* M\^ƒe _\dfj _\Z_f efkXi' kXc\j]‚idlcXj gl\[\e j\i ZlXc\j)hl`\iX' gl\j fY\[\Z\e kXej‚cf XiXqfe\j [\ lk`c`[X[* Hf ZXY\'gl\j' j\e)kXie`e^ƒe gfjklcX[f' g\if j€ j\ gl\[\ `e[X^Xi cXjZfe[`Z`fe\j hl\ _Xe [\Zldgc`i cXj]‚idlcXj [\ [\]`e`Z`‚e gXiXhl\ g\idXe\qZXe `emXi`XYc\j\ecfj ZXdY`fj [\ j`jk\dXj Zf_\i\ek\j*

M\XleX ]‚idlcX [\ [\]`e`Z`‚e6

McXj \ZlXZ`fe\j #1'.$ j\ Zfem\ik`i~e \e6

"klg! u$@6cc………"k^g! e$@6-e 9 \Ul''''''''''''''''''''''' T1'0V''''''''''''' '

$"klg! O#50;O RRR "k^g! ^#:2f^2 \Ufn

JXiX hl\ \c el\mf j`jk\dX j\X Zf_\i\ek\' \j gi\Z`jf hl\ [\jXgXi\qZXecfj Zf\]`Z`\ek\j gXi~j`kfj' gfi cf hl\ _XYi~[\ j\i6

h & V"gf ''' $g^#' T1'4V

Page 26: Análisis dimensional

h! 2 Q"_!)3 RRR % _! Y# T1'5V

DP* M@BOH?I JIMNOF<?I (&(% <H{FDMDM?DG@HMDIH<F

?\j[\ cl\^f' \jkX \ZlXZ`‚e gi\jZi`Y\ gfi j€ d`jdX cXle`[X[ Eh$ \ehl\ _X [\ d\[`ij\ cXdX^e`kl[ h$ ZlXe[f j\ _Xe ]`aX[f cXj le`[X[\j

E E ^ Ikif j`jk\dX [\ le`[X[\j' E!*3 fff % E! ^$ hl\ j\X Zf_\ifek\L\! ttt $ k'

Zfe cXj \ZlXZ`fe\j ]le[Xd\ekXc\j p Zfe T1'4V'_XYi~[\ gifgfiZ`feXi

d\[`[Xj hl\ jXk`j]X^XecX\ZlXZ`‚e6

'! 5BAFA>O>?OKHQP>OT NBH>PFR>O!

_XYi~[\ jlZ\[\i hl\6

Q"bWG!)3 RRR % bY_! Y#2 1`Q"_! E! RRR % G!Ya% T1'-,V

@e kf[X d\[`Z`‚e j\ ZfdgXiX leX ZXek`[X[ Zfe fkiX [\ jl d`jdX €e[fc\hl\ j\ X[fgkX Zfdf le`[X[* >lXe[f \jkX le`[X[ \j XiY`kiXi`X'cXd\[`[X j\ ccXdXi\cXk`mX'XcgXjf hl\' ZlXe[f ]fidX gXik\ [\ le j`jk\dX Zf_\i\ek\' cXd\[`[Xj\ ccXdXXYjfclkX*M`'gfi \a\dgcf' j\ d`[\e Zfii`\ek\j \c•Zki`ZXjZfe le ^XcmXe‚)d\kif [\ \jg\af p' _\Z_Xj cXj fgfikleXj Zfii\ZZ`fe\j' j\ \ogi\jXe cfj i\jlckX[fj\e d`c€d\kifj [\ cX\jZXcX'cXj d\[`[Xj j\i~e i\cXk`mXj*JXiX hl\ leX d\[`[Xj\X XYjfclkX \j gi\Z`jf X]fiXi \c XgXiXkf[\ dXe\iX hl\ j\ gl\[X gXjXi [\ cfjd`c€d\kifj c\€[fj \e cX\jZXcXXcmXcfi [\ cX`ek\ej`[X[ \ogi\jX[X \e le`[X[\jZf_\i\ek\j' gfi \a\dgcf' \e Xdg\i`fj*

JXiX i\Xc`qXi d\[`Z`fe\j XYjfclkXj _Xp hl\ Zfejkil`i f i\Xc`qXi le gXki‚eZlpf mXcfij\X ZfefZ`[f \e ]leZ`‚e [\ cXle`[X[ i\jg\Zk`mX*@e \c \a\dgcf gif)gl\jkf' _XYi~ hl\ dXe[Xi Xc^XcmXe‚d\kif leX Zfii`\ek\ Zlpf mXcfi \e Xdg\)i`fj j\X ZfefZ`[f*

JXiX hl`\e\j fg`eXe hl\ YXjkXleX YXj\ ]fidX[X Zfe ki\j dX^e`kl[\j d\Z~)e`ZXj' p hl\ •jkXj _Xe [\ j\i gi\Z`jXd\ek\ cXcfe^`kl[' cXdXjX p \c k`\dgf' \cZfekiXjk\ [\ cfj gXkife\j _XYi~ [\ Zfej`jk`i \e d\[`Z`fe\j [\ cfe^`kl[\j6 [\dXjXj p [\ k`\dgfj* <j€' gXiX Zfejkil`i le gXki‚e [\ ZXgXZ`[X[\j' j\ gf[i~i\Zlii`i X le Zfe[\ejX[fi gcXef' gl\j d`[`\e[f \c ~i\X [\ jlj XidX[liXj p cX[`jkXeZ`X \eki\ cXj d`jdXj _Xp [Xkfj YXjkXek\j gXiX ZXcZlcXijl ZXgXZ`[X['XZfe[`Z`‚e [\ hl\ \c [`\c•Zki`Zf j\X \c mXZ€f*>fdf' \e \jk\ ZXjf' kf[f j\ i\[lZ\ Xd\[`Z`fe\j [\ cfe^`kl[\j' cfj ]€j`Zfj hl\' X[\d~j [\ fg\iXi Zfe cXYXj\ dlk`cX[XZi\\e hl\ cX[`d\ej`‚e [\i`mX [\c gifZ\jf [\ d\[`[X' X]`idXe hl\ cXZXgXZ`[X['\c•Zki`ZX\j _fdf^•e\X Zfe cXcfe^`kl[ p [\Y\ \ogi\jXij\ \e Z\ek€d\kifj*

<c lk`c`qXi cXYXj\ Zfdgc\kX' ZXdY`X\c ZfeZ\gkf hl\ j\ k\e€X [\ cXjd\[`[XjXYjfclkXj' gl\j gXiX ZfekiXjkXi cfj gXkife\j ef _Xp e\Z\j`[X[ [\ Xk\e\ij\ Xd\[`Z`fe\j [\ cfe^`kl[\j' dXjXj p k`\dgfj' gi\Z`jXd\ek\* M\gl\[\' gfi \a\dgcf'\c\^`i XiY`kiXi`Xd\ek\ leX le`[X[ \c•Zki`ZXi\gi\j\ekX[X gfi le Zfe[\ejX[figXki‚e ZlXchl`\iX' p \ekfeZ\j cXZfdgXiXZ`‚e [\ ZXgXZ`[X[\j Zfe [`Z_f gXki‚e[Xi~ d\[`[Xj XYjfclkXj*@cgifYc\dX hl\ gcXek\X cXX[fgZ`‚e [\c j`jk\dX [\B`fi^` Zfej`jk\' gi\Z`jXd\ek\' \e Zfejkil`i le gXki‚e [\ Xc^leX [\ cXj le`)[X[\j \c\ZkifdX^e•k`ZXj [\ kXcdf[f hl\ cX g\id\XY`c`[X[ [\c mXZ€fmXc^X'\oXZkXd\ek\' #*Ff 2 03k *-,)3 7 R ]+Q6+X'

p Zfdf T1'4Vj\ Zfem`\ik\ \e6

3hh! 2 Q"1WG!)3 RRR % 1Y_! Y#%

[\Y`\e[f j\i \c ]XZkfi 3h 2 E! h 2 Eh `e[\g\e[`\ek\ [\ cXj d\[`[Xjg! )3 RRR % g!^' L\Zfi[Xe[f cX[\]`e`Z`‚e [\ cXj]leZ`fe\j Zfe[`Z`feXcd\ek\

_fdf^•e\Xj i\jlckX hl\6 *@Qcs^YSQc Vrb]e\Qc TU TUVY^YSYraeU QT]YdU^ cYcdU]QcTU e^YTQTUc

S_XUbU^dUcc_^ \Qc S_^TYSY_^Q\]U^dUX_]_Wp^UQc$h \Qc S_^TYSY_^UcQ aeUXQ^ TU cQdYcVQSUb\_c VQSd_bUc1)3 ''' % 3^ Ucdo^ Y]`eUcdQc `_b \Qc USeQ&

SY_^UcT1'3V*Hf _Xp gi\Z\gkf c‚^`Zf e` c\p eXkliXchl\ fYc`^l\ Xlk`c`qXi\oZclj`)

mXd\ek\ cXj ]leZ`fe\j Zfe[`Z`feXcd\ek\ _fdf^•e\Xj' p Yl\eX gil\YX\j hl\ \c `= Zldgc\ jl Zfd\k`[f X jXk`j]XZZ`‚e[\ kf[fj cfj hl€d`Zfjp Y`‚cf^fj* J\if \c <e~c`j`j [`d\ej`feXc' j\^ƒe m\i\dfj' j‚cf gl\[\fg\iXi Zfe dX^e`kl[\j gi`dXi`Xj f Zfe dX^e`kl[\j [\]`e`[Xj gfi ]‚idl)cXj hl\ j\Xe `emXi`Xek\jZfe i\cXZ`‚e X cfj ZXdY`fj \eki\ j`jk\dXj [\le`[X[\j Zf_\i\ek\j* Ffj fikf[fofj \e dXk\i`X [`d\ej`feXc gl\[\e XeX)k\dXk`qXiX hl`\e\j lk`c`Z\e \c `= f cXZfejkXek\ hl€d`ZX' g\if •jkfjgf[i~e Zfek\jkXiZfe le \eZf^`d`\ekf [\ _fdYifj' p e\^Xij\ Xdf[`]`ZXikf[fj jlj c`Yifj' kXYcXjp XgXiXkfj[\ d\[`[X gXiXZfdgcXZ\i X cfj [`)

d\ej`feXc`jkXj*H‚k\j\ hl\ cXj \ZlXZ`fe\j ]le[Xd\ekXc\j ]`aXecXdlck`gc`Z`[X[ [\

cXYXj\' g\if ef [\k\id`eXe cXjdX^e`kl[\j hl\ cX]fidXe* Jl\[\e j\igi`dXi`Xj f j\Zle[Xi`Xj' `e[`jk`ekXd\ek\' p _XjkXj\ gl\[\e `eZcl`i \e\ccXjcXj ZfejkXek\j \jg\Z€]`ZXjp cXj le`m\ijXc\j* Jfi \jf i\jlckX `eX[\)ZlX[f ccXdXiVe^TQ]U^dQ\UcX cXjdX^e`kl[\j \jZf^`[Xj gXiX]fidXi cXYXj\ p TUbYfQTQcXcXj[\d~j* @cljf' j`e \dYXi^f' _X ZfejX^iX[f \jkX[\efd`eXZ`‚e*

(! 4KOOWI?KHKOABH>OB@Q>@FKJBOCWOF@>O!

HX[`\ e`\^X hl\ cfj j€dYfcfj hl\ ]`^liXe \e cXj\ZlXZ`fe\j [\ cXA€)j`ZXi\gi\j\ekXe cfj eƒd\ifj #d\[`[Xj$ fYk\e`[fj Zfe le j`jk\dX [\le`[X[\j Zf_\i\ek\j Zfe [`Z_Xj \ZlXZ`fe\j' g\if dlZ_fj ]€j`Zfj fg`eXehl\ kXc\j j€dYfcfj gl\[\e i\gi\j\ekXi kXdY`•e ZXek`[X[\j p •jkX \j cXiXq‚e gfi cXhl\ cXOe`‚e Dek\ieXZ`feXc[\ A€j`ZXef _XpXgf[`[f _XjkXX_fiX i\jfcm\i \c gifYc\dX jljZ`kX[f gfi cXiXZ`feXc`qXZ`‚e[\ cXjle`)[X[\j [\c \c\ZkifdX^e\k`jdf* PXdfj X [\dfjkiXi hl\ cfj j€dYfcfj efgl\[\e `ek\igi\kXij\ Zfdf ZXek`[X[\j*

Page 27: Análisis dimensional

4 2 5Q3AH ''' w\eki\ d\[`[Xjz T3'-V

(' <H{FDMDM?DG@HMDIH<F

>fej`[\i\dfj cX \ZlXZ`‚e6

p jlgfe^Xdfj hl\ cX\ZlXZ`‚e6

w\eki\ ZXek`[X[\jz 2*!%3

\j kXdY`•e m~c`[X*M``ekif[lZ`dfj le ]XZkfi eld•i`Zf XiY`kiXi`f' V%\e\jkXj \ZlXZ`fe\j' i\jlckX6

4\ 2 WP4

"4#\ 2 WN"4#'

T3'1V

T3'2V

><J€NOFI P

04 .76.08;7 /0 /3506:3V6

4\ 2 WN5Q36H '

"4#\ 9 V"5#Q3"6#H '

T3'/V

T3'0V

f j\X6

FXj le`[X[\j [\ "4# p [\ "4#\ [\Y\e j\i Zf_\i\ek\j' i\jg\Zk`mX)d\ek\' Zfe T3'-Vp T3'/V*Jfi kXekf6

p' \e Zfej\Zl\eZ`X62*!*3

"! 1XNIQH>OAFIBJOFKJ>HBO!

"4# 2 E4

"4#\ 2 E4\

j` 5b6H 2 )

j` WP5b6H 2 -

M\XleX k\fi€X ]€j`ZXZlpXj \ZlXZ`fe\j ]le[Xd\ekXc\j ZldgcXe el\j)kif gi`d\i gfjklcX[f* @dgc\Xe[f le j`jk\dX [\ le`[X[\j Zf_\i\ek\Zfe [`Z_Xj \ZlXZ`fe\j' ef _XYi~ Zf\]`Z`\ek\j gXi~j`kfj' p' j` gXiX j`d)gc`]`ZXicXZl\jk`‚e' j\ Xki`Ylp\ \c mXcfilef X kf[Xj cXj ZfejkXek\j jl)g\i]clXj' [`Z_Xj \ZlXZ`fe\j gf[i~e \jZi`Y`i Xj€6

cf hl\ j`^e`]`ZX hl\ cX `ekif[lZZ`‚e [\c ]XZkfi WPfYc`^X X ZXdY`XicXle`[X[ [\ "4#'

Jfi fkiX gXik\' Xgc`ZXe[f cX\ZlXZ`‚e SQ^dYTQT2 ]UTYTQ < e^YTQT$j\ k`\e\6

T-'-V

T3'4V

T3'5V

"4# 2 4E4

"4#\ 2 4\E4\

"4#\ 9 4E4 9 "4#% T3'-,V

@eki\ cXj _ ]`^liXe cXj ZfejkXek\j `e\cl[`Yc\j' hl\ hl\[Xe [\]`e`[Xjj`e XdY`^„\[X[ Zfe el\jkif j\^le[f gfjklcX[f* @e Zfej\Zl\eZ`X' kf[fjcfj \ogfe\ek\j 8^U j\i~e eƒd\ifj ZfefZ`[fj*

CX^Xdfj \c gXjf X fkif j`jk\dX [\ le`[X[\j kXdY`•e Zf_\i\ek\ p'gXiX Xk\e\iefj X cXefkXZ`‚e \e ljf' hl\ ]l\ `ekif[lZ`[X gfi GXon\cc'\dgc\Xi\dfj cfj j€dYfcfj TRcV' *** ' I_^O gXiX [\j`^eXi cXiXq‚e \eki\c*Xjel\mXj le`[X[\j p cXj gi`d`k`mXj6

p jljk`klp\e[f \e T3'5V4\ p E4\ gfi jlj mXcfi\j kfdX[fj [\ T3'1Vp T3'3Vi\jlckX6

hl\ \jk~ \e ZfekiX[`ZZ`‚e Zfe T3'2V*@jkf j`^e`]`ZXhl\6@_c cq]R_\_c aeU VYWebQ U^ \Qc USeQSY_^UcTU\Q ;qcYSQ ^_ `eUTU^ bU&

`bUcU^dQbSQ^dYTQTUc'<[\d~j' cX\ZlXZ`‚e T3'-,V dl\jkiX hl\6@QcSQ^dYTQTUcVqcYSQcc_^ Y^fQbYQ^dUcS_^ bU\QSYr Q \_c VQSd_bUc^e]p&

bYS_caeU$ QbRYdbQbYQ]U^dU$cU Y^db_TeiSQ^ U^ \Qc USeQSY_^Uc'

T-'.V

Page 28: Análisis dimensional

T-'/V

P* @F >IH>@JNI ?@ ?cc`@HMD2H 13() <H{FDMDM?DG@HMDIH<F

>fe \jkX efkXZ`‚e' cXjZfe[`Z`fe\j hl\ _Xe [\ Zldgc`i cfj eƒd\ifj MLYO

j\i~e' j\^ƒe i\jlckX [\ T1'3V' ZXg€klcfDP6

I_C0Y ''' I_YJ !<Y 9 -

hl\ \j cXVrb]e\Q TY]U^cY_^Q\ [\ cXdX^e`kl[ G\ Zfe i\cXZ`‚e X cXYXj\GW! fff % GXf 0H Zfealekf [\ cfj \ogfe\ek\j >Rci' ………' 6GX\% Zfejk`klp\ cXTY]U^cYr^ [\ G\ Zfe i\cXZ`‚e X [`Z_XYXj\*

@_c cq]R_\_c aeU VYWebQ U^dbU\_c `Qbp^dUcYcbUSd_cTU \Qc Vrb]e\QcTY]U^cY_^Q\Ucc_^ \Qc bQi_^UcU^dbU\Qc e^YTQTUcTUT_c cYcdU]QcS_XUbU^dUcSeQ\UcaeYUbQ'

FXj ]‚idlcXj [`d\ej`feXc\j [\ cXjdX^e`kl[\j j\Zle[Xi`Xj j\ fYk`\)e\e ]~Z`cd\ek\ XgXik`i [\ jl ]‚idlcX [\ [\]`e`Z`‚e Zfe kXc[\ hl\ Zld)gcXe \c i\hl`j`kf [\ j\i _fdf^•e\Xj Zfe cXj Zfe[`Z`fe\j T-'0E' cf hl\\o`^\' \e m`ikl[ [\c k\fi\dX .*( [\c ZXg€klcfgi`d\if' hl\ k\e^Xe cX]fidX6

hl\ j\ _XpXX[fgkX[f gXiXjl i\gi\j\ekXZ`‚e* FX \o`jk\eZ`X [\ kXc\j \ek\j \jk~jlYfi[`eX[X X cXZfe[`Z`‚e [\ hl\ cXji\cXZ`fe\j hl\ c`^Xe\eki\ j€ cXj ZXek`[X)[\j j\Xe i\cXZ`fe\j [\ gifgfiZ`feXc`[X[ \eki\ gfk\eZ`Xj Zfe \ogfe\ek\j ]`afj'`e[\g\e[`\ek\j [\ cXeXkliXc\qX[\ cfj Zl\igfj' p [\ hl\ \o`jkX le Zi`k\i`f gXiX[`jZ\ie`i cXj ZfejkXek\j jlg\i]clXj [\ cXj `e\cl[`Yc\j*

JXiX cfj Zfej\Zl\ek\j Zfe cXc‚^`ZXgfj`k`m`jkX' cX]‚idlcX [`d\ej`feXc [\kf[X dX^e`kl[ _X [\ [\[lZ`ij\ [\ jl [\]`e`Z`‚e fg\iXkfi`X' \oZclj`mXd\ek\' j`ei\Zlii`i X cXjc\p\j ]€j`ZXj*@cgif]\jfi ?`e^c\ #/0$' gfi \a\dgcf' cc\mX\c fg\iX)Z`feXc`jdf _XjkXjl ƒck`df \oki\df p fg`eX hl\ cXZXi^X\c•Zki`ZX\j _fdf^•)e\X Zfe cX]l\iqX' gfihl\ gXiX d\[`i ZXi^Xj\c•Zki`ZXjYXjkXd\[`i cXj ]l\iqXjhl\ \a\iZ\e jfYi\ fkiX hl\ j`im\ [\ le`[X[ p j\ ZfcfZXX [`jkXeZ`X[\k\id`eX[X*>fdf \c Zi`k\i`f [\ ?`e^c\ \j Xgc`ZXYc\X cXjdXjXj' i\jlckXi€X hl\ cX]l\iqX' cXZXi^X\c•Zki`ZXp cX dXjX jfe dX^e`kl[\j _fdf^•e\Xj* S Xƒe ZXYi€Xi d~jc\afj' gfihl\ gf[i€X kfdXij\ Zfdf XgXiXkfgXiXd\[`i ZXi^Xj\c•Zki`ZXjle \c\Z)kifjZfg`f [\ k`gf [\k\id`eX[f' p cXd\[`[X j\ i\[lZ`[X X [`jkXeZ`Xjf ~e^lcfj'Zfe cf hl\ cXZXi^X\c•Zki`ZX'gf[i€X' X el\jkiX mfclekX[' f k\e\i cX[`d\ej`‚e[\ cXcfe^`kl[' f k\e\i [`d\ej`‚e elcX* @cglekf ]cXZf[\ \jk\ df[f [\ iXqfeXi\j hl\ cXj ]‚idlcXj [`d\ej`feXc\j Zfe •c fYk\e`[Xj jfe \ek\iXd\ek\ `eƒk`c\jgXiX cfj ]`e\j [\c <e~c`j`j [`d\ej`feXc*

M\^ƒe el\jkiX k\fi€X' kXe j‚cf cXj dX^e`kl[\j j\Zle[Xi`Xj fYk`\e\e jl [`)d\ej`‚e d\[`Xek\ jl [\]`e`Z`‚e fg\iXkfi`X* FXj [`d\ej`fe\j [\ kf[Xj cXj dX^)e`kl[\j gi`dXi`Xj \jk~e jlYfi[`eX[Xj X cXj c\p\j ]le[Xd\ekXc\j [\ cX k\fi€X]€j`ZX\e hl\ j\ lk`c`Z\e* >fe el\jkif d•kf[f [\jXgXi\Z\ \c ZXi~Zk\id`jk\i`fjf[\ cXj [`d\ej`fe\j* HX[X k`\e\e hl\ m\i e` Zfe cXjZXek`[X[\j e` Zfe cXj d\[`)[Xj* < g\jXi [\ jl efkXZ`‚e `ej‚c`kX jfe i\cXZ`fe\j \eki\ eƒd\ifj*

NiXkXi\dfj' gfi m€X[\ \a\dgcf' [\ _XccXicXj]‚idlcXj [`d\ej`feXc \j [\ cXjdX^e`kl[\j hl\ `ek\im`\e\e \e cX [`e~d`ZX e\nkfe`XeX [\c glekf dXk\i`Xc*CXp \e \jkX k\fi€X ki\j \ZlXZ`fe\j ]le[Xd\ekXc\j' X jXY\i6

M\XeGW! fff %GX cXjdX^e`kl[\j \jZf^`[Xj gXiX]fidXi cXYXj\*@e \cgXjf [\ le j`jk\dX Zf_\i\ek\ X fkif kXdY`•e Zf_\i\ek\ j\i~e [Xkfj cfjmXcfi\j [\ I_<% ''' %I_]O$ p cXj\ZlXZ`fe\j T-'/Vg\id`k`i~e [\jg\aXi cfjmXcfi\j [\ cfj eƒd\if I_%JZfii\jgfe[`\ek\j XcXji\jkXek\j dX^e`kl[\j'i\jlckXe[f \ogi\j`fe\j dfefd`Xj kXc\j Zfdf6

=> = >"#" IN I&G\ 9 GW D;''' 8GX % T-'0V

A*/Q & ]!&&!& N Td+! Q2 < X+T'

. "/T-'1V

h 9 G !W) - "J 2 ^&]#$

hl\ i\cXZ`feXe Z`eZf dX^e`kl[\j gi`dXi`Xj6 4' XT' d$W'XR' p cXZfejkXek\ [\ cX^iXm`kXZ`‚e'9' FXj [\d~j dX^e`kl[\j hl\ j\ dXe\aXe \e cXk\fi€X #m\cfZ`[X['XZ\c\iXZ`‚e' dfd\ekf' kiXYXaf'€dg\kl' `dglcjf ***$ jfe dX^e`kl[\j j\Zle[Xi`XjZlpX ]‚idlcX [`d\ej`feXc j\ [\[lZ`i~ [\ cXi\jg\Zk`mX ]‚idlcX [\ [\]`e`Z`‚e\e ZlXekf j\ ZfefqZXe cXj [`d\ej`fe\j [\ cXj dX^e`kl[\j hl\ ]`^liXe \e \ccX*>fdf kf[Xj cXj]‚idlcXj [\ [\]`e`Z`‚e jfe dfefd`Xj' hl\[X Zldgc`[X cXZfe[`)Z`‚e [\ \o`jk\eZ`X [\ cXj [`d\ej`fe\j*

Jfi ZfdgXiXZ`‚e Zfe cXj \ZlXZ`fe\j T1'-V[\c ZXg€klcfDP j\ m\ hl\ cXdX)ki`q ]fidX[X Zfe cfj \ogfe\ek\j !YZ \j6

[fe[\ @c" ………' @d jfe cfj \ogfe\ek\j [`d\ej`feXc\j [\ h$p cfj dfefDe`fj6

G]$W# $$ "

&^

NiXj cXi^f if[\f _\dfj cc\^X[f Xcd`jdf ZfeZ\gkf [\ [`d\ej`‚e hl\' ZfegXjdfjX `ekl`Z`‚e* \jkXYc\Z`‚Afli`\i \e jl k\fi€X XeXc€k`ZX[\c ZXcfi*Jf[\dfj`dX^`eXi cX[`d\ej`‚e Zfdf le \ek\ XYjkiXZkf'Xki`Ylkf [\ ZX[XdX^e`kl[' hl\j\ [\aX i\gi\j\ekXi gfi \c Zfealekf fi[\eX[f [\ ] eƒd\ifj X[jZi`kfj X cXYXj\

4 XT

& ) & -% "%I & -

; <k`\e\e [`d\ej`‚e elcX gfi iXq‚e [\ T-'0V*

. -,,1 $ $ 1I I ) -+. -

p Zfdf jl ZXiXZk\i€jk`ZX\j S 9 /' _XYi~ ] 9 2 ) / 9 / dX^e`kl[\j ]le[X)d\ekXc\j* Jf[i~e \jZf^\ij\ gXiX ]fidXi cXYXj\ ki\j dX^e`kl[\j ZlXc\jhl`\iX

Page 29: Análisis dimensional

14 <H{FDMDM?DG@HMDIH<F m* @F >IH>@JNI ?@ ?DG@HMD|H (,

Zfe kXc[\ hl\ j\Xe Y^TU`U^TYU^dUc$\jkf \j' Zfe kXc[\ hl\ ef j\X elcf \c [\k\id`)eXek\ ]fidX[f gfi cXj ZfcldeXj Zfii\jgfe[`\ek\j X cXj dX^e`kl[\j i\jkXek\j*Ffj ƒe`Zfj [\k\id`eXek\j [\ k\iZ\i fi[\e elcfj jfe6

YXjkXi~ jljk`kl`i \e T.'-V gXiX fYk\e\i6

I_J 2 I?!C W ''' I?!X^!X T.'/V

c ^ XT <

) - . I). I )-) - I ) -+.

Mcfj el\mfj \ogfe\ek\j [`d\ej`feXc\j mXc[i~e6&)

.I

.I9

))I

gfi cf hl\ ZlXchl`\i ZfdY`eXZ`‚e k\ieXi`X ]fidX[X Zfe cXj dX^e`kl[\j [X[Xjgl\[\ j\im`i gXiX]fidXi cXYXj\' Zfe \oZ\gZ`‚e [\ cXj[fj j`^l`\ek\j6 "XT%9%XR#

M#j' d'XR#'>XY\' kf[Xm€X'kfdXi \e Zfej`[\iXZ`‚e cXj ]‚idlcXj [\ [\]`e`Z`‚e [\ cXj

dX^e`kl[\j j\Zle[Xi`Xj* >fe \ccf Xld\ekX \c eƒd\if [\ `eZ‚^e`kXj M \c [\\ZlXZ`fe\j' g\if cXdlck`gc`Z`[X[ [\ cXYXj\ ef j\ Xck\iXgfihl\ ZX[Xm\q hl\ j\X^i\^X leX dX^e`kl[ j\Zle[Xi`X j\ X•X[\ cX i\jg\Zk`mX ]‚idlcX [\ [\]`e`Z`‚ehl\' \m`[\ek\d\ek\' ef \j Zfej\Zl\eZ`X [\ cXj \jZi`kXj Xek\i`fid\ek\*

M\ _X Zfem\e`[f \e X[fgkXi \e G\Z~e`ZX cXYXj\ #j' XT%^# M\e jljk`kl`i cfjj€dYfcfj I]J% IXTJ% I^< gfi cXj c\kiXj >%?%D' >fe \jkfj Zfem\e`fj' cXj\ZlXZ€f)e\j T-'1VZfe[lZ\e X6

T.'0V

+$! 1>@PKNBOAB@KJRBNOFXJ!

>&* ?&* D+IQJ2 )

F. ?&+IQJI)J&* 2 )

I?J&* I)J&*(+ IXRJ 2 >

BiXZ`Xj X cX`ek\igi\kXZ`‚e [\ cXj ]‚idlcXj [`d\ej`feXc\j [X[X \'g \cXgXikX[fXek\i`fi' i\jlckX dlp j\eZ`ccf Xm\i`^lXi \e hl• j\ Zfem`\ik\ cXle`[X[ [\ ZlXchl`\i dX^e`kl[ ZlXe[f j\ Xck\iXe [\ ZlXchl`\i dXe\iX cXjle`[X[\j ]le[Xd\ekXc\j f \c mXcfi Xki`Yl`[f X leX ZfejkXek\ le`m\ijXc*

M\X' gfi \a\dgcf' leX dX^e`kl[' g$ Zfe cXj`^l`\ek\ ]‚idlcX [`d\e)j`feXc6

[\ [fe[\6

IQJ2 >?D&+

TIV 2 >,?&*D&+

IXRJ 2 >,(+?;Q+D&*'

M` IY$ I]$ Id p I!Y$ I! d' I!l jfe' i\jg\Zk`mXd\ek\' cXj le`[X[\j ]le[X)d\ekXc\j \e \c j`jk\dX gi`d`k`mf p \e \c el\mf' j\i~6

#! .>I?FKO AB ?>OB!T/'-V

M\X6T.'-V

Zfe cf hl\ hl\[X i\jl\ckf \c gifYc\dX*Jfi jl g\Zlc`Xi dXe\iX [\ j\i' cXj ZfejkXek\j le`m\ijXc\j ZXi\Z\e [\

le`[X[ gifg`X' gfi cf hl\' \e m\q [\ cXiXq‚e \eki\ le`[X[\j' _XYi~ hl\gfe\i cXiXq‚e `em\ijX [\ cXj d\[`[Xj* <j€' [\6cX]‚idlcX [`d\ej`feXc [\ cXdX^e`kl[ _ Zfe i\cXZ`‚e XcXYXj\ "?;3 ''' %

?]#' M\ kiXkX[\ Xm\i`^lXi jl ]‚idlcX [`d\ej`feXc Zfe i\cXZ`‚e X fkiXYXj\ "?! c"***' ?! ]#$ \e cXhl\ gl\[\e ]`^liXi dX^e`kl[\j ZlXc\jhl`\iX'gi`dXi`Xj f j\Zle[Xi`Xj* M`cXj ]‚idlcXj [`d\ej`feXc\j [\ cXj Xek`^lXjdX^e`kl[\j Y~j`ZXj Zfe i\cXZ`‚e X cXj el\mXj jfe6

\\ [\[lZ\6

# t' $ 9 # k\ I "N0i #t6IT.'.V

FX \ZlXZ`‚e T/'-V aljk`]`ZX \c ccXdX[f So\Se\_ S_^ e^YTQTUc$hl\6j`im\ gXiX Xm\i`^lXi Z‚df j\ Xck\iXe cXj le`[X[\j [\i`mX[Xj ZlXe[f j\

Page 30: Análisis dimensional

2, <H{FDMDM?DG@HMDI"<F m* @F >IH>@JNI ?@ ?DG@HMD|H 2-

ZXdY`XecXjle`[X[\j Y~j`ZXj'g\if \j gi\Z`jf k\e\i \e Zl\ekX hl\ [`Z_f)Z~cZlcfj‚cf gl\[\ lk`c`qXij\ ZlXe[f XdYfj j`jk\dXj jfe Zf_\i\ek\j Zfele d`jdf j`jk\dX [\ \ZlXZ`fe\j ]le[Xd\ekXc\j*

hl\ j\ [\efd`eXe Zfdgfe\ek\j [\c m\Zkfi' Zfe cXZfe[`Z`‚e [\ hl\' j` j\*Xgc`ZXle ZXdY`f [\ \a\j' cXjel\mXj Zfdgfe\ek\j \jk•e c`^X[XjZfe cXjgi`d`k`mXj gfi \ZlXZ`fe\j c`e\Xc\j6

Ffj j`^l`\ek\j \a\dgcfj j\im`i~e gXiX XZcXiXicf hl\ gi\Z\[\*L# MXY`\e[f hl\ \e \c j`jk\dX Z^j* cX ZfejkXek\ [\ cX ^iXm`kXZ`‚e mXc\)

"9# 2 2'23, R -,)4 Zd! ^)c M).' Xm\i`^lXi jl mXcfi \e \c j`jk\dX [\ B`fi^`' #d7b^' J#'

T0'-V

"9!# 2 2'23, -,)-- F/ b^)c M).*

!=XjkX \e\iXc`qXi \jkX [\]`e`Z`‚e X le \jgXZ`f [\ ] [`d\ej`fe\j' p Zfd)gXiXi T0'-VZfe T.'0VgXiXm\i hl\ \o`jk\ leX XeXcf^€X]fidXc Zfdgc\kX'!Q `jfdfi]`jdf' [\ kXcdf[f hl\ Xcfj \ogfe\ek\j [`d\ej`feXc\j' )<)! RRR%6<F%

[\ cXdX^e`kl[ _ Zfe i\cXZ`‚e XcXYXj\ "? )3 RRR % ? d$ Zfii\jgfe[\e cXjZfdgfe\ek\j [\ le m\Zkfi \e le \jgXZ`f [\ ] [`d\ej`fe\j*

<j€ Zfdf \e A€j`ZX\o`jk\e cfj m\Zkfi\j Zfe `e[\g\e[\eZ`X* [\c j`jk\dXgXik`ZlcXi[\ \a\j \c\^`[fj gXiXjl i\gi\j\ekXZ`‚e' Xj€kXdY`•e' [\ XZl\i)[f Zfe MXeElXe' gf[\dfj `dX^`eXi hl\ X kf[X dX^e`kl[ ]€j`ZXZfii\j)gfe[\ leX TY]U^cYr^$ hl\ \o`jk\ Zfe `e[\g\e[\eZ`X [\ cXYXj\ hl\ j\X[fgk\* Ffj \ogfe\ek\j [`d\ej`feXc\j _XZ\e cXj m\Z\j [\ Zfdgfe\ek\j[\ cX[`d\ej`‚e Zfej`[\iX[X Zfdf m\Zkfi' p mXi€XeXcZXdY`XicXYXj\*

MfclZ`‚e6

I9J 2 >,*WQ&*H&+

# $/ # $)-<! P ) Zd t W DK)/

2'23, R -,)4 ) - d - b^ )

[\ [fe[\6

R# <m\i`^lXi Zl~c _X [\ j\i cXle`[X[ [\ k`\dgf gXiX hl\' Zfej\imXe[f \c Z\ek€d\kif M \c ^iXdf' X[hl`\iX cXZfejkXek\ [\ cX^iXm`kXZ`‚e\c mXcfi -*

MfclZ`‚e6

% ! %M$W.2'23, -,)4 2 J!d

E!c &K -,0

[j\^le fj*F.%./)

$&$ ->OBOOQLBN>?QJA>JPBOT ?>OBOBOPNF@P>O!

%! ,J>HKDW>OBJPNBAFIBJOFKJBO' RB@PKNBO!

C\dfj m`jkf hl\' ZlXe[f j\ kfdXe \e Zfej`[\iXZ`‚e kf[Xj cXj dX^)e`kl[\j hl\ `ek\im`\e\e \e leX k\fi€X' cXdlck`gc`Z`[X[ [\ cXYXj\ hl\[X[\k\id`eX[X gfi \c j`jk\dX [\ \ZlXZ`fe\j ]le[Xd\ekXc\j* J\if jl\c\jlZ\[\i hl\' \e [\k\id`eX[f fi[\e [\ ]\e‚d\efj' ef \eki\e kf[Xj cXjdX^e`kl[\j [\ cXk\fi€X' p cXi\]\i`[X YXj\ gl\[\ j\i \oZ\j`mX*

M\Xe mXi`XjdX^e`kl[\j' Rc" ' GY% ZlpXj ]‚idlcXj [`d\ej`feXc\jZfe i\cXZ`‚e X Z`\ikXYXj\ #GD" ' ?]# jfe6

0H ZfeZ\gkf [\ [`d\ej`‚e Zfdf \ek\ `e[`m`[lXc i\jlckX dlp ZcXif)^iXZ`XjX hl\ L* MXeElXe #-2$ _X gl\jkf [\ dXe`]`\jkf hl\ \eki\ cX[`d\ej`‚e [\ leX dX^e`kl[ p jlj \ogfe\ek\j [`d\ej`feXc\j i\jg\Zkf X*leX YXj\ [\k\id`eX[X' \o`jk\ cX d`jdX i\cXZ`‚e ]fidXc hl\ \eki\ lem\Zkfi p jlj Zfdgfe\ek\j i\jg\Zkf X le j`jk\dX [\ \a\j Zffi[\eX[fj'i\cXZ`‚e ]fidXc hl\ j\ [\efd`eX Yc_]_bVYc]_ #%$*

M\ [\]`e\e cfj m\Zkfi\j \e A€j`ZXZfdf dX^e`kl[\j [\ kXceXkliXc\qX*hl\' gi\m`X cXX[fgZ`‚e [\ le j`jk\dX [\ \a\j Zffi[\eX[fj p [\ j\e[Xj*\jZXcXj\e cfj d`jdfj' gl\[\e i\gi\j\ekXij\ gfi ki\j eƒd\ifj' Rc" L+$ L,$'

\ 2 -' ***' Y'

\ kiXkX[\ jXY\i j` [`Z_X YXj\ \j jlg\iXYle[Xek\ p' \e ZXjfX]`idXk`mf'[\ Xm\i`^lXi Z‚df _X[\ j\i cXYXj\ \jki`ZkX*

NiX[lZ`[f \jk\ gifYc\dX Xcc\e^lXa\ m\Zkfi`Xcj\ \eleZ`X Xj€6?X[fjmXi`fj m\Zkfi\j' ZlpXj Zfdgfe\ek\j Zfe i\cXZ`‚e X [\k\id`eX[X YXj\d)[`d\ej`feXc jfe "6<G% RRR% )<)F#% RRR% ";GY*3 f'' % ;GYX#% Xm\i`^lXi j` \jgfj`Yc\ lk`c`qXigXiXjl i\gi\j\ekXZ`‚e leX YXj\ d\efi' p cXdXe\iX [\fYk\e\icX*

M\ kiXkX[\ le ZfefZ`[f gifYc\dX [\ {c^\YiX' p cXi\jgl\jkX \j6:\ ^s]Ub_ TU fUSd_bUc#f dX^e`kl[\j$ aeU cU bUaeYUbU^QbQ V_b]Qb

e^Q RQcUUcdbYSdQUcYWeQ\Q \Q SQbQSdUbqcdYSQ$_' TU\Q ]QdbYi V_b]QTQS_^

#t$ CX [\dfjkiX[f L* MXeElXe hl\ cX [`d\ej`‚e \j le \ek\ XYjkiXZkf*[\]`d[p gfi leX i\cXZ`‚e [\ `^lXc[X[' p cX]‚idlcX [`d\ej`feXc \j cX\ogi\j`‚em\Zkfi`Xc\t ]leZ`‚e [\ cX YXj\ X[fgkX[X* @jkfj \jgXZ`fj m\Zkfi`Xc\j [\ [`d\e)jcIt\j jfe `jfiefi]fj' f j\X Xc^•Yi`ZXd\ek\ \hl`mXc\ek\j X cfj ]fidX[fj Zfe cfjZI>c\tk\j [\ le`[X[\j' hl\ gfi \jkf _\dfj X[fgkX[f \e cX[\]`e`Z`‚e [\ cX]‚idl)cX [`d\ej`feXc' \m`k~e[fefj Zfej`[\iXZ`fe\j XYjkiXZkXj`ee\Z\jXi`Xj \e cXjXgc`ZXZ`fe\j*

Page 31: Análisis dimensional

)% <H{FDMDM?DcU-@HMDIH<F

\Qc S_]`_^U^dUc #I Zfe cfj \ogfe\ek\j [`d\ej`feXc\j$ U^ _dbQRQcUSeQ\&

aeYUbQ'>fdf m\Zkfi\j #f dX^e`kl[\j$ [\ cXel\mX YXj\ gl\[\e kfdXij\ S'

ZlXc\jhl`\iX \eki\ cfj [X[fj' Zfe kXc[\ hl\ j\Xe \Y^UQ\]U^dUY^TU`U^TYU^&dUc$\jkf \j' _Xe [\ j\i kXc\j hl\ cX\ZlXZ`‚e

@cRc $ ''' $ @+cR+D2 Pj‚cf X[d`kXcXjfclZ`‚e ki`m`Xc@c 9 @. 9 ***9 @+D9 ,' cf ZlXc\hl`mXc\)X [\Z`i hl\ cXZXiXZk\i€jk`ZX[\ cXdXki`q ]fidX[X gfi jlj Zfdgfe\ek\j#f \ogfe\ek\j [`d\ej`feXc\j$ _X[\ mXc\iS' ?\ Xhl€j\ [\[lZ\ cXj`^l`\e)

k\ i\^cX6JXiX ]fidXi leX YXj\ \jki`ZkXj\ ]fidX cXdXki`q [\ cfj \ogfe\ek\j

[`d\ej`feXc\j Zfe i\cXZ`‚e X fkiX YXj\ ZlXchl`\iX6

p \eki\ cfj d\efi\j ef elcfj j\ j\c\ZZ`feXe cfj [\ dXpfi iXe^f* < ZX[X*lef [\ \ccfj Zfii\jgfe[\ leX YXj\ \oki`ZkX']fidX[X gfi cXjdX^e`kl[\j*Zlpfj \ogfe\ek\j [`d\ej`feXc\j ]`^liXe \e •c*

@a\dgcf6

@e cXifkXZ`‚e [\ le j‚c`[f i€^`[f jfd\k`[f X le gXi \c~jk`Zf p Zfe Xdfik`)^lXd`\ekf gifgfiZ`feXc X cXm\cfZ`[X[ Xe^lcXi' cXj dX^e`kl[\j hl\ `ek\im`\e\ep jlj ]‚idlcXj [`d\ej`feXc\j Zfe i\cXZ`‚e XcXYXj\ ">%?%D#jfe6

<dgc`kl[ Xe^lcXi *Gfd\ekf `e\iZ`Xc* *J\i€f[f *>f\]`Z`\ek\ [\ ifqXd`\ekf *JXi \c~jk`Zf *

T2V2 @CA_H_

=)>2 @+AH_

I^J 2 @CA_HMQO2 @+AH&*M[O2 @+AH&+

p cXdXki`q [\ cfj \ogfe\ek\j [`d\ej`feXc\j \j6

2 Q [*

.-I

,..I - -- ) - ) .

# 1$ 1% 1

@e \ccXjfe elcfj kf[fj cfj d\efi\j [\ k\iZ\i fi[\e' p ef cfj [\ j\^le[f' gficf hl\ S 2 .' S cXj YXj\j \jki`ZkXj ZfejkXi~e [\ [fj dX^e`kl[\j* FXj dX^e`kl)[\j *$ d$Q$[$ jfe [`d\ej`feXc\j `e[\g\e[`\ek\j [fj X [fj' gfi cf hl\' Zfe leX*

P* @F >IH>@JNI ?@ ?DG@HMD|H )&

gXi\aX ZlXchl`\iX' gl\[\ ]fidXij\ leX YXj\ \jki`ZkX*>fe cX gXi\aX *%Q$gfi\a\dgcf' cXj ]‚idlcXj [`d\ej`feXc\j jfe6

T2V2 T-V, MQ>_3 Md\ 2 =)> ILJ&*1 IVJ 2 =)>&)TXE.*

@e \jk\ \a\dgcf' cXYXj\ ">%?% D#\j jlg\iXYle[Xek\*

'! ->OBOIQPFH>A>O!

FXjlgi\j`‚e [\ Xc^leX[\ cXjZfejkXek\j `e\cl[`Yc\j \e cXj\ZlXZ`fe\j]le[Xd\ekXc\j cc\mXZfej`^f cXi\[lZZ`‚e \e leX le`[X[ [\ cXdlck`gc`)Z`[X[ [\ cXYXj\' Zfe cf hl\ kf[f \c j`jk\dX [`d\ej`feXc i\jlckX Xck\iX[f*@j Zfdf j` \e le \jgXZ`f m\Zkfi`Xcj‚cf j\ Zfej`[\iXj\ [\ ZX[Xm\Zkfi jlgifp\ZZ`‚e jfYi\ \c jlY\jgXZ`f hl\ i\jlckX [\ gi\jZ`e[`i [\ leX [`d\e)j`‚e* <c dlk`cXi cXYXj\' gl\[\ jlZ\[\i hl\ [fj dX^e`kl[\j hl\ k\e€Xe[`jk`ekX[`d\ej`‚e \e cXYXj\ Zfdgc\kX' XgXi\qZXeZfdf \hl`[€d\ej`feX)c\j \e cXdlk`cX[X' gl\j YXjkXi~hl\ cfj Zfii\jgfe[`\ek\j m\Zkfi\j k\e^Xe`^lXc gifp\ZZ`‚e \e \c jlY \jgXZ`f i\jkXek\*

M`' gfi \a\dgcf' j\ jlgi`d\ cX ZfejkXek\ [\ cX ^iXm`kXZ`‚e'cXj \ZlXZ`fe\j]le[Xd\ekXc\j [\ cX[`e~d`ZX [\c glekf dXk\i`Xc j\ Zfem`\ik\e \e6

p YXjkXleX YXj\ Y`[`d\ej`feXc* <[fgkXe[f cXYXj\ @$H$gfi \a\dgcf* i\jlckX6

FXj d`jdXj ]‚idlcXj [`d\ej`feXc \j j\ _lY`\iXe fYk\e`[f j`' \e cl^Xi [\_XZ\i < 2 -' j\ _lY`\iX `dgl\jkf X [`Z_X ZfejkXek\ le mXcfi eld•i`Zf ZlXc)hl`\iX* M\ m\ hl\ cXj dX^e`kl[\j XT S XR% hl\ k\e€Xe [`jk`ekX [`d\ej`‚e \e cXYXj\ Zfdgc\kX' i\jlckXe j\i \hl`[`d\ej`feXc\j \e cXYXj\ dlk`cX[X*

Kl`\e\j Zi\\e _XY\i i\Xc`qX[f mXc`fjfj _XccXq^fjXc]fidXi j`jk\dXj [`d\ej`f)eXc\j Zfe YXj\j dlk`cX[Xj \jk~e \e \c ZXjf [\ hl`\e fg`eXj\ hl\ m`\e[f cXjjfdYiXjgifp\ZkX[Xj jfYi\ leX gXi\[' j\ X[hl`\i\ d~j `e]fidXZ`‚e hl\ m`\e[f cX\jZ\eX \ei\c`\m\* Hf _Xp `eZfem\e`\ek\' XgXik\[\c [\ cX eƒk`cZfdgc`ZXZ`‚e' \e lk`c`qXiYX)j\j jlg\iXYle[Xek\j' e` kXdgfZf gl\[\ \jg\iXij\ m\ekXaXe`e^leX* J\if Zfe YXj\j[\]\ZklfjXj j\ cf^iXi~' \e ^\e\iXc' d\efj `e]fidXZ`‚e hl\ Zfe YXj\j Zfdgc\kXj*

(! 4>O I>DJFPQABOABAFIBJOFXJJQH>!

< [`]\i\eZ`X [\ cf hl\ jlZ\[\ Zfe cfj m\Zkfi\j elcfj' cXjdX^e`kl[\j[\ [`d\ej`‚e elcX k`\e\e ^iXe `dgfikXeZ`X\e A€j`ZX*

?\j[\ cl\^f' YXjkXhl\ leX dX^e`kl[ k\e^X [`d\ej`‚e elcX \e leXYXj\ Zfdgc\kX gXiXhl\ c\ jlZ\[X cf d`jdf \e kf[Xj cXj[\d~j' `eZcljf

Page 32: Análisis dimensional

)' <H{FDMDM?DG@HMDIH<F

\e cXjdlk`cX[Xj*J\if gl\[\ fZlii`i hl\ c`cXdX^e`kl[ hl\ k\e^X [`)d\ej`‚e ef elcX \e cXjYXj\j Zfdgc\kXj XgXi\qZXZfe [`d\ej`‚e elcX

\e cXjYXj\j dlk`cX[Xj*

@j k\dX [\ [`jZlj`‚e \c j` j\ [\Y\ Zfej`[\iXi \c ~e^lcf Zfdf dX^e`kl[ [\[`d\ej`‚e elcX* ?\j[\ cl\^f' j\ kiXkX[\ leX dX^e`kl[ gi`dXi`X' gl\j jt gl\)[\e \jkXYc\Z\i cfj Zi`k\i`fj [\ `^lXc[X[ p [\ jldX j`e i\Zlii`i X cXd\tc[X [\fkiXj dX^e`kl[\j* Jfi kXekf' cXgifgfiZ`feXc`[X[ [l6\ZkX Zte \c XiZf \ dm\ijXZfe \c iX[`f \j leX c\p ^\fd•ki`ZX \eki\ cXj dX^e`kl[\j dj\gXiX;c\j ~etlcfp ZfZ`\ek\ XiZf)iX[`f* J\if jlZ\[\ hl\ \jk\ ZfZ`\ek\ ef \j leX dX^e`kl[ gedX)i`X' j`ef j\Zle[Xi`X' gfi cf hl\' [\ XZl\i[f Zfe \c j\^le[f gfjklcX[f' \c ]XZkfi

[\ gifgfiZ`feXc`[X[ \j jlg\i]clf' p \c ~e^lcf k\e[i~ [`d\ej`‚e elcX*@e ZfiifYfiXZ`‚e [\ \jkX Zfej\Zl\eZ`X' fZlii\ hl\ \c ~e^lcf ef ]`^liX \e

\c \eleZ`X[f [\ e`e^leX c\p ]le[Xd\ekXc' gfi cf hl\ gl\[\ gi\jZ`e[`ij\ [\

[`Z_f ]XZkfi [\ gifgfiZ`feXc`[X[ j`e Xck\iXicXj [`d\ej`fe\j [\ cXj [\d~j dX^)

e`kl[\j*Ff [`Z_f [\c ~e^lcf gcXef \j Xgc`ZXYc\Xc~e^lcf j‚c`[f* NXdY`•e j\ c\ gl\[\

Xki`Yl`i [`d\ej`‚e elcX j`e hl\ j\ i\j`\ekX \c <e~c`j`j [`d\ej`feXc*

)! 5>DJFPQABONBH>PFR>O!

Hf j\ dXe\aXe \e <e~c`j`j [`d\ej`feXc d~j lk\ej`c`fj hl\ cXj]‚idlcXj [`d\e)X`feXc\j' gfi cf hl\ ZlXekf X]\Zk\ X cX `ek\^i`[X[ [\ cXj d`jdXj gl\[\ gfe\i\e g\c`^if cX\]`ZXZ`X[\ Xhl•c* M`\e[f cXj ]‚idlcXj [`d\ej`feXc\j i\cXZ`fetj \e)ki\ cXj iXqfe\j [\ le`[X[\j [\ [fj j`jk\dXj Zf_\i\ek\j' hl\[Xi~e dlk`cX[XjrdXe[f' [\ le df[f l fkif' j\ ]`aX[\ Xek\dXef cXle`[X[ [\ Xc^leX dX^e`kl[\o`^`\e[f hl\ g\idXe\qZX `emXi`XYc\XcZXdY`Xi[\ le`[X[\j* >f*e \ccf*j\ Xe`)hl`cX cX[`d\ej`‚e [\ cXdX^e`kl[ \e Zl\jk`‚e' p j\ Xck\iXecXj [`t\ejcIe\j [tcXj i\jkXek\j* Jfi \jkX iXq‚e Zfem`\e\ jlgi`d`i cXj ccXdX[Xj ]Qa^YdeTUc bU\QdY&fQc #%$kXc\j Zfdf cX[\ej`[X[ Zfe i\cXZ`‚e XcX^lX f XcX`i\' cXi\cXZ`‚e \eki\cXj m\cfZ`[X[\j [\ gifgX^XZ`‚e [\ cXclq \e [fj d\[`fj [`]\i\ek\j' cXZfejkXek\

[`\c•Zki`ZX Zfe i\cXZ`‚e XcX`i\ #f XcmXZ€f$'\kZ*<gXik\ [\ cXiXq‚e X[lZ`[X gXiX \c`d`eXi cXj dX^e`kl[\j i\cXk`mXj'\j \m`)

[\ek\ hl\ gXiX \jkl[`Xi le ]\e‚d\ef YXjkXZfej`[\iXi cXj ZlXek€Xj[\ cXj dX^)

#%$ L\p JXjkfi ",)# ccXdXdX^e`kl[\j i\cXk`mXjXce`m\c p t cXk\dg\iXkliXd\[`[X \e \jZXcXjXiY`kiXi`Xjgfihl\ \e \ccXjef j\ gl\[\ [\]`e`i cXjldX* J\if\e A€j`ZXef j\ fg\iX eleZX Zfe e`m\c\j' j`ef Zfe [`]\i\eZ`Xj [\ Xc*kliX'gXiXtXjZlXc\j \j fYm`XcX[\]`e`Z`‚e [\ cXjldX* <[\d~j' \e cXjk\fi€Xj ]]j`ZXj \j gi\Z`jffg\iXi j`\dgi\ Zfe cX \jZXcXXYjfclkX [\ k\dg\iXkliX* @e e`e^ƒe Ztf' gfikXekf' \j gi\Z`jf `ekif[lZ`i le Z\if XiY`kiXi`f Zfdf w\c\d\ekf \okiXeIc$ X cXA€j`ZX*

Ff\[\c #0.$ gifgfe\ ccXdXi i\cXk`mXjX cXj hl\ \jk~e X]\ZkX[Xj [\ jt^ef'gfj`k`mf f e\^Xk`mf' p [X Zfdf \a\dgcfj cXXckliX [\ le glekf Zfe i\cXZ`‚e Xle gcXef _fi`qfekXc' \c k`\dgf' \c gfk\eZ`Xc' \kZ*J\if \j \c ZXjf hl\ _X6p*dX^)e`kl[\j Zfdf \c ZXcfi' \c kiXYXaf'cXZXi^X\c•Zki`ZX'\kZ*' hl\ jfe gfjckcmXtfe\^Xk`mXj [\ df[f XYjfclkf' gl\jkf hl\ jl j`^ef ef gifZ\[\ [\ cX jc\ZZ`‚eXiY`kiXi`X[\ le fi`^\e*

m* @F >IH>@JNI ?@ ?DG@HMD|H 21

e`kl[\j hl\ \e •c `ek\im`\e\e' p hl\ e`e^ƒe gXg\c [\j\dg\•Xe cXjhl\ j\ i\]`\i\eX Zl\igfj \okiX•fj' Xlehl\ j\Xe kXe [\jkXZX[fj Zfdf \c mXZ€f*

<]fikleX[Xd\ek\' _Xe [\jXgXi\Z`[f [\ cfj Yl\efj c`Yifj cX[\ej`[X[ i\cXk`mXp \c g\jf \jg\Z€]`Zf i\cXk`mf' hl\ _Xe kfikliX[f [liXek\ le j`^cf cXj d\ek\j`e]Xek`c\j [\ cfj Xcldefj [\ \ej\•XeqX d\[`X*

@eki\ cXj dX^e`kl[\j i\cXk`mXj]`^liXe cfj dXc ccXdX[fj `Uc_c Qdr]YS_c h`Uc_c ]_\USe\QbUc' Ml efdYi\ \j dfk`mf [\ Zfe]lj`‚e* C\dfj ZfefZ`[f hl€d`Zfj\d`e\ek\j' [\ cfj hl\ d~j _Xe Zfeki`Yl`[f XcXZfe]\ZZ`‚e [\ cXjkXYc\j`ek\ieX)Z`feXc\j [\ g\jfj Xk‚d`Zfj' hl\ gfi Zi\\i hl\ j\ kiXkXYX[\ g\jfj' d`[`\ifeZl`[X[fjXd\ek\ cX `ek\ej`[X[ [\ cX ^iXm\[X[ \e jl cXYfiXkfi`f Zfe \c ]`e [\_XZ\i cXZfii\ZZ`‚e Zfii\jgfe[`\ek\* CXjkX Xc^lefj ]€j`Zfj' hl\ jXY\e hl\ j\kiXkX[\ dXjXj p ef [\ g\jfj' fcm`[Xe hl\' gfi j\i dX^e`kl[\j i\cXk`mXj'jfeeƒd\ifj ]`afj* ?\ Xhl€ hl\ p\ii\e XckfdXi \c eƒd\if [\ dfc\j Zfdf leX dX^)e`kl[ [\ [`d\ej`‚e elcX* @e kXc\iifi `eZlii\' gfi \a\dgcf' ?leZXejfe #0/$*

<]fikleX[Xd\ek\' fZlii\ hl\ \e e`e^leX \ZlXZ`‚e ]€j`ZX `ek\im`\e\e cXjdXjXj dfc\ZlcXi\j i\cXk`mXj'j`ef \c eƒd\if [\ dfc\j' hl\ k`\e\ cXd`jdX [`d\e)j`‚e hl\ cXdXjX p ZlpX le`[X[' gfi Zfej`^l`\ek\' ef hl\[X gi\]`aX[X*

*! 4>O OBQAKI>DJFPQABOABH>9BKHKDW>

C\dfj YXjX[f \c <e~c`j`j [`d\ej`feXc jfYi\ \c gfjklcX[f [\ j\i cXjc\p\j ]€j`)ZXji\cXZ`fe\j [\ gifgfiZ`feXc`[X[ \eki\ gfk\eZ`Xj [\k\id`eX[Xj [\ cXj ZXek`[X)[\j hl\ `ek\im`\e\e \e \c ]\e‚d\ef Zfej`[\iX[f* Jfi kXekf' j\^ƒe el\jkif glekf[\ m`jkX'\c <e~c`j`j [`d\ej`feXc j‚cf j\i~ Xgc`ZXYc\X]\e‚d\efj i\^`[fj gfi \ZlX)Z`fe\j hl\ ZldgcXe [`Z_f i\hl`j`kf* M\ kiXkX[\ le gfjklcX[f p ef [\ cXZfej\)Zl\eZ`X [\ Xc^ƒe gi`eZ`g`f d\kX]€j`Zf' p cXd\afi gil\YX [\ \ccf \j hl\ \e L\fcf)^€X_Xe \eZfekiX[f MZfkk=cX`i #/5$ p jlj ZfcXYfiX[fi\j hl\ gXiX Zl\igfj hl\ef jfe e` j‚c`[fj [\ Cffb\ e` ]cl`[fj e\nkfe`Xefj j\ Zldgc\ leX i\cXZ`‚e hl\'\e cX]fidX fi`^`eXc [X[X gfi Hlkk`^' \j6

T5'-V

[fe[\ C \j cXk\ej`‚e' Zi cX[\]fidXZ`‚e' d \c k`\dgf p "S' -/' V%ZfejkXek\j ZXiXZ)k\i€jk`ZXjhl\ mXi€Xe[\ le Zl\igf X fkif*

Hfj \eZfekiXdfj \e gi\j\eZ`X [\ leX c\p hl\' j` Y`\e gl\[\ \eleZ`Xij\Zfdf i\cXZ`‚e [\ gifgfiZ`feXc`[X[ \eki\ ZXek`[X[\j' gi\j\ekX cXgXik`ZlcXi`[X[[\ hl\ cfj \ogfe\ek\j ef jfe eƒd\ifj ]`afj' j`ef eƒd\ifj hl\ [\g\e[\e [\cZl\igf hl\ j\ fYj\imX* >fe cX YXj\ [`d\ej`feXc >%?%D%cX]‚idlcX [`d\e)

j`feXc [\ "]! \j6

p \jkXi€Xi\gi\j\ekX[X gfi le m\Zkfi [`jk`ekf gXiX ZX[XjljkXeZ`X*<ek\ \jk\ \jkX[f [\ ZfjXj' cf hl\ gifZ\[\ [\j[\ el\jkif glekf [\ m`jkX'\j

X]`idXi hl\ \c <e~c`j`j [`d\ej`feXc ef k`\e\ iXq‚e [\ j\i \e L\fcf^€X' gl\j efj`im\ gXiXe`e^lef [\ cfj ]`e\j hl\ g\ij`^l\6 e` i`^\ \c Zi`k\i`f [\ _fdf^\e\`[X['e` j\ gl\[\ _XZ\i gi\[`ZZ`fe\j YXjX[Xj \e Zfej`[\iXZ`fe\j [`d\ej`feXc\j*

?`e^c\' j`e \dYXi^f' _XZ\ le cXi^f iXqfeXd`\ekf #00$kiXkXe[f [\ [\dfjkiXihl\ cX\ZlXZ`‚e [\ Hlkk`^ \j leX gil\YX [\ hl\ \c j€dYfcf [`d\ej`feXc \j leX

,6U43:3: /3506:376,4! '

Page 33: Análisis dimensional

Mhl\ 4 M 6> mXi`Xj\e [\ le Zl\igf X fkif* ?\[lZt hl\ 6> _X [\ j\i le eƒd\ifglif Mhl\ wcXj[`d\ej`fe\j [\ 4 _Xe [\ j\i TXek`cf #cf^ @ncf^ D#<d% g\if ef[`Z\ hl• gXik`[f gf[\dfj jXZXi[\ \jk\ i\jlckX[f ZlXe[f efj \eZfeki\dfj Xek\

le gifYc\dX [\ <e~c`j`j [`d\ej`feXc* * * *< Zfek`elXZ`‚e' p kiXj cXi^f if[\f' [\[lZ\ ?`e^c\ hl\' M-cX\ZlXZ-‚e T5'.V

_X [\ g\idXe\Z\i `emXi`XYc\XcZXdY`XicXjle`[X[\j' wcXj[`d\ej`fe\j [\ 4 _Xe[\ j\i' f TXek`cf #cf^ > cf^ D#J% f Y`\e >D&6>d' @jk\ ƒck`df i\jlckX[f \j \c hl*\ZlXchl`\iX \jZi`Y`i€XX cXm`jkX[\ T5'.V' p ef j\ Zfdgi\e[\ Zfdt \e cX JiD)d\iX \ogi\j`‚e [\ cXj [`d\ej`fe\j ef ]`^li\ 6> Mj€ \e cXj\^le[X' il hl\ leX M ><J€NOFI =3fkiX j\Xe wi\gi\j\ekXZ`fe\j [\ le gifZ\jf [\ d\[`[Xz* @e ]`e' ]XckXjXY\i gXiXhl• j`im\ cXgi`d\iX \ogi\j`‚e' hl\ \j cXfYk\e`[X gfi m€Xfg\iXZ`feXc* 04 ;07905, /0 83

)) <H{FDMDM?DG@HMDIH<F

i\gi\j\ekXZ`‚e [\c gifZ\jf [\ d\[`[X* ?\aX XgXik\ cX ]‚idlcX [\ Hlkk`^ MZfej`[\iX \c ZXjf [\ cXZX€[X[\ cfj Zl\igfj' jlgfe`\e[f hl\ cXi\cXZ`‚e \eki\

\c ZXd`ef 4 M\c k`\dgf d ]l\j\6/ 2 4^6> T5'.V

"! 2KIKDBJBFA>AABH>OCXNIQH>OCWOF@>O!

SX Afli`\i `e[`Z‚ hl\ leX [\ cXjm\ekXaXj[\ Xki`Yl`i leX [`d\ej`‚eXZX[XdX^e`kl[ Zfej`jk€X\e gf[\i [\jZlYi`i ]~Z`cd\ek\ \iifi\j [\ Z~cZl)cf' gl\j jlZ\[€X hl\ kf[fj cfj k•id`efj [\ ZlXchl`\i \ZlXZ`‚e hl\ i\jlc)kXiX[\ Xgc`ZXicXj\ZlXZ`fe\j ]le[Xd\ekXc\j Xle ZXjfgXik`ZlcXi_XY€Xe[\ k\e\i cXd`jdX [`d\ej`‚e* M\ _X Zfem\e`[f \e [\Z`i aeU T_c _ ]oc]QW^YdeTUcc_^ X_]_Wp^UQcU^dbUcq SeQ^T_ dYU^U \Q ]Yc]Q TY]U^cYr^p' gfi kXekf' cXgifgfj`Z`‚e [\ Afli`\i gl\[\ \eleZ`Xij\ Xj€6

H_T_c \_c dpb]Y^_c TUe^Q USeQSYr dqcYSQTURU cUbX_]_Wp^U_c'NXe dXe`]`\jkX cc\^‚ X j\i cXlk`c`[X[ [\ \jkX i\^cX' p [\ kXcdf[f

i\jlck‚ Zfe]`idX[X \e kf[fj cfj [\jXiifccfj k\‚i`Zfj' hl\' d~j f d\efjk~Z`kXd\ek\' j\ Zfem`ik`‚ \e le gi`eZ`g`f d\kX]€j`Zf' Xc hl\ [\Y€Xejfd\k\ij\ kf[Xj cXjk\fi€Xj ]€j`ZXj*Jfi \jf' j\ `dgfe€Xe Zfe[`Z`fe\j XcXj]‚idlcXj [\ [\]`e`Z`‚e gXiX hl\ \jklm`\j\e [\ XZl\i[f Zfe \c ccXdX[f`bY^SY`Y_ TUX_]_WU^UYTQT$p cXj\ZlXZ`fe\j \dg€i`ZXj hl\ cf mlce\iXYXej\ Zfej`[\iXYXeZfdf \)*'i\j`fe\j `dg\i]\ZkXj [\ Xc^leXc\p dXc ZfefZ`[X*

@c\mX[fX cXZXk\^fi€X[\ gi`eZ`g`f*\c i\hl`j`kf [\ _fdf^\e\`[X['gifZ\[€X' j` ef jl [\dfjkiXZ`‚e' gfi cf d\efj jl aljk`]`ZXZ`‚e'hl\ Zfe)j`jk€X\e i\Zlii`i X Xi^ld\ekfj mX^Xd\ek\ `ekl`k`mfj' kXc\j Zfdf [\Z`ihl\ ef k\e€Xj\ek`[f cXjldX f cXi\jkX [\ ZXek`[X[\j_\k\if^•e\Xj p hl\'aljkXd\ek\' cX[`d\ej`‚e \iX cf hl\ ZXiXZk\i`qXYXcX_fdf^\e\`[X[* ?\cX]XcXZ`X[\ \jkX Xi^ld\ekXZ`‚e' hl\ Zfe]`\jf _XY\i k\e`[f gfi Yl\eX'\j Yl\eX gil\YX \c _\Z_f [\ hl\ cXjldX [\ ZXek`[X[\j [X[Xj k`\e\ f efj\ek`[f j\^ƒe \c gifg‚j`kf hl\ j\ g\ij`^X*

Page 34: Análisis dimensional

)+ <H{FDMDM?DG@HMDIH<F

Jfi \a\dgcf' ef j\ gl\[\ jldXi p\^lXj Zfe ZXYXccfjgXiX fYk\e\i p\^lXjf ZXYXccfjjfcXd\ek\' g\if k`\e\ g\i]\Zkf j\ek`[f X]`idXi hl\

. p\^lXj $ / ZXYXccfj2 1 •hl`[fj*

?\ cX d`jdX dXe\iX' ef k`\e\ j\ek`[f \e N\idf[`e~d`ZX jldXi cX \e\i^€X`ek\ieX' E%Zfe \c gif[lZkf [\ cX gi\j`‚e gfi \c mfcld\e Zfe cXgi\k\ej`‚e [\hl\ \c i\jlckX[f j\X \e\i^€X `ek\ieX* J\if j€ ZXY\X]`idXi hl\ cX[`jd`elZ`‚e [\cXdX^e`kl[ = 22 I & Z J [X \c ZXcfi [\jgi\e[`[f \e ZlXchl`\i kiXej]fidX)

Z`‚e `jfYXiX'

GlZ_fj Xlkfi\j `ek\ekXe' [\ lef l fkif df[f' Zfej\imXi \c gi`eZ`g`f[\ _fdf^\e\`[X[ Zfdf ZfjX `e[\g\e[`\ek\ [\ cXj k\fi€Xj ]€j`ZXjp' \e\jk\ j\ek`[f' hl`\e d~j _X gif]le[`qX[f \e cXZl\jk`‚e \j \c gif]\jfiL* MXeElXe #-2$' hl`\e _Xcf^iX[f [\dfjkiXi hl\ cXj\ZlXZ`fe\j _Xe [\j\i e\Z\jXi`Xd\ek\ _fdf^•e\Xj j` i\cXZ`feXe dX^e`kl[\j [\]`e`[Xj [\kXcdf[f hl\ \c Zi`k\i`f [\ jldX j\X `e[\g\e[`\ek\ [\c j`jk\dX [\ le`[X)[\j hl\ j\ X[fgk\*

< el\jkif df[f [\ m\i' \c gi`eZ`g`f [\ _fdf^\e\`[X[ ef gl\[\ [Xij\Zfdf ZfjX\m`[\ek\' e` \jk~ jlYfi[`eX[f jfcXd\ek\ XcXdXe\iX Zfem\e)Z`feXc[\ [\]`e`i cXjdX^e`kl[\j j\Zle[Xi`Xj' j`ef hl\ \j Zfej\Zl\eZ`X [\el\jkif gi`d\i gfjklcX[f' j\^ƒe mXdfj X[\dfjkiXi*

#! ;BKNBI> AB LF!

M\XleX k\fi€X ]€j`ZXZlpXj \ZlXZ`fe\j ]le[Xd\ekXc\j' gfi \jkXi [\XZl\i[f Zfe el\jkif gi`d\i gfjklcX[f' \jkf \j' gfi Zfej`jk`i \e i\cXZ`fe\j\eki\ dfefd`fj' jfe `eZfe[`Z`feXcd\ek\ _fdf^•e\Xj* Mlg‚e^Xj\ hl\Zldgc\e `^lXc i\hl`j`kf kf[Xj cXj]‚idlcXj [\ [\]`e`Z`‚e [\ cXj dX^e`)kl[\j j\Zle[Xi`Xj hl\ j\ lk`c`Z\e \e cXk\fi€X*L\jlckXi~ le j`jk\dX [\\ZlXZ`fe\j `emXi`Xek\jZfe i\cXZ`‚e X kf[fj cfj ZXdY`fj [\ le`[X[\jZf_\i\ek\j' p [\ `^lXc gifg`\[X[ ^fqXi~' gfi Zfej`^l`\ek\' ZlXchl`\i\ZlXZ`‚e6

V"gf ''' $ g^# 9 I' T.'-V

hl\ j\ [\[lqZX [\ Xhl•ccXjgfi Xgc`ZXZ`‚e[\ cXk\fi€XXle ZXjfgXik`ZlcXi\e hl\ j\ kiXk\[\ Xm\i`^lXiZ‚df [\g\e[\ Z`\ikXdX^e`kl[' L^$ [\ fkiXj'Rc" ***' L^&\! hl\ ]`^liXe Zfdf mXi`XYc\je[\g\e[`\ek\j \e \c ]\e‚d\efZfej`[\iX[f*

@e cX\ZlXZ`‚e T.'-V ]`^liXi~e' X df[f [\ gXi~d\kifj' ef j‚cf cXjZfejkXek\j \jg\Z€]`ZXj[\ cfj Zl\igfj hl\ `ek\im\e^Xe \e \c ]\e‚d\ef'j`ef kXdY`•ecXjZfejkXek\j le`m\ijXc\j g\Zlc`Xi\j [\ cXk\fi€X'

PD* @F N@IL@G< ?@ JD ),

*Ok`c`qXe[t*le j`jk\dX [\ le`[X[\j Zf_\i\ek\j' ef _XYi~\e T.'VEZf\)]`f`\ek\j gXi~\`kfj' p XcgXjXiX fkif j`jk\dX kXdY`•e Zf_\i\ek\ [\Y\i~g\idXe\Z\i `emXi`XYc\cX\ZlXZ`‚e hl\ efj fZlgX* M\XeG -

)3 RRR % G] XjdX^e`kl[\j \jZf^`[Xj gXiX]fidXi cXYXj\ p j\Xe6

c5^&]'''''''''''''''''''''''''''''''''''''''''''''''' T.'.V

cXj ]‚idlcXj [`d\ej`feXc\j [\ cXj [\d~j dX^e`kl[\j* <c gXjXi X fkifj`jk\dX Zf_\i\ek\' cXjd\[`[Xj Lf ''' $ L^ j\ Zfem\ik`i~e \e g!c"***' L! ^$Zldgc`•e[fj\ hl\6

% E!W %Rc 9 L - &E9 L cTRcV7*** 7L^ 9 L! ^ML^O

-

! T.'/V

p cX\ZlXZ`‚e [X[X j\ kiXej]fidXi~ \e6

T.'0V

>fdf cXZfe[`Z`‚e [\ `emXi`XY`c`[X[\o`^\ hl\ j\X6

V"g!\$ ''' $ L!^# 2 9 T.'1V

hl\[X [\dfjkiX[f hl\ cX ]leZ`‚e \e Zl\jk`‚e \jZfe[`Z`fe\j T.'.V* <[\d~j7 Xgc`ZXe[f \c k\fi\dXi\jlckX hl\ cX\ZlXZ`‚e _X [\ k\e\i cX]fidX6

_fdf^•e\X Zfe cXj/*x [\c ZXg€klcf-'

.#

gk]1 !

&^"J 2 ^&]#

p Zfdf' \e m`ikl[ "[\ T.'.V' cfj dfefd`fj

&^

k`\e\e [`d\ej`‚e elcX' hl\[Xe [\dfjkiX[Xj cXjj`^l`\ek\j gifgfj`Z`fe\j6-*X* @QV_b]Q]oc WU^UbQ\TUd_TQUSeQSYr^

l"Lf ''' $ L^# 2 I'

Page 35: Análisis dimensional

*# <H{FDMDM?DcU"c@HMDIH<F

aeUcUQS_^cUSeU^SYQTUe^Q dU_bqQSehQc \UhUcVe^TQ]U^dQ\UccUQ bU\QSY_^UcTU `b_`_bSY_^Q\YTQTU^dbU_dU^SYQcS_^ Ug`_^U^dUcVYZ_c$Uc2

T_^TU \Qc D6T c_^ \_c ]_^_]Y_c Y^TU`U^TYU^dUcTUTY]U^cYr^ ^e\Q _ ]_^_&]Y_c `Y$ aeU `eUTU^ V_b]QbcUS_^ \Qc ]QW^YdeTUcS_^cYTUbQTQc'

+',) :\ ^s]Ub_ TUUcd_c]_^_]Y_c Y^TU`U^TYU^dUcUcC2 G& _' T_^TUBUc\Q SQbQSdUbqcdYSQTU\Q ]QdbYi V_b]QTQS_6(&\_c Ug`_^U^dUcTY]U^cY_^Q&\UcS_^ bU\QSYr Q e^Q RQcUS_]`\UdQ SeQ\aeYUbQ'

FXj gifgfj`Z`fe\j Xek\i`fi\j jfe leX mXi`Xek\ [\c k\fi\dX [\ g`' hl\ ]l\\eleZ`X[f gfi =lZb`e^_Xd "))# [\c j`^l`\ek\ df[f6

)' H FX ]fidX d~j ^\e\iXc [\ ZlXchl`\i \ZlXZ`‚e ]€j`ZXZfdgc\kX6

\j6/; Y# 2 ,'

[fe[\ cXj .) jfe cfj dfefd`fj `e[\g\e[`\ek\j [\ [`d\ej`‚e elcX hl\ gl\[\e ]fi)dXij\ Zfe cXj^ dX^e`kl[\j Zfej`[\iX[Xj*

.*f @ceƒd\if [\ \jkfj dfefd`fj `e[\g\e[`\ek\j \j C2 ^ & a$ [fe[\ a \j\c eƒd\if [\ le`[X[\j ]le[Xd\ekXc\j e\Z\jXi`Xj gXiXd\[`i cXj ^ dX^e`kl[\j*

FcXdX =lZb`e^_Xd Zfdgc\kX Xkf[X \ZlXZ`‚e hl\ jlYj`jk\ j`e Xck\iXZ`‚e[\]fidX Xc ZXdY`Xi cXj le`[X[\j ]le[Xd\ekXc\j' cf hl\ \hl`mXc\ X gfjklcXi cX*_fdf^\e\`[X[ Zfe[`Z`feX[X [\ cX\ZlXZ`‚e [\ hl\ j\ kiXkX*>fe \jkf' cX[\dfj)kiXZ`‚e [\c k\fi\dX [\ g` \j `ed\[`XkX j` j\ lk`c`qX cXk\fi€X [\ cXj ]leZ`fe\j_fdf^•e\Xj ^\e\iXc`qX[Xj* J\if \jkX k\fi€X ef ]l\ [X[X XZfefZ\i gfi @_i\e]\jk)<]]XeXjja\nX #-1$' j`ef [fj X•fj [\jgl•j [\ hl\ =lZb`e^_Xd glYc`ZXj\ jlkiXYXaf*Jfi fkiX gXik\' j` Y`\e \j Z`\ikf hl\ ef j\ \eZl\ekiX \e e`e^leX [\ cXjk\fi€Xj ]€j`ZXjXZklXc\jleX jfcX \ZlXZ`‚e hl\ ef jXk`j]X^X\c gi`eZ`g`f [\ _fdf)^\e\`[X[' \c X[d`k`i \jk\ gi`eZ`g`f [\ Yl\eXj X gi`d\iXj \j ZfjX hl\ i\gl^eX X*cfj c‚^`Zf)gfj`k`m`jkXj' p gXiX aljk`]`ZXi \jkX i\gl^eXeZ`X _XZ\ efkXi =i`[^)dXe #..$ hl\ j\ gl\[\e Zfejkil`i X[i\[\ \ZlXZ`fe\j hl\ \jk•e \e [\jXZl\i[fZfe [`Z_f gi`eZ`g`f j`e d~j hl\ jldXi [fj \ZlXZ`fe\j hl\ j\ i\]`\iXe Xle d`jdf]\e‚d\ef' [\jgl•j [\ _XY\icXj \c\mX[f X gfk\eZ`Xj ZlXc\jhl`\iX* Jfi \a\dgcf'\e cXZX€[Xc`Yi\ [\ le Zl\igf j\ Zldgc\ hl\6

f 2 Wd3)

4 2 & Wd+

.

p' \e Zfej\Zl\eZ`X' cX\ZlXZ`‚e6

"f & Wd#$ #4 ) &Wd+Q2 I' T.'2V

PD* @F N@IL@G< ?@ JD *$

X*g\jXi [\ ef j\i _fdf^•e\X' jlYj`jk\ Xlehl\ j\ ZXdY`\e cXj le`[X[\j ]le)

[Xd\ekXc\j*FX fYa\Z`‚e [\ =i`[^dXe hl\[X `emXc`[X[Xj`e d~j hl\ `ek\igi\kXi cX`emX)

i`XY`c`[X[[\ ]fidX' gfjklcX[X gfi =lZb`e^_Xd' Zfdf \o`^\eZ`X [\ hl\ cX]le)Z`‚e j\ Zfej\im\ Q\WpRbYSQ]U^dUY^fQbYQR\U$gl\j fZlii\ hl\' XcZXdY`XicXj le`)[X[\j ]le[Xd\ekXc\j' ZX[X lef [\ cfj gXi•ek\j`j [\ cX \ZlXZ`‚e T.'2V hl\[Xdlck`gc`ZX[f gfi le ]XZkfi [`]\i\ek\ p' j` cX\ZlXZ`‚e jlYj`jk\' \j gfihl\ ZX[X

lef [\ jlj k•id`efj \j elcf gfi j\gXiX[f*>fej`[\iXe[f m~c`[XcXfYa\Z`‚e [\ =i`[^dXe' fg`eX \c gif]\jfi Q* C`cc #01$

hl\ j\ [\Y\ X•X[`i leX Zfe[`Z`‚e Zfdgc\d\ekXi`X XcgfjklcX[f [\ =lZb`e^_Xd*J\if' Zfdf _XZ\efkXi L* MXeElXe #-2$' kf[f \ccf j\ \m`kXj` j\ gXik\ [\c gi`eZ`)g`f [\ _fdf^\e\`[X[' f Y`\e j` j\ ZXcXd~j _fe[f p j\ [\[lZ\ [`Z_f gi`eZ`g`f [\cX*Zfe[`Z`‚e [\ hl\ kXej‚cf k\e^Xe ZXY`[X\e cXA€j`ZXXhl\ccXj dX^e`kl[\j [\]`)e`[Xj [\ dXe\iX hl\ cX`^lXc[X[ p cXjldX [\ jlj ZXek`[X[\j j\X `e[\g\e[`\ek\[\c j`jk\dX [\ le`[X[\j* EljkXd\ek\ \c d•i`kf [\c kiXYXaf[\ L* MXeElXe Zfej`jk\\e _XY\i [\dfjkiX[f hl\ [\ \jkX Zfe[`Z`‚e [\i`mX \c gi`eZ`g`f [\ _fdf^\e\`[X[*

< el\jkif al`Z`f' cXgi`eZ`gXcfYa\Z`‚e hl\ gl\[\ _XZ\ij\ Xc\eleZ`X[f gi`d`)k`mf [\c k\fi\dX [\ g` \j hl\ \c eƒd\if [\ dfefd`fj [\ [`d\ej`‚e elcX "M\[\)k\id`eX \e ]leZ`‚e [\c weƒd\if [ [\ dX^e`kl[\j ]le[Xd\ekXc\j e\Z\jXi`Xj gXiXd\[`i cXj^ dX^e`kl[\jz' p ef j\ \jkXYc\Z\i\^cX e` Zi`k\i`f gXiXXm\i`^lXi Zl~ekfmXc\a \e ZX[XZXjf gXik`ZlcXi*@jkXmX^l\[X[ \e \c \eleZ`X[f' hl\ [\aX mXZ€f\ci\]\i`[f k\fi\dX' j\ gfe\ ZcXiXd\ek\ [\ dXe`]`\jkf ZlXe[f j\ kiXkX[\ _XccXi[ [\XZl\i[f Zfe cXjefidXj \jki`ZkXd\ek\ fg\iXZ`feXc`jkXj' gfi \a\dgcf' j`^l`\e[f \cd•kf[f hl\ gifgl^eX ?`e^c\ p hl\ _\dfj [`jZlk`[f pX \e \c v - [\c ZXg€klcfP*

>fe el\jkifj gfjklcX[fj p Zfe cXZfe[`Z`‚e `dgl\jkX* X cXj ]‚idlcXj [\ [\]`)e`Z`‚e [\ cXjdX^e`kl[\j j\Zle[Xi`Xj' cX[\dfjkiXZ`‚e [\c k\fi\dX [\ g` \j ]XZ`)c€j`dX p i`^lifjX' ^iXZ`XjX cXk\fi€X [\ cXj ]leZ`fe\j _fdf^•e\Xj ^\e\iXc`qX[Xj'p \c eƒd\if [\ dfefd`fj `e[\g\e[`\ek\j [\ [`d\ej`‚e elcX hl\[X [\k\id`eX[f

j`e XdY`^„\[X[ #%$*

#%$ G\i\Z\ j\i \oXd`eX[f Zfe Xc^leX [\k\eZ`‚e \c ttk€Ztf [\* F\m` #//$'gfihl\ Zfejk`klp\ le `ek\ekf [\ [Xi YXj\ c‚^`ZXXct~_jcM [`d\ej`feXc)

F\m` Zf`eZ`[\ Zfe =i`[^dXe \e X]`idXi hl\ wd\[`i \j _XZ\i Zfii\jgfe[tiX leX [\k\id`eX[X dX^e`kl[ ]€j`ZXle eƒd\if f le j`jk\dX [\ t} cc\ifj%' j`e`dgfe\i fkiX c`d`kXZ`‚e hl\ cX`emXi`XY`c`[X[[\c XgXiXkf[\ d\[`Z`‚e' \c ZlXc_X [\ \jkXi Zfejk`kl`[f gfi w[\k\id`eX[Xj fg\iXZ`fe\j ]€j`ZXj*, Y`\e Xle E;fifg\iXZ`fe\j dXk\d~k`ZXjz* >i`k`ZXcXwm`\aXZfjkldYi\z [\ Zfej`[\iXi cXefZc‚t[\ dX^e`kl[ Zfdf Xc^f `ekl`k`mf p Q `b_bY$ p i\Z_XqX cf hl\ ccXdXgtf;t[c)d`\ekf j `ekl`k`mfj hl\ t\id`k\e \jkXYc\Z\i cX`^lXc[X[' cXjldX p cX[`m`j`‚e\e gXik\j* < Zfek`elXZ`‚6"*'p Zfe dXe`]`\jkX `eZfej\Zl\eZ`X' \jkXYc\Z\ leX \oZ\g)Z`‚e gXiX cXj ki\j dX^e`kl[\j' cfe^`kl[' dXjX p k`\dg8';' p j\ cXeqXgfi cfj t\)i`Zl\kfj [\ cXd\kX]€j`ZXXcX]`idXi #g~^*1$ hl\ wffejk`Ylp\ \c jlYjkiXkf c‚^`>*fhl\ gi\Z\[\ XcXA€j`ZXz'p \e \jkX gifgfj`Z`‚e Xgi`fi€jk`ZXj\ YXjXgXiX [\[lZ`ihl\ \c w\jgXZ`f]€j`Zf \j ki`[`d\ej`feXc \e \c j\ek`[f [\ cXk\fi€X [\ cXj dX^e`)kl[\j XZ\gkX[Xgfi cXA€j`ZXz* *

Hf gf[\dfj X[`m`eXi X hl• k\fi€X XZ\gkX[Xj\ i\]`\i\ F\m`' gl\j* Xle gitj)Z`e[`\e[f [\ cXk\dg\iXkliX' \c j`jk\dX [\ B`fi^`' hl\ \j \c XZ\gkX[f aek*\iiiXZif)eXcd\ek\' \j k\kiX[`d\ej`feXc* J\if kXdgfZf j\ ZfdgX^`eX jl Xjtikf Zfe -*, hl\[`Z\ d~j X[\cXek\* gl\j X]`idX hl\ \c eƒd\if [\ dX^e`kl[\j d[\g\e[c\ek\jgl\[\ i\[lZ`ij\ X . f X -* * *

?`Z\ cl\^f hl\ kf[f fkif ZfeZ\gkf j\ `ekif[lZ\ \e G\Z~e`ZXJ;i w[\]`e`Z`fe\jefd`eXc\j' i\gi\j\ekX[Xj ^\e\iXcd\ek\ gfi [\]`e`Z`fe\j dXk\d•*k€ZXjj' jd i\gX)

Page 36: Análisis dimensional

3. <H{FDMDM?DG@HMDIH<F

$! 4>O B@Q>@FKJBO@KJHKD>NFPIKO!

@e dlZ_Xj \ZlXZ`fe\j k\idf[`e~d`ZXj \e hl\ `ek\im`\e\e cf^Xi`kdfj' gXi\Z\X gi`d\iX m`jkXhl\ ef j\ Zldgc\ \c gi`eZ`g`f [\ _fdf^\e\`[X[' gl\j ]`^liXeZfdf Xi^ld\ekfj dX^e`kl[\j ZlpX [`d\ej`‚e ef \j elcX* <j€' \e cX\ogi\j`‚e[\ cX\ekifg€X [\ cfj ^Xj\j `[\Xc\j'

G 2 AZ De2 ) F DeZ $ Zfejk'

`ek\im`\e\e cXk\dg\iXkliX XYjfclkX' 2' p cXgi\j`‚e' Z%Zfdf Xi^ld\ekfj [\ccf^Xi`kdf* M`e \dYXi^f' cX ]‚idlcX \j Zfii\ZkX ^iXZ`Xj X cX gi\j\eZ`X [\ cXZfejkXek\ XiY`kiXi`X'hl\ `e[`ZX hl\ hl\[X `e[\k\id`eX[f \c fi`^\e [\ \ekif)g€Xj p' gfi kXekf' cX \ZlXZ`‚e j‚cf gl\[\ j\im`i gXiX ZXcZlcXi[`]\i\eZ`Xj* JXiXgfe\i \jk\ _\Z_f [\ dXe`]`\jkf' \j gi\]\i`Yc\ \jZi`Y`i6

. `G & G_ 2 AZ De) ) B De)'

/) D_

Zfe cf hl\ \j \m`[\ek\ hl\ j\ Zldgc\ \c i\hl`j`kf [\ _fdf^\e\`[X[*

%! 4> @KJOP>JPBMQWIF@>!

>fdf Zfej\Zl\eZ`X [\c gi`eZ`g`f [\ H\iejk)JcXeZb #%$'j\ [X \e cfj c`Yifj [\Kl€d`ZX ]€j`ZXcXj`^l`\ek\ \ogi\j`‚e gXiX \c mXcfi XYjfclkf [\ cX\ekifg€X [\le ^Xj `[\Xc6

. V/ I # 1$C 2 * B De2 ) B De` & f \ O. & C& * B' T0'-V

iXi \e hl\ cX]l\iqX k`\e\ kXekf [\i\Z_f Zfdf cXdXjX X j\i Zfej`[\iX[X ZfdfdX^e`kl[ gi`d`k`mX' gl\j ef _Xp gXiX leX e` gXiX fkiX [\]`e`Z`‚e efd`eXc Xd\efj [\ hl\ j\ Zfej`[\i\ Zfdf kXccXj\^le[X c\p [\ H\nkfe*

Hf gXi\Z\ _XY\ij\ [X[f Zl\ekX F\m` [\c gXg\c `dgfikXek€j`df hl\ [\j\dg\)•Xe cXj ZfejkXek\j le`m\ijXc\j \e <e~c`j`j [`d\ej`feXc' gl\j [`Z\ #g~^*--$' hl\wcXZfejkXek\ [\ cX^iXm`kXZ`‚e\j le eƒd\if "cYS# Z`\ikXd\ek\ `emXi`XYc\gficXk\fi€Xz*

<c gXjXi X cX N\idf[`e~d`ZX' [`Z\ hl\ cX k\dg\iXkliX \j leX "`[\X gi`)d`k`mX' hl\ j\ Zfem`\ik\ \e [\i`mX[X j` j\ ]`aX\c mXcfi [\ cXZfejkXek\ [\ cfj^Xj\j' g\if ef cc\^X X \jkXYc\Z\i cX]‚idlEX [`d\ej`feXc [\ \jkX el\mX dX^e`)kl[* Jfi fkiX gXik\' _Xi\dfj m\i hl\' gXiX cfj ]`e\j [\c <e~c`j`j [`d\ej`feXc' cXk\dg\iXkliX _X [\ j\i Zfej`[\iX[X Zfdf [`d\ej`feXcd\ek\ `e[\g\e[`\ek\ [\cXj dX^e`kl[\j d\Z~e`ZXj** @e \c ZXdgf \c\ZkifdX^e•k`Zf' Zfej`[\iX jfcXd\ek\ [fj m\Zkfi\j' cXj `ek\e)

X€[X[\j' Zfe cf hl\ \cl[\ \c gifYc\dX hl\' [\j[\ \c glekf [\ m`jkX[`d\ej`feXc'gcXek\Xe cXj [fj g\id\XY`c`[X[\j \6 S O8%S ef XYfi[X cXZl\jk`‚e [\ j` \j e\Z\jX)iDI f ef Xdgc`Xi cXYXj\ d\Z~e`ZX Xc\jkl[`Xi cXjk\fi€Xj \c\ZkifdX^e•k`ZXj** @e ]`e' gXiX [\dfjkiXi \c k\fi\dX [\ g`' gXik\ [\ leX _`g‚k\j`j QT X_S$ efEljk`]`ZX[Xe` c‚^`ZXe` \og\i`d\ekXcd\ek\' p [\aX j`e kiXkXicXj\^le[X gXik\'cX hl\ j\ i\]`\i\ Xceƒd\if [\ dfefd`fj g` hl\' ZlXchl`\iX hl\ j\X cX YXj\X[fgkX[X' _Xe [\ ]`^liXi \e cXjfclZ`‚e [\ ZX[XgifYc\dX*

#%$ P•Xj\' gfi \a\dgcf' \c c`Yif [\c Xlkfi #02$*

PD* @F N@IL@G< ?@ JD .+

@jkX \ZlXZ`‚e Zfejk`klp\ leX ifkle[X ZfekiXm\eZ`‚e [\c gi`eZ`g`f [\ _fdf)^\e\`[X[' gl\j "ef j‚cf ]`^liXe cfj cf^Xi`kdfj [\ 2 p [\ Z j`e gfj`Yc\ Xii\^cf'j`ef hl\ cXS_^cdQ^dUaeY]YSQ$ `' XgXi\Z\ jldX[X Zfe \c eƒd\if 1+.' gfi cf hl\[\Y`\iX j\i [\ [`d\ej`‚e elcX' j`\e[f Xj€hl\' Zfdf \j jXY`[f' jl mXcfi[\g\e[\[\ cXj le`[X[\j hl\ j\ X[fgk\e*

JXiX _XccXicX\ogi\j`‚e Zfii\ZkX' i\Zl•i[\j\ hl\ \c ZXcfi dfcXi [\ le ^Xj\jk~ [X[f gfi cX\ogi\j`‚e6

AZ 2 @B $ I'

[fe[\ @ \j le eƒd\if hl\ mXc\1+. \e cfj ^Xj\j dfefXk‚d`Zfj p 3+. \e cfj[`Xk‚d`Zfj' p I \j leX ]leZ`‚e [\ cXk\dg\iXkliX hl\ k`\e[\ XZ\if ZlXe[f \ &$&I*>fe \jkf' [\ cX Xgc`ZXZ`‚e[\ cfj [fj gi`d\ifj gi`eZ`g`fj [\ N\idff*d~d`ZXi\jlckX6

\H ]\ fG 2 F De)) $ & [\ $ Zfejkf` f 2

T0'.s

@cgi`eZ`g`f [\ H\iejk \o`^\ hl\ cX \ekifg€X k\e^X le mXcfi [\k\id`eX[f\e ZX[X\jkX[f "Z%\$' cl\^f cXZfejkXek\ ef \j XiY`kiXi`X*L\gi\j\ek~e[fcX "gfi

Zfejk 2 B"WY= $ @#

cX\ogi\j`‚e T0'.Vj\ Zfem`\ik\ \e

#\H$ ]\ fG 2 F De ? Z $ f - O. $ @F$ T0'/E

hl\ \jk~ [\ XZl\i[f Zfe \c gi`eZ`g`f [\ _fdf^\e\`[X[ j` j\ Xki`Ylp\ X cXZfej)kXek\ = cX]‚idlcX [`d\ej`feXc7

I=J 2 >&;?D&+U&B T0'0s

FX ]XckX[\ _fdf^\e\`[X[ [\ DX\ZlXZ`‚e T0'-V gifZ\[\ [\ hl\' Xc[\]`e`i cXZfejkXek\ hl€d`ZX' ef j\ lk`c`q‚ leX ]leZ`‚e Zfe[`Z`feXcd\ek\ _fdf^•e\X' gl\j[\ cXZfdgXiXZ`‚e [\ c0'-V MT0'/E j\ [\[lZ\6

=2 \`' T0'1$

T0'2Vf Y`\e'

cf^ ? 9 ,'0/0 C9 Q'

Jfi \a\dgcf' gXiX\c _`[i‚^\ef j\ \eZl\ekiX \e cXjkXYcXj\c mXcfiQ2 & /'/13'p j\ X[m`\ik\ hl\ cXk\dg\iXkliX _X [\ d\[`ij\ \e ^iX[fj Z\ek€^iX[fj' p cXgi\)j`‚e' \e Xkd‚j]\iXj* M`j\ hl`\i\ _XccXi\c mXcfi [\ Q Zfe fkiXj le`[X[\j' j\ kif)g`\qX Zfe cX [`]`ZlckX[ [\ hl\ ZXi\Z\ [\ ]‚idlcX [`d\ej`feXc* @e ZXdY`f' cX]‚idlcX T0'2V[X gXiX cXZfejkXek\ = \c mXcfi

? 2 I ,,,0/5 Xkd' f Mj.*

p pX i\jlckX j\eZ`ccf \c ZXdY`XicXj le`[X[\j [\ gi\j`‚e p [\ k\dg\iXkliX*

Page 37: Análisis dimensional

30 <H{FDMDM?cG@HMEIH<F

&! 0H BSLKJBJPBABHEFANXDBJK!

@c `=$ f \ogfe\ek\ [\c _`[i‚^\ef' j\ [\]`e\ Zfdf \c cf^Xi`kdf [\Z`dXc'ZXdY`X[f [\ j`^ef' [\ cX ZfeZ\ekiXZ`‚e [\ cfj _`[if^\e`fe\j \ogi\jX[X \edfc\j)^iXdf gfi c`kif [\ X^lX6

`= 2 )cf^ Z*

>fdf cXZfeZ\ekiXZ`‚e' \' ef k`\e\ [`d\ej`‚e elcX' \jkX ]‚idlcX [\ [\]`e`)Z`‚e ef Zldgc\ \c i\hl`j`kf [\ j\i Zfe[`Z`feXcd\ek\ _fdf^•e\X' gfi cf hl\ \j`dgfj`Yc\ Xki`Yl`i ]‚idlcX [`d\ej`feXc Xc`=$ p cXj \ZlXZ`fe\j \e hl\ ]`^li\\jkX dX^e`kl[ ef jXk`j]Xi~e \c gi`eZ`g`f [\ _fdf^\e\`[X[* @e Zfej\Zl\eZ`X'ef gf[i~ ]`^liXi \c `= \e e`e^ƒe gifYc\dX [\ <e~c`j`j [`d\ej`feXc M[\Y\i~lk`c`qXij\ cXZfeZ\ekiXZ`‚e \ \e jl cl^Xi* 8,9;0 M@BOH?<

,843.,.3760:

Page 38: Análisis dimensional

S,',U

<:I~MNEH OBB

7909 01 :6-8=1-; 69< :;9.617-< 01 -8U65<5<05718<598-6

$" <FNOCH?NAJHKGCOJNBC HJIJHFJN BC BFHCINF\IIPG?"

>l_Z[dj[c[dj[' i_ i[ \ehcW [b fheZkYje Z[ Zei e c|i d•c[hei f_'Z[ifk}i Z[ ^WX[hbeiW\[YjWZeZ[ [nfed[dj[i hWY_edWb[iYkWb[igk_[hW'h[(ikbjWh|kd dk[le cedec_e Z[ Z_c[di_€d dkbW5

>b j[eh[cW Z[ f_ \_`W[b d•c[he Z[ cedec_ei f_' _dZ[f[dZ_[dj[i' gk[fk[Z[d \ehcWhi[ Yed bWicW]d_jkZ[i ZWZWi'f[he Z[`Wb_X[hjWZfWhWbW[b[YY_€dZ[ bei c_icei) L[ Z_Y[gk[ kd Yed`kdje Z[ jWb[icedec_ei ied_dZ[f[dZ_[dj[i YkWdZebW[YkWY_€d

i€be WZc_j[ bWiebkY_€djh_l_WbPb 7 ?)$ &_& $ 7 ?M 7 H) NdWl[p gk[ i[^WdeXj[d_Ze jWdjei cedec_ei _dZ[f[dZ_[dj[i Yece _dZ_YWZ_Y^ej[eh[(cW' YkWbgk_[hejhe feZh| eXj[d[hi[ ZWdZelWbeh[iWZ[YkWZeiWbei [nfe(d[dj[i Z[ bW[YkWY_€dS,C ,U) Ieh [ie' fk[Z[ Z[Y_hi[gk[ N`LW\`TP]NZY&U`Y_ZOP=XZYZXTZ^ TYOP[PYOTPY_P^OPOTXPY^TmYY`WLQZ]XLY `Y ^T^_PXLNZX[WP_ZOPXZYZXTZ^ [T'

Eei cedec_ei Z[ Z_c[di_€d dkbWde j_[d[d YWX_ZW[d bWh[fh[i[djW()Y_€d l[Yjeh_WbZ[ bWiZ_c[di_ed[i fehgk[' YkWbgk_[hWgk[ i[W bWXWi[WZefjWZW'iki Yecfed[dj[i ied dkbWi)>d YWcX_e'YWX[WZefjWhfWhW[bbei

Page 39: Análisis dimensional

'( :GyEBLBL =CbT_>GLBHG:E

kd dk[le [ifWY_el[Yjeh_WbYkoWXWi[[ijWh~W\ehcWZWfeh kde YkWbgk_[hW)Z[ bei i_ij[cWi Yecfb[jei) <kWbgk_[hejhe cedec_e f_ [ijWh~Wh[fh[i[d(jWZefeh kd l[Yjeh YkoWiYecfed[dj[i \k[i[d bei [nfed[dj[i Z[ bW[YkW(Y_€dS,',U)

%" ;CEG?KMXAOFA?K?M?DJMH?MPI NFNOCH?AJHKGCOJBCHJIJHFJN KF"

>iYh~XWdi[bWi\€hckbWiZ_c[di_edWb[iZ[ bWicW]d_jkZ[i ZWZWiYedh[bWY_€dWkdWXWi[YkWbgk_[hW5

2<Pbc""" ! %

89 2Yndb =NcYX?R / b!"! Q!

IWhWgk[ kd cedec_e

j[d]W Z_c[di_€d dkbW' WXh|Z[ i[h5

H<bb>B # &&&# 81RP2R / 3

H<bc>B # &&&# 81RQ2R / 3

o i_ V [i bWYWhWYj[h~ij_YWZ[ bWcWjh_p\ehcWZWYed bei [nfed[dj[i 81VN

i[h|d WhX_jhWh_eibei lWbeh[i Z[ Y&VZ[ bWi_dY€]d_jWi>b8 ‚‚‚ ' 2R& EWi_dY€]d_jWiWhX_jhWh_Wifk[Z[d i[h YkWb[igk_[hW'YedjWbZ[ gk[ [d bWcW(jh_p\ehcWZWYedbWiYebkcdWi[d gk[ \_]khWdbWiV cW]d_jkZ[i h[ijWdj[i^WoWWb]•d c[deh Z[ ehZ[d O Z_ij_dje Z[ Y[he)L_' feh [`[cfbe' ^WoWb]kdeZ[ [ijei c[deh[i [d bWiV •bj_cWi YebkcdWi'WYWZWi_ij[cW Z[lWbeh[i

>b >- 2R%L

, H HH b H

H H ))) ,

Yehh[ifedZ[h| kdWiebkY_€d'o [djh[ jeZWi\ehcWh|d kd i_ij[cW Yecfb[jeZ[ cedec_ei f_)

OBB) FH=H => IE:GM>:K EHL IKH;E>F:L ')

L[ i_cfb_\_YW[b fheXb[cWi_ i[ [cf_[pW feh W]hkfWhbWicW]d_jkZ[igk[ j[d]Wd bWc_icW Z_c[di_€d) =_l_Z_[dZebWiZ[ YWZW]hkfe feh kdWZ[ [bbWi'i[ eXj_[d[d _dc[Z_WjWc[dj[bei bbWcWZeiILN_Z]P^OPQZ]XL%gk[ik[b[d h[fh[i[djWhi[ feh bWb[jhW]h_[]Wm) >ijei \WYjeh[iZ[ \ehcW fk[(Z[d i[h bWihWped[i[djh[ bWibed]_jkZ[i' bWicWiWi'bWi\k[hpWi'[jY)' gk[_dj[hl[d]Wd [d [b \[d€c[de o [djh[ [bbei i[ _dYbko[d'Z[iZ[ bk[]e' bei|d]kbei) A[Y^e [ije' i[ ^WbbWdbei cedec_ei f_ jecWdZe [d Yedi_Z[hW(Y_€dkdWjWdi€be Z[ bWicW]d_jkZ[i Z[ YWZW]hkfe' o Wbei cedec_ei Wi~eXj[d_Zei i[ W]h[]Wdbei \WYjeh[iZ[ \ehcW)

&" 5IDJMH?AF\ILPCKPCBCJ@OCICMNCAJI CG-IXGFNFNBFHCINFJI?G":MFIAFKFJBC NFHFGFOPB"

L[ iWX['H i[ ZWfeh ikfk[ije' gk[ [d Z[j[hc_dWZe\[d€c[de _dj[h(l_[d[d bWicW]d_jkZ[i Pb8 ‚‚‚ ' ?R$ _dYbko[dZe[d [bbWibWiYedijWdj[iYWhWYj[h~ij_YWio bWiYedijWdj[ikd_l[hiWb[i'fhef_WiZ[ bWj[eh~W'o gk[ bWYkWdj~WZ[ kdWZ[ [bbWigk[ZWZ[j[hc_dWZWfeh bWiYWdj_ZWZ[iZ[ bWiejhWi)=[X[h| i[h5

Q"BPg% ''' %BP_# / H'

ZedZ[ M[r' ‚‚‚ ' BP_ [i kde YkWbgk_[hWZ[ bei i_ij[cWi Yecfb[jei Z[ cede(c~ei f_' o rkdW\kdY_€dkd_l[hiWb_dZ[j[hc_dWZW)<ece i_[cfh[ i[ fk[Z[be]hWhgk[ Wgk[bbWcW]d_jkZ' FW! gk[ _dj[h[iW[nfh[iWh[d \kdY_€dZ[ bWiejhWi'\_]kh[ iebWc[dj[ [d kde Z[ bei cedec_ei' feh [`[cfbe' [d [b fh_(c[he' bW[YkWY_€dfeZh| jecWh bW\ehcW [nfb~Y_jW5

gk[ [i bW\ehcW ][d[hWbZ[ bWi\kdY_ed[i YedZ_Y_edWbc[dj[ece]}d[Wi)EW_d\ehcWY_€dc|i Yecfb[jWi[ be]hWYkWdZe=/ ,' [ije [i' YkWdZe

[b i_ij[cW Yecfb[je Z[ cedec_ei f_' _dYbko[dZebei \WYjeh[iZ[ \ehcW'YedijWZ[ kd iebe c_[cXhe' fk[i fk[Z[ W\_hcWhi[gk[ Z_Y^ecedec_e^WZ[ i[h _]kWbWkd d•c[he \_`e' gk[ de Z[f[dZ[ Z[ bWikd_ZWZ[iZ[c[Z_ZW)

1GWl[h_]kWhbW\ehcW Z[ bW\kdY_€dkd_l[hiWbYf' YkWdZede i[ h[ZkY[Wkd d•c[he \_`e' YW[\k[hWZ[bWbYWdY[Z[b :d|b_i_i Z_c[di_edWb'f[he [dckY^Wi eYWi_ed[iXWijWdi[dY_bbWiYedi_Z[hWY_ed[iXWiWZWi[d kd Yede(Y_c_[dje [b[c[djWb Z[ bWj[eh~WZ[b\[d€c[de [d Yk[ij_€d fWhWh[ZkY_h[bd•c[he Z[ lWh_WXb[igk[ \_]khWd[d bWc_icW' o ^WijWfWhWZ[j[hc_dWh[dj[hWc[dj[ ik \ehcW' iWble kd \WYjehYedi_ij[dj[ [d kd d•c[he \_`e)

Page 40: Análisis dimensional

:GyEBLBL =BF>GLBHG:E

Nd YWieZ[ ]hWd_dj[h}i [i Wgk}b[d gk[ bW\kdY_€d_dZ[j[hc_dWZWi€be Yedj_[d[ \WYjeh[iZ[ \ehcW5

L_i[ Wfb_YW[ijW [YkWY_€dWZei ^T^_PXL^ PXPULY_P^%[ije [i' jWb[igk[ bei\WYjeh[iZ[ \ehcW Z[ kde i[Wd_]kWb[iWbei Z[b ejhe' bW\kdY_€dkd_l[h(iWbN[ j[dZh| lWbeh[i_]kWb[i[d WcXei' o XWijWh|Wl[h_]kWhik lWbeh[dkde Z[ [bbei c_Z_[dZe bWicW]d_jkZ[i 6?0 KKK $ ?R [d kd YWiefWhj_YkbWh)>d [ije Yedi_ij[ [b []TYNT[TZOP^TXTWT_`O%gk[ [i [b \kdZWc[dje Z[ bei[diWoei YedceZ[bei h[ZkY_Zei'Z[ jWdjW_cfehjWdY_W[d bWYedijhkYY_€dZ[ Wl_ed[i' dWl~eio eXhWi _Zh|kb_YWi)G€j[i[ gk[ bWi[c[`WdpW[djh[[b i_ij[cW Z[ jWcW•edWjkhWbo [b ceZ[be i[ h[\_[h[ WjeZei bei \WYjeh[iZ[ \ehcW' de i€be Wbei ][ec}jh_Yei' i_de jWcX_}dWbei Z[ ~dZeb[\~i_YW)

>`[cfbei5

,) e ?kYO`WZ ^TX[WP'

>d [b cel_c_[dje eiY_bWjeh_eZ[ kd f}dZkbe i_cfb[' bW•d_YW\k[hpWgk[ _dj[h(l_[d[ [i [b f[ie b / QK& Ieh jWdje' [b f[h~eZe' _%[ijWh| Z[j[hc_dWZe feh bWcWiW X%bWbed]_jkZ ( o bWWcfb_jkZ Z[ bWieiY_bWY_ed[i+5' gk[ [i kd \WYjehZ[\ehcW' Eei [nfed[dj[i Z_c[di_edWb[i Z[ [ijWi cW]d_jkZ[i Yed h[bWY_€dWbWXWi[6$7$ ;$ ied bei Yedj[d_Zei [d [b i_]k_[dj[ YkWZhe5

X b

& -' -( ,

3(H

((-

(HH

EWYWhWYj[h~ij_YWZ[ [ijW cWjh_p[i S / . Q ^WXh|' feh jWdje' kd iebe cede(

c_e f_' WfWhj[Z[b \WYjehZ[ \ehcW)<ece [d jeZWi bWiYebkcdWi ^Wo Wb]•d [b[c[dje gk[ de [i dkbe' fk[Z[

([b[]_hi[ WhX_jhWh_Wc[dj[kdW YkWbgk_[hWZ[ bWi_dY€]d_jWi)AWY_[dZe1E / ,'

h[ikbjW[b i_ij[cW Z[ [YkWY_ed[i5

>b & >m / H7X$7b2>

, ( +7b / H)

([koWiebkY_€d[i5

1E / ,6,

-!,7 2X0

AWXh|Z[ i[h' feh jWdje5

2"5, / _ ,* b %D XW

K

OBB) FH=H => IE:GM>:K EHL IKH;E>F:L

e X_[d' fk[ije gk[ b 7 QK$

3,

2"5, / _D KP !

o' jecWdZe [d Yedi_Z[hWY_€d[b \WYjehZ[ \ehcW , bkY_€ X' Wie N<b d kiYWZWi[h|5

_= < / r#e5$'

e i[W5

_ / O&r#e5$'

\_o)fk[Z[ W\_hcWhi[gk[ [d r#e5$de fk[Z[ \_]khWh'WfWhj[Z[ e5 cWi"gk[ "CHi) " dkc[hei

>b h[ikbjWZe[i Yehh[Yje'fk[i' Yece [i iWX_Ze'bW[YkWY_€dYecfb[jW [i5

_ / -2"5= ( $ # G # &"K ,1vvv '

o bW\kdY_€d r#e5$'gk[ [b :d|b_i_i Z_c[di_edWbZ[`W_dZ[j[hc_dWZW'h[ikbjWi[h5

r#e5$/ -2"5 $ # G # ",1 ))))

+') ?]ZMWPXLOP<LMZNP__L"-.#'

=[ceijhWh )gk[ ,' cWdj[d_[dZe YedijWdj[i bWiZ[di_ZWZ[iZ[ jeZei beifqi gk[ '\ehcWd [b i_ij[cW iebWh'i[ ckbj_fb_YWdjeZWi bWibed]_jkZ[i fe5k5

657qW5kcorhe' i[_b

Ye)di€

[hlWd _dWbj[hWZeibei f[h~eZei Z[ h[lebkY_€d Z[ jeZei bei' ) [ ei[ W[_d Z[ jeZei bei f}dZkbei)

EWi kcYWi \kqhpWi gk[ _dj[hl_[d[d [d [b fheXb[cW ied bWi]hWl_jWjeh_Wi

I5Wqq€qk[ YkWbgk_[hf[hqeZe ^)WXh|Z[ i[h \kdY_€d Z[ bWicWiWi o Z[ bWYed\_qq _€ Z[b LBij[cW'Z[X_[dZecj[hl[d_h bWYedijWdj[ Z[ bW]hWl_jWY_€dEWYedo]qWq d gk[ZWh| Z[\_d_ZWfeh Y_[hjed•c[he Z[ bed]_jkZ[i5 hWZ_ei'Z_ijWdY_W6

qq] ei' o bWicWiWi feZh|d ikij_jk_hi[ feh bei fheZkYjei Z[ Z[di_ZWZ[i o

57d5' o Yece [ijei) •bj_cei ied \kdY_ed[i Z[ bed]_jkZ[i' bWicW]d_jkZ[i gk[

Bed _jkq[i |d Yece lWdWXb[ii[h|d Y_[hjWiZ[di_ZWZ[i' Ie" Ib" ))) o Y_[hjWi] ' WZ%''' WY%fk[i bei |d]kbei i[ ikfed[d YedijWdj[i=[iZ[ bk[]e' [n_ij[d bei \WYjeh[iZ[ \ehcW5 )

bT271Ie

D P&b' / &*&1

e

] / ,'-' )))

^ 7 ,'-' )))

:GyEBLBL =BF>GLBHG:E) ( 1

Page 41: Análisis dimensional

(% :GyEBLBL =bF>GLBHG:E

o XWijWh|jecWh [d Yedi_Z[hWY_€dkdW Z[di_ZWZ'kdW bed]_jkZ o bWYedijWdj[Z[ bW]hWl_jWY_€d'WZ[c|i Z[b f[h~eZe gk[ i[ XkiYW)

>b Y|bYkbei[ Z_ifed[ Yed Whh[]beWbi_]k_[dj[ [igk[cW5

VM I_ WT 9

6 3 %* , *7 3 , 3 ( ,B , 3 3 (-

'+ , ,*- 3 ,*-

S 7 *- =7 ,

% *1C # 2P # *24 7 3

1C % 1B 7 3

2V % )24 7 3

F ^WXh|Z[ i[h5

o i[h| VM/ Yedij i_ bWiZ[di_ZWZ[io bWihWped[i W^(W_i[ cWdj_[d[d YedijWdj[i)

'" ;CEG?NK?M?KG?IOC?MGJNKMJ@GCH?N"

NdWl[p ^[Y^WbWb_ijWZ[ bWicW]d_jkZ[i gk[ _dj[hl_[d[d [d kd fhe(Xb[cWZ[ :d|b_i_i Z_c[di_edWb'bWh[iebkY_€dYW[[d [bZec_d_eZ[byb][XhW[b[c[djWb5EWZ_\_YkbjWZ'feh jWdje' Yedi_ij[ [nYbki_lWc[dj[ [d bW\eh(cWY_€dZ[ Z_Y^Wb_ijW)

MeZei bei jhWjWZ_ijWi[ij|d Z[ WYk[hZe[d gk[ de [n_ij[d dehcWi gk[f[hc_jWd fbWdj[WhZ[X_ZWc[dj[ kd fheXb[cW YkWbgk_[hW)>i YeiWgk[Z[`WdWbW_djk_Y_€dZ[ YWZWkde) L_d [cXWh]e' [i fei_Xb[ ZWhWb]kdWih[]bWi][d[hWb[igk[ \WY_b_j[dbWYk[ij_€d)

b)W 7^ []PNT^Z\`P PWQPYmXPYZNZY^TOP]LOZNLTRLPY PWOZXTYTZOPLWR`YL OP WL^_PZ]lL^Ql^TNL P^_LMWPNTOL^%Z[ jWbceZe gk[ ik iebkY_€dYecfb[jWi[h~Wfei_Xb[i_ i[ fkZ_[hWdl[dY[h bWiZ_\_YkbjWZ[icWj[c|j_YWi)

>ijW dehcW [ij| `kij_\_YWZWfeh [b ^[Y^e Z[ [ijWh [b :d|b_i_i Z_c[di_edWbikXehZ_dWZeWbWij[eh~Wi\~i_YWi'o de Wbh[l}i) Okbd[hWdZe[ij[ fh[Y[fje' fk[(Z[d fbWdj[Whi[fheXb[cWi Wbei gk[ [b :d|b_i_i Z_c[di_edWbZWkdW h[ifk[ijWjWdfh[Y_iWYece _di[diWjW)A[ Wgk~kd [`[cfbe fhefk[ije feh L[bmod #/3$)

x<k|dje j_[cfe' _%j[dZh| gk[ [ijWh [djh[d|dZei[ kd `k]WZeh Z[ ]eb\' Z[cWiWX%fWhWbWdpWhkdWf[bejW WbWZ_ijWdY_WW3

<ece [i [l_Z[dj[ gk[ bWWY[b[hWY_€dZ[ bW]hWl[ZWZ_dj[hl_[d[) [d [b `k[]e'bWicW]d_jkZ[i ied `kijWc[dj[ bWic_icWi gk[ [d [b fheXb[cW Z[b f}dZkbe

K

%C%/ Q"f+! & #4" ] ]] ! $# J ]]

Ie

OMB) FH=H => IE:GM>:K EHL IKH;E>F:L 3.

i_cfb[' iWble bWWcfb_jkZ Z[ bWieiY_bWY_ed[i)Ieh jWdje' bWiebkY_€d[i' fh[(Y_iWc[dj[5

_ / "I O&"ZedZ[ "I [i kd d•c[he \_`e)

-)W ALWaZWLXLRYT_`O TYNmRYT_L%_ZOL^WL \`P QTR`]PYPY WLWT^_LSLYOP^P] Z NZY^_LY_PZ aL]TLMWP^TYOP[PYOTPY_P^'>ijW h[]bW[gk_lWb[WZ[Y_hgk[ [djh[ bWicW]d_jkZ[i jecWZWi[d Yedi_Z[hWY_€di€be ^WZ[ [n_ij_hkdW[YkWY_€d)

Lkf€d]Wi[' feh [`[cfbe' gk[ [d [b fheXb[cW Z[ bWYW~ZWb_Xh[Z[ kd Yk[hfei[ jecWd bWii_]k_[dj[i cW]d_jkZ[i5 j_[cfe' _1 \k[hpW' Q1 cWiW' Q. Z_ijWdY_W)h[Yehh_ZW'36 l[beY_ZWZWZgk_h_ZW'a%o WY[bWhWY_€d'L'

J X , a L

< 3 , 3 , , ,= 3 , , 3 3 3B , (- 3 3 (, (-

'+$ 3 , (, 3 3 ( ,'+% , 3 3 , , 3',. , 3 3 3 , ,

EWiebkY_€d

3 / a_W;!" f% 0_#[i _dWY[fjWXb['fehgk[ [d [b \[d€c[de Yedi_Z[hWZei€be ^Wojh[i lWh_WXb[i_dZ[(f[dZ_[dj[i5 bWcWiW'bW\k[hpWF [b j_[cfe) >b Wl[h_]kWhYk|dje lWb[dbWih[ijWdj[icW]d_jkZ[i ZWeh_][d Wi[dZei fheXb[cWi Yed iki h[if[Yj_lWi iebkY_ed[i' gk[ ied5

a 2''< V.X

( V, /% DV+o

) ,L / %!%-

X

.)W 6PMPY_ZXL]^P PY NZY^TOP]LNTmY_ZOL^WL NZY^_LY_P^%_LY_ZNL]LN&_P]l^_TNLNZXZ `YTaP]^LWP^%N`dL []P^PYNTLP^_k[]PaT^_L[Z] WL_PZ]lLOPWQPYmXPYZNZY^TOP]LOZ'

>i [l_Z[dj[ gk[ de fk[Z[ eXj[d[hi[ kdWiebkY_€diWj_i\WYjeh_Wi_ [dkd fheXb[cWZ[ [bWij_Y_ZWZ'feh [`[cfbe' i[ ikfh_c[ Wb]kdWZ[ bWiYedi(jWdj[i [b|ij_YWigk[ _dj[hl[d]Wd [d [b c_ice) EWiYedijWdj[i kd_l[hiW(b[i _d[bkZ_Xb[iied bWifh[l_ijWi feh dk[ijhe i[]kdZe feijkbWZe)

L_[d [b i[]kdZe fheXb[cW Z[b WfWhjWZeWdj[h_ehi[ ^kX_[i[ ec_j_Ze bWYedi(jWdj[ Z[ bW]hWl_jWY_€d'kX_[hWh[ikbjWZebWiebkY_€dZ[iYWX[bbWZW5

Page 42: Análisis dimensional

3/ :GyEBLBL =BF>GLBHG:E

i[]•d bWYkWb'bWh[bWY_€d[djh[ bWiZ[di_ZWZ[i Z[ Zei Yk[hfei [ij| _cfk[ijWfeh bei h[ijWdj[i \WYjeh[iZ[ \ehcW)

EWd[Y[i_ZWZZ[ jecWh [d Yedi_Z[hWY_€dbWiYedijWdj[i kd_l[hiWb[i Yedij_(jk\W bWc|n_cW Z_\_YkbjWZc_[djhWi de i[ iWX~WZ_iY[hd_h[djh[ bWiikf[h\bkWi obWi_d[bkZ_Xb[i)@hWY_WiWdk[ijhe i[]kdZe feijkbWZe' gk[ZW eXl_WZWbWZ_\_(YkbjWZ'o fk[Z[ Z[Y_hi[ gk[

E# >d F[Y|d_YWd[mjed_WdWde _dj[hl_[d[ d_d]kdWYedijWdj[ kd_(l[hiWb' iWble bWYedijWdj[ Z[ bW]hWl_jWY_€d'gk[ i€be \_]khWYkWdZei[jecWd [d Yedi_Z[hWY_€dbWiWYY_ed[i]hWl_jWjeh_Wi)

F# >d bei fheXb[cWi Z[ F[Y|d_YWh[bWj_l_ijW_dj[hl_[d[ bWl[beY_ZWZZ[ bWbkp)

[$ >d F[Y|d_YW[ijWZ~ij_YW\_]khWbWYedijWdj[ Z[ ;ebjpcWdd' O$obWZ[ IbWdYa'L&

H# >d bei \[d€c[dei [djh[ Yehf•iYkbei [b[c[djWb[i' _dYbko[dZebei\ejed[i' \_]khWbWYedijWdj[Z[ IbWdYa'L&

[$ >d bei fheXb[cWi Z[b YWcfe [b[YjhecW]d}j_Ye[d [b lWY~e_dj[h(l_[d[d bWiYedijWdj[i >H Q be5

EWi fh[Y[Z[dj[i dehcWi h[l[bWd gk[ bei fheXb[cWi Z[ :d|b_i_i Z_(c[di_edWbi€be fk[Z[d i[h fbWdj[WZeifeh gk_[d YedepYWbei \kdZWc[djeiZ[ bWij[eh~Wi\~i_YWi'fk[i i€be Wi~feZh| Z[Y_Z_hgk} cW]d_jkZ[i ^WdZ[_dj[hl[d_h Yece lWh_WXb[i_dZ[f[dZ_[dj[i o gk} YedijWdj[i kd_l[hiWb[i^Wogk[ jecWh [d Yedi_Z[hWY_€d)

(" 6?N @?NCNBCDFAFCIOCN"

:b ikfh_c_h kdWYedijWdj[ kd_l[hiWbWjh_Xko}dZeb[kd lWbehdkc}(h_YeWhX_jhWh_e'feh [`[cfbe ,' Z_ic_dko[ bWckbj_fb_Y_ZWZZ[ bWXWi['oh[ikbjWd\€hckbWiZ_c[di_edWb[iYedbWigk[ [b :d|b_i_i Z_c[di_edWbf_[h(Z[ [\_YWY_W'fk[i bW_d\ehcWY_€dgk[ ikc_d_ijhW[i c|i lW]Wgk[ bWgk[ i[eXj_[d[ kj_b_pWdZekdWXWi[Yecfb[jW)

Lkf1d]Wi[ gk[ [d bW\€hckbW

J / 4 XTX!TK,)

i[ ikfh_c[ bWYedijWdj[ Z[ bW]hWl_jWY_€d4& EWckbj_fb_Y_ZWZZ[ bWXWi[' fWhWbWicW]d_jkZ[i c[Y|d_YWi' i[ h[ZkY[ W- o' jecWdZe bWbed]_jkZ o [b j_[cfeYece cW]d_jkZ[i X|i_YWi'i[ eXj_[d[d bWii_]k_[dj[i \€hckbWi Z_c[di_edWb[i'i[]•d i[ l_e [d [b s 0 Z[b YWf~jkbeO5

K

o bWkd_ZWZZ[ cWiWi[h| bWcWiWZ[ W]kWYedj[d_ZW[d [b YkXekd_ZWZ)

OBB) FH=H => IE:GM>:K EHL IKH;E>F:L 30

IWhWl[h i_ [ij[ i_ij[cW [i l_WXb['jhWj[cei Z[ eXj[d[h Yed ik Wkn_b_ebW\€hckbW Z[b f}dZkbe i_cfb[5

X b

& -( (

,./3 % ) % +

H ( , .*/, ( , ,*-

S 7 -6 =7 ->b # .>@ # -7b / 3

1E % )1@ % -7b / 3

o' WfWhj[Z[b \WYjehZ[ \ehcW b / [n' h[ikbjW [b i_]k_[dj[ i_ij[cW Z[ cede(c_ei f_5

e X_[d' i_ fWhW\WY_b_jWhbWYecfWhWY_€dYed [b h[ikbjWZeeXj[d_Ze Wbkj_b_pWhbWXWi[Yecfb[jW' i[ ^WY[5

2j" / 2j,2j-(,`- / _D f 1

o' WZ[c|i Z[b cedec_e BP!b"gk[ \_]khW[d bW\€hckbW Yehh[YjW'WfWh[Y[[b XZ&YZXTZ P^[`]TZ BP+%Yed be gk[ bWiebkY_€di[ Yedl_[hj[ [d5

gk[ [i \WbiW'fk[i W\_hcWbW_d\bk[dY_WZ[ bWcWiWieXh[ [b f[h~eZe o' WfWhj[Z[[ije' [i c[dei fh[Y_iW'fehgk[ bW\kdY_€dZ[iYedeY_ZWZ[f[dZ[ Z[ Zei fWh|c[jhei[d l[p Z[ kde)

:b ckj_bWhbWXWi[ ikfh_c_[dZe YedijWdj[i _d[bkZ_Xb[i'i[ Yh[WdWhj_\_Y_Wb(c[dj[ h[bWY_ed[iZ_c[di_edWb[i gk[ de Yehh[ifedZ[d WdWZWh[Wbo [bbeYedZkY[Wh[ikbjWZeiY_[hjWc[dj[ Ykh_eiei' f[he gk[ de j_[d[d' d_ckY^e c[dei' [b i[dj_Zeh[Y€dZ_jegk[ b[i Wjh_Xko[dbei jhWjWZ_ijWigk[ i[ Z[Z_YWdW[ijWi [if[YkbWY_ed[i)

FWhj_dej(EW]WhZ[#/4$' feh [`[cfbe' YecfWhj[ bWef_d_€d Z[ gk[ WbZ[ife`WhZ[ ik Z_c[di_€d WbWiYedijWdj[i kd_l[hiWb[i' i[ f[d[jhW c|i W\edZe [d [b Yede(Y_c_[dje Z[ bWdWjkhWb[pW'o ZWYece fhk[XWbe gk[ eYkhh[i_' WZ[c|i Z[ ZWh[blWbeh, WbWYedijWdj[ Z[ bW]hWl_jWY_€d'i[ jecW Yece kd_ZWZZ[ Z[di_ZWZZ[bW]kWW/u <) EW\€hckbW

Xf7O(" S0'bC

fk[ije gk[ ^WZ[ i[h _dZ[f[dZ_[dj[ Z[b i_ij[cW Z[ kd_ZWZ[i'eXb_]WWgk[ i[W5

ScC / EL

Page 43: Análisis dimensional

(& :GyEBLBL =BF>GLBHG:E

EW\€hckbW S0',U YecX_dWZWYed bWi

:),( / X& B+$)C.O_+

XX!(0%%

,)S0'.U

gk[ Yehh[ifedZ[d WbWb[o Z[ 5h[mjedo WbWb[o Z[ bW]hWl_jWY_€d'YedZkY[dWbWii_]k_[dj[i \€hckbWi Z_c[di_edWb[i5

BVC/ H'

o h[ikbjWkd i_ij[cW kd_Z_c[di_edWb[d [b gk[ [b j_[cfe j_[d[ Z_c[di_€d dkbW'be gk[ i_]d_\_YWgk[ ik kd_ZWZ WZ[ j[d[h kd lWbehZ[j[hc_dWZe' _dZ[f[dZ_[dj[Z[bfWjh€d gk[ i[ WZefj[ fWhWc[Z_h bed]_jkZ[i)

IWhW\_`WhbWi_Z[Wi' jec[cei [b Y[dj~c[jhe Yece kd_ZWZZ[ bed]_jkZ) EW\€hckbW S0',U' Yed I / , fWhW[b W]kWW/+ [' _cfed[ [b ]hWce Yece kd_ZWZZ[cWiW)>d l_hjkZ Z[ S0'.U bWkd_ZWZZ[ \k[hpW i[h| Wgk}bbWYed gk[ i[ WjhW[dZei cWiWiZ[ , ]hWce YebeYWZWiW, Yc) ?_dWbc[dj[' bW\€hckbWS0'-Ue ik [gk_(lWb[dj[ ( / )QUNV+%Z_Y[gk[ bWkd_ZWZZ[ j_[cfe ^WZ[ i[h [b j_[cfe gk[ jWhZ[bWcWiWZ[ , ]hWce [d h[Yehh[h,*- Y[dj~c[jhe YkWdZe[ij| iec[j_ZW WbWkd_ZWZZ[ \k[hpW)A[Y^ei bei Y|bYkbeih[ikbjW5

/!)QU

_ 7 &*&7 .31-3 7 , ^ehWo -1- i[]kdZei)

?|Y_bc[dj[ i[ Yecfhk[XW gk[ Yed YkWbgk_[hejhWkd_ZWZZ[ bed]_jkZ i[ bb[]WWbc_ice h[ikbjWZe)

E_ffcWdd #0+$bbWc€t^ehWdWjkhWbwWbWkd_ZWZZ[ j_[cfe Ye^[h[dj[ Yed [bi_ij[cW gk[ WYWXWceiZ[ Yedi_Z[hWh)L_d [cXWh]e' dWZWkij_\_YW[b Wjh_Xk_hfh_l_b[]_ei WjWbkd_ZWZ'fk[i [i jWdWhX_jhWh_WYece ejhWYkWbgk_[hWo' WZ[c|i'\ehcW fWhj[ Z[ kd i_ij[cW gk[ Z[X[ h[Y^WpWhi[feh i[h _dYecfWj_Xb[Yed bei\_d[i Z[b :d|b_i_i Z_c[di_edWb)

Lkfh_c_[dZe YedijWdj[i kd_l[hiWb[i' i_d Z_iYh_c_dWhi_ ied e de ikf[h\bkWi'i[ Yh[Wdi_ij[cWi Z_c[di_edWb[i ckj_bWZei)GWZWfk[Z[ ]WdWhi[Yed ik [cfb[e):dj[i X_[d' ied _dWY[fjWXb[i[d :d|b_i_i Z_c[di_edWbfehgk[ ^WY[dWfWh[Y[hcedec_ei [ifkh_ei [d bWiiebkY_ed[i) >if[YkbWhWY[hYWZ[ be gk[ ikY[Z[ YkWdZei[ Z[ife`W Z[ ik Z_c[di_€d WWb]kdWYedijWdj[ kd_l[hiWb[i _d•j_b Z[lWd[e' oi_ Yed [bbe i[ fh[j[dZ[' Wl[h_]kWhWb]eWY[hYWZ[ bW[i[dY_WZ[ bWicW]d_jkZ[i'i[ ^W[hhWZe[b YWc_de'fk[i bWiZ_c[di_ed[i' Wkdgk[ i[Wd bWiYehh[YjWi'dWZWZ_Y[dW[ij[ h[if[Yje)

)" 6?N @?NCNNPKCM?@PIB?IOCNS G?NAJINO?IOCNNPKCMDGP?N"

L[]•d i[ l_e [d [b s . Z[b YWf~jkbeBBB'YkWdZe Wb\ehckbWh kdW b[o

kd_l[hiWb i[ fWiWZ[ bWih[bWY_ed[iZ[ fhefehY_edWb_ZWZ[djh[ YWdj_ZWZ[i

WbWi[YkWY_ed[i [djh[ c[Z_ZWi' fheY[Z[' [d ][d[hWb' _djheZkY_hkdW Yedi(

jWdj[ YWhWYj[h~ij_YWe kdW YedijWdj[ kd_l[hiWb) A[cei YbWi_\_YWZe[ijWi

O_b) FH=H => IE: M>:K EHL IKH;E>F:L ('

•bj_cWi [d _d[bkZ_Xb[i o ikf[h\bkWi' o ^[cei l_ije gk[' i_ i[ ikfh_c[

Wb]kdWZ[ bWifh_c[hWi' [b :d|b_i_i Z_c[di_edWb fk[Z[ YedZkY_hWiebk(

Y_ed[i \WbiWifeh bWWfWh_Y_€dZ[ cedehd_ei [ifkh_ei' [ije [i' Z[ ce(

dec_ei gk[' i_[dZe Z_c[di_edWZei [d bWXWi[ Yecfb[jW' WfWh[Y[dYece

Z[ Z_c[di_€d dkbW [d bWckj_bWZW)

NdW YedijWdj[ kd_l[hiWb i[h| ikf[h\bkW YkWdZe i[ eXj[d]W [b c_ice

i_ij[cW Z[ cedehd_ei f_ Yed [bbWgk[ i_d [bbW'Z[ ZedZ[ h[ikbjW gk[ YZSLd TYNZYaPYTPY_PPY TY_]ZO`NT]NZY^_LY_P^YTaP]^LWP^`[P]QW`L^%f[he

jWcfeYe ^Wo [d [bbe d_d]kdW l[djW`W o i[ Yecfb_YWd bei fheXb[cWi)

>d h[ikc[d6 ^T ZN`]]P\`P LWLX[WTL]OPLWRnYXZOZ `YL ML^P%OT^XT&Y`dP PWYnXP]Z OPXZYZXTZ^ [T TYOP[PYOTPY_P^PY_]P l%^P [`POP LQT]XL]\`P WLML^P[]TXT_TaLP]L OPQTNTPY_P%XTPY_]L^\`P% ^T ^P ZM_TPYPTPX[]P PWXT^XZ ^T^_PXL OP _LWPXZYZXTZ^%WLML^P[]TXT_TaL P^ NZX[WP_L%d WLLX[WTLOL% [P]LM`YOLY_P'

Lkf€d]Wi[' feh [`[cfbe' gk[ [d bWb[o Z[ G[mjed5

i[ fed[ bWYedijWdj[ Z_d|c_YW E$gk[' i[]•d dk[ijhe i[]kdZe feijkbWZe' [iikf[h\bkW)@hWY_WiWik fh[i[dY_W'ikXi_ij[ bWb_X[hjWZ[d bW[b[YY_€dZ[ kd_ZWZ[ifWhWjeZWi bWicW]d_jkZ[i fh_cWh_Wigk[ \_]khWd[d Z_Y^Wb[o' be YkWbWY[gk[i[ fk[ZW [cfb[Wh kdW XWi[ j[jhWZ_c[di_edWb'feh [`[cfbe' bW"6$ 7$ ;$ 3#&L_ckbj|d[Wc[dj[' i[h| Z[ fh[l[h' [d jeZe fheXb[cW Z_d|c_Ye' bWfh[i[dY_WZ[ EYed bWi_]k_[dj[ \€hckbW Z_c[di_edWb5

SHU/ 6%57%5;)3&

AW]Wcei l[h gk[ [d [b fheXb[cW Z[b f}dZkbe i_cfb[ bWYedijWdj[ E [i ik(f[h\bkW)>b fheXb[cW i[ fbWdj[Wo h[ik[bl[ Yece _dZ_YW[b WZ`kdje[igk[cW5

X X E

6 e , e e ( ,7 e e ( e %(B ( e 3 e %8 e e e , ,

'$*, !% , ( ( (

S2 -1 _7 (

MWdje[b d•c[he Z[ cW]d_jkZ[i Yece bWYWhWYj[h~ij_YWZ[ bWcWjh_pWkc[d(jWd[d kdWkd_ZWZ'feh be gk[ i_]k[ ^WX_[dZekd iebe cedec_e f_' gk[ [i5

Page 44: Análisis dimensional

(( :GyEBLBL =BF>GLBHG:E

o' jed_[dZe [d Yk[djWbW_dj[hl[dY_€d Z[ bWWcfb_jkZ [n Yece \WYjehZ[ \ehcW'bWiebkY_€di[h|5

_ / DZ f Q"Pc#'

>ijW [YkWY_€d']hWY_WiWbWYedijWdj[ Z_c[di_edWZW+' gk[ [i kd Ye[\_Y_[dj[fWh|i_je' [i l|b_ZW fWhWkd_ZWZ[i YkWb[igk_[hWZ[ bed]_jkZ' cWiW' j_[cfe F\k[hpW)Ge ^Wo'"fk[i' _dYedl[d_[dj[ [d ^WY[hI / ,' Yed bWYedi_]k_[dj[ h[i(jh_YY_€d[d bWb_X[hjWZZ[ [b[YY_€d'[ije [i' kj_b_pWdZekd i_ij[cW Z[ jh[i kd_(

ZWZ[iYe^[h[dj[i Yed I / ,)

*" :?KCGLPCBCNCHKC[?IG?NAJINO?IOCNPIFQCMN?GCN"

>d jeZe fheXb[cW Z[ :d|b_i_i Z_c[di_edWbi[ jhWjWZ[ Wl[h_]kWh' WY_[dZeiebWc[dj[ kie Z[ bei h[Ykhiei Z[b c_ice' YkWdjei[Wfei_Xb[ WY[hYWZ[ bWh[bWY_€dgk[ b_]WbWicW]d_jkZ[i gk[ _dj[hl_[d[d [d Z[j[hc_dWZe \[d€c[de) IWh[Y[' fehjWdje' gk[ bWYk[ij_€d gk[ZWh~Wik\_Y_[dj[c[dj[ fbWdj[WZW[d YkWdjei[ Z_[hWbWb_ijWZ[ bWicW]d_jkZ[i lWh_WXb[i)L_d[cXWh]e' fWhWbe]hWhbWiebkY_€dYehh[Y(jW' ^Wogk[ W]h[]Wh'Wl[Y[i' Z[j[hc_dWZWiYedijWdj[i kd_l[hiWb[i' o de i[ Yede(Y~Wdh[]bWifWhWWl[h_]kWhZ[ Wdj[cWde gk} YedijWdj[i ^Wogk[ jecWh [d Yedi_(Z[hWY_€d)Ieh [ie Z_Y[;h_Z]cWd #--$ gk[ [b :d|b_i_i Z_c[di_edWbde Z[X[ i[hWfb_YWZefeh Xeigk_cWd[i' i_de feh \~i_Yei [nf[hjei) L_d [cXWh]e' [d [b s / Z[[ij[ YWf~jkbe [cei feZ_Ze ZWhWb]kdWidehcWi fWhWh[iebl[h [ijW Z_\_YkbjWZ'ojeZWl~Wi[ fk[Z[ fhe\kdZ_pWhWb]ec|i [d [b fWf[b Z[ jWb[iYedijWdj[i)

L_ de i[ ^kX_[hWZ[iYkX_[hje bWh[bWY_€dZ[ fhefehY_edWb_ZWZ[djh[ bWcWiW_d[hj[ o bW]hWl_jWjeh_W'bWi[YkWY_ed[i\kdZWc[djWb[i Z[ bWc[Y|d_YW d[mje(d_WdWi[h~Wd5

J0 S2',U

o Yed [bbWii[ ^kX_[hW[bWXehWZe[b i_ij[cW Z[ cW]d_jkZ[i c[Y|d_YWi [d [b gk[de ^WXh~Wd_d]kdW YedijWdj[ kd_l[hiWb _d[bkZ_Xb[):b h[iebl[h [b fheXb[cW [dgk[ _dj[hl_d_[i[d \k[hpWi ]hWl_jWjeh_Wi'i[ jecWh~Wd[d Yedi_Z[hWY_€d'WZ[c|iZ[ bWicW]d_jkZ[i gk[ Z[\_d_[i[d bWfei_Y_€d Z[ bei Z_ij_djei Yk[hfei' bWicWiWi]hWl_jWjeh_Wi'fehgk[ Z[ [bbWiZ_cWdWdbWi\k[hpWi' o bWicWiWi_d[hY_Wb[i'fehgk[YedZ_Y_edWd[b cel_c_[dje Z[ YWZWYk[hfe) L[ jhWjWZ[ l[h bWceZ_\_YWY_€dgk[[d bWiebkY_€dWi~eXj[d_ZW_djheZkY[ bWb[o Z[ fhefehY_edWb_ZWZ5

S2'-U

Yed bWgk[ i[ _djheZkY[ bWYedijWdj[ _d[bkZ_Xb[4&>ijW b[o ^Wi[hl_Ze fWhW[b_c_dWhZ[ jeZWi bWi[YkWY_ed[ibWcWiW]hWl_jWje(

h_W'Yed be gk[ [b i_ij[cW \kdZWc[djWb i[ Yedl_[hj[ [d5

S2'.U

K

OBB) FH=H => IE:GM>:K EHL IKH;E>F:L ()

o i[ ikfh_c[ [b ikX~dZ_Y['fehgk[ i[ ieXh[d j_[dZ[ gk[ i[ jhWjWi_[cfh[ Z[ cWiWi_d[hY_Wb[i)=[ Wgk~h[ikbjW gk[' WbfbWdj[WhYkWbgk_[hfheXb[cW' XWijWh|jecWh[d Yedi_Z[hWY_€dbWicWiWi _d[hY_Wb[iWYedZ_Y_€dZ[ W]h[]WhbWYedijWdj[ 4&@hWY_WiW S2'-U gk[ZW Wi[]khWZWbW_Z[dj_ZWZZ[ bWiiebkY_ed[i eXj[d_ZWifehWcXei fheY[Z_c_[djei) =[iZ[ bk[]e' bWikfh[i_€d Z[ jeZWi bWicWiWi ]hWl_jWje(h_Wii_cfb_\_YW]hWdZ[c[dj[ bei fheXb[cWi)

Ee Z_Y^eZ[ bWYedijWdj[ Z[ bW]hWl_jWY_€d[i Wfb_YWXb[WbWiZ[c|i YedijWdj[ikd_l[hiWb[i) >d l_hjkZ Z[ dk[ijhe feijkbWZe' i€be ied _d[bkZ_Xb[ibWigk[ \_]kh[dYece \WYjeh[iZ[ fhefehY_edWb_ZWZ[djh[ Zei cW]d_jkZ[i fh_cWh_Wi_di[fWhWXb[i'feh be gk[ WfWh[Y[h|d[d [YkWY_ed[ijWb[iYece5

>ijW [YkWY_€dfeZh| i[hl_h' Yece [d [b YWieZ[ bWb[o Z[ bW]hWl_jWY_€d'fWhWZ[ij[hhWhZ[ jeZWbW?~i_YWkdW Z[ bWicW]d_jkZ[i Pb e c+! Yed bWi_cfb_\_YWY_€dYedi_]k_[dj[ Z[ jeZei Wgk[bbeifheXb[cWi [d gk[ [ijkl_[i[ fh[l_ijW ik _dj[hl[d(Y_€d'f[he WYedZ_Y_€dZ[ W]h[]WhbWYedijWdj[ +' Yed ik Z_c[di_€d YWhWYj[h~ij_YW'WbWb_ijWZ[ cW]d_jkZ[i)

BZOL WPdOP []Z[Z]NTZYLWTOLOPY_]P OZ^ XLRYT_`OP^ []TXL]TL^ TY^P[L]LMWP^[P]XT_PTRYZ]L] WLPcT^_PYNTLOP`YL OPPWWLL NZYOTNTmYOPTY_]ZO`NT]WLNZ]]P^[ZY&OTPY_PNZY^_LY_P YTaP]^LW'

<WZWl[p gk[ i[ fh[i[dj[ bWeYWi_€d'Yed\_hcWh[cei bWW\_hcWY_€dfh[Y[Z[dj[)Ieh W^ehW'dei b_c_jWh[cei W[dkdY_WhkdW_cfehjWdj[ Yedi[Yk[dY_W)

Lkf€d]Wi[ gk[ [d Z[j[hc_dWZWj[eh~Wi[ Z[iYkXh[ kdW dk[lW b[o kd_l[hiWbgk[ de _dlWb_Z['i_de gk[ i[ W]h[]k[ WbWioW[ijWXb[Y_ZWi)xF[`ehWh| feh [bbebW_d\ehcWY_€dgk[ fk[Z[ fhefehY_edWh[b :d|b_i_i Z_c[di_edWb9 EWh[ifk[ijW [id[]Wj_lWi_ bWb[o [d Yk[ij_€d [ijWXb[Y[kdWfhefehY_edWb_ZWZ[djh[ cW]d_jkZ[ifh_cWh_WioW[d kie' fk[i be •d_Ye gk[ feZh| ^WY[hi[[i Z[ij[hhWhkdW Z[ [bbWi_djheZkY_[dZe bWh[if[Yj_lW YedijWdj[ kd_l[hiWb) <ed [bbe i[ i_cfb_\_YWh|dbeiY|bYkbei'f[he bWiiebkY_ed[i ZWZWifeh Z_Y^eWd|b_i_ii[]k_h|d i_[dZe bWic_icWi)

+" 6?N @?NCNPIFQCMN?GCN"

<WZWYedijWdj[ kd_l[hiWbj_[d[ ik h[if[Yj_lW Z_c[di_€d' o [b gk[ i[ fh[i[dj[i_[cfh[ Yed _]kWbYkWdj~Wde [i eXij|Ykbe fWhWgk[ \_]kh[ [d bWXWi[Z[ kd i_i(j[cW Z_c[di_edWb)<ed [ije' i[ j_[d[ bWfei_X_b_ZWZZ[ [b[]_h WhX_jhWh_Wc[dj[ikkd_ZWZWb\ehcWh i_ij[cWi Ye^[h[dj[i' o fk[Z[ [b[]_hi[ Z[ ceZe gk[ bWYedi(jWdj[ WZgk_[hW[b lWbeh,) Ge ^Wo' fk[i' _dYedl[d_[dj[ [d WZefjWhi_ij[cWi Z[kd_ZWZ[i[d gk[ lWb]W, bWYedijWdj[ Z[ bW]hWl_jWY_€d'e [d jecWh Yece kd_ZW(Z[i Wb]kdWiZ[ bWiYedijWdj[i Z[b lWY~e'jWb[i Yece bWl[beY_ZWZZ[ bWbkp' bWYedijWdj[ Z_[b}Yjh_YW'bWf[hc[WX_b_ZWZcW]d}j_YW'Yed bWiebWYedZ_Y_€dZ[ gk[bWikd_ZWZ[i[iYe]_ZWiYehh[ifedZWd WcW]d_jkZ[i Z_c[di_edWbc[dj[ _dZ[f[d(Z_[dj[i Z[ WYk[hZeYed [b Yh_j[h_e[ijWXb[Y_Ze[d [b s , Z[b YWf~jkbeO)

>d ?~i_YWi[ Z_ifed[ Z[ c|i YedijWdj[i Z_c[di_edWbc[dj[ _dZ[f[dZ_[dj[i gk[bWid[Y[iWh_WifWhW\ehcWh kdW XWi[Yecfb[jW' Z[ ZedZ[ h[ikbjWbWfei_X_b_ZWZZ[ Yh[WhckY^Wi ML^P^`YTaP]^LWP^%i_d gk[ ^WoWhWp€dfWhWWjh_Xk_hc}h_jei[if[Y_Wb[iWd_d]kdW Z[ [bbWi)

Page 45: Análisis dimensional

)# :GyEBLBL =BF>GLBHG:EOBB) FH=H => IE:GM>:K EHL IKH;E>F:L 4,

K

>b [cfb[e Z[ kdWXWi[kd_l[hiWbZ[j[hc_dWZWfeZh| i[h Y€ceZe [d Wb]kdeiYWiei' f[he Yece [bbe de Wbj[hW[b i_ij[cW Z_c[di_edWb' de fk[Z[ [di[•WhdeidWZWdk[le)

NdWYeiW[i [b[]_h WhX_jhWh_Wc[dj[bWikd_ZWZ[iZ[ bWXWi[o ejhW[i Z[ife`WhZ[ ik Z_c[di_€d WbWh[if[Yj_lW cW]d_jkZ) >b jecWh Yece kd_ZWZbWl[beY_ZWZZ[ bWbkp [d [b lWY~e'feh [`[cfbe' de Wkjeh_pWWWjh_Xk_hZ_c[di_€d dkbWWbWl[beY_ZWZo WYedi_Z[hWhbWbed]_jkZ o [b j_[cfe Yece cW]d_jkZ[i ^ece]}d[Wigk[ fk[Z[d c[Z_hi[ Yed bWc_icW kd_ZWZ)<WZWl[p gk[ i[ Z[ife`W Z[ ik Z_(c[di_€d WkdWcW]d_jkZ i[ ckj_bWbWXWi['Yedbegk[ [b Yh_j[h_eZ[ ^ece][d[_ZWZf_[hZ[ [d [\_YWY_Wo [b :d|b_i_i Z_c[di_edWbfk[Z[ YedZkY_hWiebkY_ed[i [hhWZWifeh bWWfWh_Y_€dZ[ cedec_ei [ifkh_ei) Bdi_ij_cei [d [ijWi Yedi_Z[hWY_ed[i'gk[fk[Z[d fWh[Y[hjh_l_Wb[i'fehgk[ h[ik[bl[d [b l_[`e o Wkd[dYedWZefheXb[cW Z[i_ fheY[Z[ e de fh_lWh Z[ Z_c[di_€d WbWYedijWdj[ Z_[b}Yjh_YWZ[b lWY~e)MWbZ[ife`e i€be fk[Z[ j[d[h Yedi[Yk[dY_Wi\kd[ijWi' o bWYe[n_ij[dY_W_d[bkZ_Xb[Z[ Zei i_ij[cWi Z_\[h[dj[i Z[ kd_ZWZ[i[d kdW c_icW j[eh~W[i Xk[dWfhk[XWZ[ [bbe)

L[ Z_iYkj[ WYjkWbc[dj[WY[hYWZ[ be gk[ i_]d_\_YWbW[YkWY_€d

] / cT# dU# eV%

gk[ [nfh[iW [b i[]c[dje Z_h_]_ZeT[d \kdY_€dZ[ iki Yecfed[dj[i p' d%p'o Z[ bei aPN_Z]P^YT_L]TZ^M$N$O$jecWZei Wbe bWh]eZ[ YWZWkde Z[ bei[`[i YeehZ[dWZei)<ece [ijW[YkWY_€dde h[bWY_edWc|i gk[ bed]_jkZ[i' gk[ied cW]d_jkZ[i Z_h[YjWc[dj[YecfWhWXb[i'de ^Wo_dYedl[d_[dj[ [d Yed(i_Z[hWhbWYece kdW[YkWY_€d[djh[ YWdj_ZWZ[io' fk[ije gk[ c%d%e iedbWic[Z_ZWiZ[ bWiYeehZ[dWZWi'bWi_'U%V ^WXh|dZ[ h[fh[i[djWh bWih[if[Y(j_lWikd_ZWZ[i)<WZWj}hc_de h[fh[i[djW' fk[i' kdWYWdj_ZWZo beYehh[Yjei[h~W[iYh_X_h5

"T#7 TT 7 cT# dU# eV'

," 0FNAMFHFI?AF\IBCG?NBFHCINFJICNBCGCNK?AFJ"

<ed hWp€dW\_hcWAkdjb[o #0,$ gk[ Z[iZ[ bei j_[cfei Z[ ?ekh_[h dei[ ^Wh[Wb_pWZe[d :d|b_i_i Z_c[di_edWbkd WlWdY[YecfWhWXb[Wbbe]hWZeYed [b c}jeZe gk[ }bZ[dec_dW Z[ bWiYecfed[dj[i tZ[ bWiZ_c[di_ed[i\kdZWc[djWb[iw'fk[i' [d [\[Yje' Wfb_Y|dZebeZ[X_ZWc[dj[ i[ Yedi_]k[[d ckY^ei YWieikdW_d\ehcWY_€dckY^e c|i Yecfb[jW gk[ bWgk[ i[eXj[dZh~Wfeh [b c}jeZe Yb|i_Ye#%$)

>b c}jeZe fhefk[ije feh Akdjb[o Yedi_ij[ [d h[[cfbWpWhbWXWi["6$ 7$ ;# feh ejhWgk[ i[ eXj_[d[ Yedi_Z[hWdZefeh i[fWhWZebWijh[iYecfed[dj[i' <c%<d% <e%Z[ bWbed]_jkZ o Z_ij_d]k_[dZe [djh[ bWcWiW_d[hY_Wb'7!5$ o bW]hWl_jWjeh_W'7 K$ Yed be gk[ i[ Yedl_[hj[ [d i[_i bWckbj_fb_Y_ZWZZ[ bWXWi[)

B]dehWAkdjb[o [b j[eh[cW Z[ f_' o bei bWh]eihWpedWc_[djeiYed gk[jhWjWZ[ `kij_\_YWhik c}jeZe de fWh[Y[dcko Yedl_dY[dj[i) =[iZ[ bk[]e'feh bWihWped[i[nfk[ijWi [d [b s 2' de [i Z[ [if[hWh gk[ i[ Yedi_]WdWZWdk[le ^WY_[dZe_dj[hl[d_h i_ckbj|d[Wc[dj[ [d bWXWi[=T o = K& I[hebW'Z_iYh_c_dWY_€dZ[ bWijh[i Z_c[di_ed[i Z[b [ifWY_eYedij_jko[ kd ]hWdWY_[hje'o fk[Z[ hWpedWhi[\|Y_bc[dj[ Yed Wkn_b_eZ[ dk[ijhW j[eh~W)

>ijW ikcW' Z[ WYk[hZeYed be Z_Y^e[d [b s / Z[b YWf~jkbeBO' [i l|(b_ZWjWdi€be fWhWbei [\[Yjei Z[b Y|bYkbel[Yjeh_Wb'fk[i de ZWbWc_ice'[d ][d[hWb' h[Yehh[h[b i[]c[dje T gk[ bWb~d[Wgk[XhWZW\ehcWZWfehiki Yecfed[dj[i)

<ed Whh[]beWdk[ijhW _dj[hfh[jWY_€d'i[h|5

>d fheXb[cWi [d gk[ jeZWi bWiZ_h[YY_ed[ii[Wd [gk_lWb[dj[i' [ij|_dZ_YWZejecWh bWc_icW kd_ZWZ[d jeZWiZ_h[YY_ed[i'f[he [d ejhei YWiei'Yece ikY[Z[ [d <h_ijWbe]hW\~W'^Wo l[djW`W [d kj_b_pWhkd_ZWZ[iZ_\[(h[dj[i [d YWZW[`[' o [iYh_X_h5

"T# / c!T!# d!U!# e!V!%i_[dZe5

_"7 C_i N!/ <! 5. O! / <!^

Yed be YkWb5

= N

N!

<d '

<! 5 !_"

) #%$ <ehde Wdj[Y[Z[dj[ Z[b c}jeZe Z[ Akdjb[o fk[Z[ Y_jWhi[[b _dj[dje Z[cjhe)Zk<BhbWiZ_c[di_ed[i l[Yjeh_Wb[i_di_dkWZefeh @k_bbWkc[#0-$ [d bWXhW(ZN<<B€d\hWdY[iWZ[b Whj~YkbeZ[ Kkd][ #0.$) E[l_ #..$ Yh_j_YW[ij[ _dj[dje' oW\_hcWgk[ tfheXWXb[c[dj[ de j[dZh| d_d]kdW kj_b_ZWZw)>d bei YWf~jkbeii_(]k~[dj[i Yh[[cei ^WX[hZ[ceijhWZe gk[' feh [b YedjhWh_e'[b c}jeZe Z[ bWZ~i(Yh_hd_dWe_€dZ[ bWiZ_c[di_ed[i [ifWY_Wb[i[i Z[ ]hWd \[YkdZ_ZWZ)IWhWc|ifehc[deh[i l}Wi[ [b Whj~YkbeZ[ C)=~Wp;[`WhWde' 7Y_P^ IT^TNZ d /`!]P[]P^PY_L&NTmYXL_PXj_TNL%[d @Pa'@' 4NLO' 5TPYNTLOP=LO]TO%j) EOB' \Wi[) .)+ o /)u',41-)

be YkWbi_]d_\_YW'feh be Z_Y^e[d [b s , Z[b YWf~jkbeO' gk[ i[ fk[Z[ Wjh_(Xk_hZ_ij_djW\€hckbWZ_c[di_edWbWbei i[]c[djei Z_h_]_Zeii[]•d YWZWkde Z[ bei [`[i5

C!cBYC/ %%/ <c1

)c

) dBZC/ k6(/ _'1

MT$B[C / %% / <e'

_T%

Page 46: Análisis dimensional

:GyEBLBL =bF> LBH ):E

=_Y^ei i[]c[djei i[ YecfehjWd' fk[i' Yece cW]d_jkZ[i Z_c[di_e(dWbc[dj[ _dZ[f[dZ_[dj[i) <ed [bbWi'bWcWiWo [b j_[cfe' i[ \ehcW kdWXWi[Z[ Y_dYecW]d_jkZ[i' o fWhWh[fh[i[djWh bWZ_c[di_€d Z[ ejhWcW]d_jkZ YkWbgk_[hWWh| \WbjWkd [ifWY_eWXijhWYje\ehcWZe feh bWijh[i Z_c[di_ed[i Z[b [ifWY_eehZ_dWh_e'bWcWiWo [b j_[cfe)

L[]•d [ije' bW\€hckbWZ_c[di_edWbZ[ kd l[Yjeh gk[ i[ ^Wbb[Z_h_]_Zei[]•d [b [`[ c%feh [`[cfbe' de i[h| <]c=fBG% i_de <]cc<)d<>e=fBG'

Ieh [`[cfbe' bWi\€hckbWiZ_c[di_edWb[i5

i_]d_\_YWdgk[' i_ [d [b [`[ F i[ YWcX_W[b Y[dj~c[jhe feh [b c[jhe' o i[Yedi[hlW[b Y[dj~c[jhe [d bei ejhei Zei [`[i' bWkd_ZWZZ[ \k[hpWYe^[(h[dj[ Yed bW[YkWY_€d

Q2XL

i[]k_h| i_[dZe bWZ_dW[d bei [`[i @$A$f[he lWbZh|,++ Z_dWi[d [b [`[ ?&>ijW Z_iYh_c_dWY_€d^WY[Wkc[djWh[b d•c[he Z[ [YkWY_ed[i[d bei

fheXb[cWi Z[ :d|b_i_i Z_c[di_edWb'Yed be gk[ Z_ic_dko[ [b d•c[he Z[cedec_ei f_ _dZ[f[dZ_[dj[i' F bWiebkY_€d]WdW[d fh[Y_i_€d)

:b]kdei [`[cfbei i[hl_h|d fWhWceijhWh Y€ce i[ Wfb_YW[b c}jeZe gk[^[cei Z[dec_dWZe Z[ bWZ_iYh_c_dWY_€dZ[ bWiZ_c[di_ed[i [ifWY_Wb[i)

$#" >JGPHCI BCGK?M?GCGCKZKCBJ"

L[ )iWX[feh @[ec[jh~W gk[ i_ i[ ckbj_fb_YWfeh kd \WYjeh'O$kdWYkWbgk_[hWZ[ bWiWh_ijWiZ[ kd fWhWb[b[f~f[Ze'Z[`WdZe_dlWh_WXb[ibWiejhWiZei' [b lebkc[d i[ ^WY[V l[Y[i cWoeh' be gk[ _dZ_YWgk[ [b lebk(c[d [i fhefehY_edWbW YWZWkdW Z[ bWiZ_c[di_ed[i [ifWY_Wb[io ik\€hckbWZ_c[di_edWbZ_iYh_c_dWZWi[h|5

=q [ij[ ceZe' i_ i[ gk_[h[ Wl[h_]kWh[b lebkc[d Z[ kd fWhWb[b[f~f[ZeZ[ Wh_ijWiL%F$[' i[ fheY[Z[h| Wi~5

D L F [

&- , , H H&$% , H , H&- , H H ,

(. , ( , ( , (,

O_b) FH=H => IE:GM>:K EHL IKH;E>F:L 4.

o bWiebkY_€d[i5

i_[dZe Yf kdW\kdY_€dZ[ bei |d]kbei) L_[b fWhWb[b[f~f[Ze[i h[YjWd]kbWh'Z_Y^W\kdY_€di[ h[ZkY[ Wkd d•c[he \_`e' Wbgk[ i[ fk[Z[ Wjh_Xk_h[blWbeh,' Q gk[ZW5

a / LMN%

gk[ Z[\_d[ bWkd_ZWZZ[ lebkc[d i_ i[ ZWbWkd_ZWZZ[ bed]_jkZ)L_ de i[ ^kX_[i[d Z_iYh_c_dWZebWiZ_c[di_ed[i [ifWY_Wb[i'i[h~W

B=C / 6E$o bWiebkY_€d kX_[i[ i_Ze5

gk[' [l_Z[dj[c[dj[' ikc_d_ijhWc[dei _d\ehcWY_€d)

$$" -GA?IACBCPI KMJSCAOFG"

E# L[ bWdpWkd fheo[Yj_bZ[ cWiWQ$ [d Z_h[YY_€deh_pedjWb'YedkdWl[beY_ZWZ_d_Y_Wba%Z[iZ[ kdWWbjkhWL& AWbbWh[b WbYWdY['c%[ije [i' bWZ_ijWdY_Weh_pedjWbWijW[b fkdje Z[ _cfWYje L / H)

LebkY_€d5

<ed bWicW]d_jkZ[i c[dY_edWZWi[d [b [dkdY_WZe'o Yed [b f[ie X / QK$

h[ikbjWYed [b c}jeZe Yb|i_Yekd \WYjehZ[ \ehcW' c(S%o kd cedec_e f_5

LX LK(E!H/%%/%%$

Xa+ a+

feh be gk[ bWiebkY_€d[i5

F gk[ZW _dZ[j[hc_dWZWbW\kdY_€d .C&>d YWcX_e'Z_iYh_c_dWdZebWiYecfed[dj[i i[]•d [b [`[ ^eh_pedjWb'c%F [b

l[hj_YWb'[' de ^Wo \WYjehZ[ \ehcW' o [b fheXb[cW i[ fbWdj[Wo h[ik[bl[ Yecei_]k[5

c a X b S

&- , , H H H&# H H H , ,= H H , , HB H (, H (- H

(. , (, ( ,*- ,*- ( ,*-

Page 47: Análisis dimensional

c2 Za D*'

4/ :GyEBLBL =BF>GLBHG:E

<ece de ^Wo i_de kd cedec_e f_' de WfWh[Y[\kdY_€d Z[iYedeY_ZW'o bWie(

bkY_€d[i5

>b Y|bYkbeYecfb[je ZW8 / O_

F# >d [b fheXb[cWWdj[h_ehi[ ikfed[ L / Ho' [d YWcX_e'bWl[be(Y_ZWZ_d_Y_Wb\ehcW [b |d]kbe Z0 Yed[b fbWde eh_pedjWb)

>d [b fbWdj[Wc_[dje WbWcWd[hWYb|i_YW'Z[iWfWh[Y[bWWbjkhWL$f[he WfWh[Y[[b dk[le \WYjehZ[ \ehcW L%gk[ `kdjWc[dj[ Yed [b cedec_e

<:I~MNEH OBBBcb cR

(/%% /%%Xa+ a+ 058U75/- 01 <W6509< ;V3509<

YedZkY[WbWiebkY_€d5

a+

F / % GS"E#&K $" 7?EIFOPBCNKMFH?MF?N"

R

:fWhj[ Z[ bWicW]d_jkZ[i [ifWY_Wb[io Z[b j_[cfe' i[ ef[hW [d F[(Y|d_YWYedjh[i cW]d_jkZ[i fh_cWh_Wi5\k[hpW'cWiW_d[hY_Wbo cWiW]hW(l_jWjeh_W)Lk Z[\_d_Y_€d[f_ij}c_YWYedi_ij_h|[d bWZ[iYh_fY_€dZ[b[\[YjeeXi[hlWXb[YWhWYj[h~ij_Yeo' fWhWgk[ WZgk_[hWd[b YWh|Yj[hZ[ cW]d_jkZ[i\~i_YWi'[i fh[Y_ie[ijWXb[Y[hfWhWYWZWkdW'Z[ WYk[hZeYedbe Z_Y^e[d [bYWf~jkbeA$[b feijkbWZegk[ f[hc_j[ Z[\_d_hbWhWp€d[djh[ iki YWdj_ZW(Z[i feh l~Wef[hWjeh_Wo kd_l[hiWb'e X_[d[b feijkbWZe[d gk[ i[ XWiWbWZ[\_d_Y_€dZ[ bWikcW)

8`P]eL "Q#' >dj[ feh YkoWl_hjkZ i[ ceZ_\_YW[b cel_c_[dje Z[ beiYk[hfei h~]_Zei[d kdWZ_h[YY_€dZ[j[hc_dWZW)L[ feijkbW gk[ bWi\k[h(pWiYe[n_ij[dj[i [d kd c_ice fkdje i[ ikcWd feh bWh[]bWZ[bfeb~]ede6ied l[Yjeh[i #%$)

=L^L TYP]NTLW"X%#' >dj[ feh YkoWl_hjkZ YWZWYk[hfe h[gk_[h[\k[hpWiZ_\[h[dj[i fWhWgk[ [d }b i[ fheZkpYWkd c_ice YWcX_eZ[cel_c_[dje) L[ feijkbW gk[ bWcWiW_d[hY_Wb[i WZ_j_lWfeh WYkck(bWY_€d)

=L^L R]LaT_L_Z]TL"XR#' >dj[ [d YkoWl_hjkZ YWZWYk[hfe [`[hY[WYY_ed[iWjhWYj_lWiieXh[ bei Z[c|i) L[ feijkbW gk[ bWcWiW]hWl_jWjeh_W[i jWcX_}dWZ_j_lWfeh WYkckbWY_€d)

=_iYh_c_dWdZebWiYecfed[dj[i l[Yjeh_Wb[i'[b fheXb[cW i[ fbWdj[Wo h[ik[b(l[ Yece i_]k[5

c X *e *e b

<e $ 3 $ 3 3<e 3 3 3 $ $7 3 $ 3 3 $; 3 3 !$ !$ !%

!, $ !$ !$ !$ $

S2 -1 _7 $

o' Yece de ^Wod_d]•d \WYjehZ[ \ehcW' bWiebkY_€d[i5

c / 8 aeae+ !

e X_[d' Yece =Y 7 W Yei E.! =[ 7 W i[d E-

a+ i[d L Yei L

>d bWiebkY_€dYecfb[jW [i > / -)

>d bei YWf~jkbeii_]k_[dj[i j[dZh[cei eYWi_€dZ[ Wfb_YWh[ij[ c}jeZeWZ_l[hiei fheXb[cWi)

#%$ EWi \k[hpWi fheZkY[d jWcX_}d Z[\ehcWY_ed[i' o [ij[ [\[Yje fk[Z[jecWhi[ Yece Z[\_d_Y_€d[f_ij}c_YW) EWb[o Z[ bW_]kWbZWZZ[ bWWYY_€do bWh[WYY_€d]WhWdj_pWgk[ i[ eXj[dZh| [b c_ice h[ikbjWZe WbYecfWhWhbWi\k[hpWieXi[hlWdZe cel_c_[djei gk[ eXi[hlWdZe Z[\ehcWY_ed[i)

Page 48: Análisis dimensional

*2QKQ!K&

- ":

OBBB) =BGyFB<: => L{EB=HL Kz@B=HL )'41 :GyEBLBL =BF>GLBHG:E

>ijWi jh[i cW]d_jkZ[i' `kdjWc[dj[ Yed bWbed]_jkZ' ^%o [b j_[c(fe' _%\ehcWd [b i_ij[cW Z[ cW]d_jkZ[i fh_cWh_WiZ[ bWF[Y|d_YW)MeZWibWiZ[c|i ied cW]d_jkZ[i i[YkdZWh_Wigk[ i[ _djheZkY[dc[Z_Wdj[ bWh[if[Yj_lW \€hckbWZ[ Z[\_d_Y_€d)

IWhW WbbWh[b \WYjehZ[ fhefehY_edWb_ZWZ4$ XWijWWbbWh[nf[h_c[djWbc[dj[bW\k[hpWgk[ i[ [`[hY[ [djh[ Zei cWiWi' X o X!%YebeYWZWiWkdW Z_ijWdY_W%o Wfb_YWhbW•bj_cW [YkWY_€d\kdZWc[djWb)EWc[Z_ZWZ[ 9 Z[f[dZ[h| Z[ bWikd_(ZWZ[iZ[ \k[hpW'cWiWo bed]_jkZ) :i~ i[ ^WeXj[d_Ze5

%" 1AP?AFJICNDPIB?HCIO?GCN"9 / #1'12 J +'+4$ n ,+(3 Yc

L

] P 4)

<edl_[d[ ^WY[hdejWhgk[ bWcWiW_d[hj[ o bWcWiW]hWl_jWjeh_Wied _dYed\kd(Z_Xb[i)Lki Z[\_d_Y_ed[i'jWdje [f_ij}c_YWi Yece YkWdj_jWj_lWi'ied [dj[hWc[dj[Z_ij_djWi' feh be gk[ [b c}jeZe gk[ i_hlWfWhWc[Z_h bWkdW de i[hl_h| fWhWc[Z_h Z_h[YjWc[dj[ bWejhW)>ijWi Y_hYkdijWdY_Wii[ jhWZkY[d[d [b ^[Y^e Z[j[d[h WcXWicW]d_jkZ[i Z_c[di_ed[i Z_\[h[dj[i o c[Z_ZWi Z_ij_djWi [d YkWb(gk_[h i_ij[cW Ye^[h[dj[ Z[ kd_ZWZ[i[d gk[ de i[W 9 / ,) >d [b i_ij[cW N'K&A'%feh [`[cfbe' bWcWiW]hWl_jWjeh_WZ[ , ]hWce Z[ cWiW_d[hY_WblWb[5X 7 r*@7/ -'03 P ,+((! kd_ZWZ[i Y[][i_cWb[i) Ieh [ijWi hWped[i' de i[ `kij_\_YW[b gk[Wb]kdei Wkjeh[i' feh [`[cfbe' Lecc[h\[bZ #0/$' W\_hc[d gk[ WcXWi[if[Y_[i Z[cWiWied kdWc_icW YeiW"X^NSbP] / X_]LR#%be gk[ [gk_lWb[ W^WY[h4 / ,' Z[WYk[hZeYeWbe gk[ fhefed[ FWhj_dej(EW]WhZ[#/4$)

EWi Y_dYecW]d_jkZ[i c[Y|d_YWi fh_cWh_Wi[ij|d b_]WZWifeh jh[i[YkWY_ed[i\kdZWc[djWb[i5

o' Z[ WYk[hZeYed [b i[]kdZe feijkbWZe' i€be bWj[hY[hWh[gk_[h[ bWfh[(i[dY_WZ[ kdWYedijWdj[ kd_l[hiWb):Z[c|i' [ijW [YkWY_€df[hc_j[ [b_(c_dWhQK Z[ jeZWibWi[YkWY_ed[i'o oWde i[h| fh[Y_ie ^WXbWhZ[ cWiWi]hWl_jWjeh_Wi)<ed [ije' i€be gk[ZWdYkWjhecW]d_jkZ[i fh_cWh_Wio Zei[YkWY_ed[i\kdZWc[djWb[i5

(0 4 QQ!- ":

&" <FNOCH?BFHCINFJI?G"

L[]•d i[ l_e oW[d [b s , Z[b YWf~jkbeO' fWhW\ehcWh [b i_ij[cWZ_c[di_edWbZ[ bWicW]d_jkZ[i c[Y|d_YWii[ h[gk_[h[d jh[i cW]d_jkZ[iX|i_YWi'o i[ ^WYedl[d_Ze [d gk[ i[WdbWbed]_jkZ' bWcWiWo [b j_[cfe)>d [b c_ice bk]Whi[ eXjkl_[hed bWi\€hckbWi Z_c[di_edWb[i Z[ bWiZ[c|i cW]d_jkZ[i fh_cWh_Wi5ZedZ[ X 7 X%[i bWcWiW_d[hY_Wb)

<kWdZei[ jhWjWZ[ kd i_ij[cW Z[ Yk[hfei YkoWiWYY_ed[i]hWl_jWje(h_WickjkWi ied _dYecfWhWXb[c[dj[c[deh[i gk[ bWi[`[hY_ZWiieXh[ [bbeifeh bWWjhWYY_€dj[hh[ijh[' XWijWh|jecWh [d Yedi_Z[hWY_€d'WZ[c|i Z[bj_[cfe' Z[ bWiYeehZ[dWZWigk[ Z[\_dWdbWYed\_]khWY_€dZ[b i_ij[cW oZ[ bWi\k[hpWiZ[ ejhW~dZeb['bWcWiW_d[hY_Wb'X%Z[ YWZWYk[hfe' o ikf[ie X / QK&

IQJ 7 67;%).

o Z[ bWYedijWdj[Z[ bW]hWl_jWY_€d5

B4C / =7%5;%)&

<ece jeZei bei Yk[hfei Yedj_[d[d YWdj_ZWZ[ifhefehY_edWb[i Z[ WcXWi[if[Y_[i Z[ cWiW' XWijWh|c[Z_h kdWZ[ [bbWio ^WbbWhkdWl[p fWhWi_[cfh[' [b\WYjehZ[ fhefehY_edWb_ZWZ)EWc[Z_ZW Z[ cWiWi _d[hY_Wb[i[n_]_h~Wef[hWh Yed\k[hpWi' bed]_jkZ[i o j_[cfei) >d l[p Z[ fheY[Z[h Wi~'i[ h[Ykhh[ WbWXWbWdpW'gk[ i_hl[ fWhWYecfWhWhcWiWi]hWl_jWjeh_Wi)<kWdZebWXWbWdpW[ij| [d [gk_b_(Xh_e ied _]kWb[i bWicWiWi ]hWl_jWjeh_WiZ[ bei Yk[hfei YebeYWZei[d WcXeifbWj_bbeio' feh bWb[o Z[ fhefehY_edWb_ZWZ'i[h|d jWcX_}d_]kWb[ibWicWiWi_d[h(Y_Wb[i)Jk[ZW Wi~ kij_\_YWZe[b kie Z[ bWXWbWdpWfWhWc[Z_h bWcWiWgk[ \_]khW[d bWfh_c[hW Z[ bWib[o[i Z[ G[mjed) =[iZ[ bk[]e' bWcWiW gk[ Wi~i[ c_Z[[i bWXL^L PY ]P[Z^Z' EWXWbWdpWde i_hl[ fWhWc[Z_h bWicWiWi Z[ Yk[hfei gk[i[ ck[l[d Yed h[bWY_€dWbeXi[hlWZeh' f[he [d bWc[Y|d_YW d[mjed_WdWi[ ZWfeh ikfk[ije gk[ WLXL^L OP`Y N`P][Z YZ OP[PYOPOPWLaPWZNTOLONZY\`P ^P X`PaP'

EWi\€hckbWiZ_c[di_edWb[iZ[ bWicW]d_jkZ[i i[YkdZWh_Wii[ Z[Zk(Y[d _dc[Z_WjWc[dj[ WfWhj_hZ[ iki \€hckbWiZ[ Z[\_d_Y_€d)

Ieh [`[cfbe5

O[beY_ZWZ5Zi

a2&Kh& O_!

BWC/ 6;%P

:Y[b[hWY_€d5:-i

E0%%& O_+

B>C / IP Yei [n6

BEC7 6;%)

MhWXW`e5 B>C 0=7;%)&

:GyEBLBL =BF>GLBHG:E)(2

Page 49: Análisis dimensional

)( :GyEBLBL =BF>GLBHG:E OBBB) =BGyFB<: => L{EB=HL K~@B=HL ))

EW[d[h]~WWZgk_[h[[b hWd]e Z[ cW]d_jkZ fh_cWh_W]hWY_WiWkdfh_dY_f_eZ[ Yedi[hlWY_€dc[hY[Z WbYkWbkdWYkWdj~WZWZWZ[ [d[h]~Wfk[Z[ WZefjWhZ_l[hiWi\ehcWi #c[Y|d_YW'j}hc_YW'[b}Yjh_YW'[jY)$gk[ied [gk_lWb[dj[i [d [b i[dj_Ze Z[ gk[ YedjeZWi[bbWifk[Z[ eXj[d[hi[ [bc_ice jhWXW`e'[ije [i' b[lWdjWhkd f[ie ^WijWbWc_icW WbjkhW)

>f_ij}c_YWc[dj[' bW[d[h]~Wi[ Z[\_d_h|Yece [b [dj[ YWfWpZ[ h[Wb_(pWhjhWXW`e'o [b fh_dY_f_eZ[ Yedi[hlWY_€df[hc_j[ Z[Y_hgk[ kdW[d[h]~W[i [gk_lWb[dj[ WbWikcW Z[ ejhWiZei YkWdZeYed bWfh_c[hWi[ fk[Z[b[lWdjWhkd f[ie ^WijWbWc_icW WbjkhWgk[ YedbWiejhWiZei) G€j[i[ gk[fWhWZ[\_d_hbWikcW Z[ [d[h]~Wide ^Wod[Y[i_ZWZZ[ ^WXbWhZ[ kd_ZWZ[io' feh [ie' bW[d[h]~W[i kdWcW]d_jkZ fh_cWh_W)

'" 6? CICMEZ?AJHJ H?EIFOPBKMFH?MF?"

>d bWZ_d|c_YWd[mjed_WdWbW[YkWY_€d

[i Yedi[Yk[dY_WZ[ bW[YkWY_€d\kdZWc[djWb*2 XO+^QO_+%feh be gk[ [b

_dYh[c[dje [nf[h_c[djWZe feh bW[d[h]~WY_d}j_YWlWb[5

e 1Y,d 7 BI 7 X&

Ieh ejhWfWhj[' [d bei YWcfei Yedi[hlWj_lei' feh [`[cqbe' [d bei YWq(fei ]hWl_jWjeh_ei'YWX[Z[\_d_h[d YWZWfkdje ejhWcW]d_jkZ i[YkdZWh_W'

[b fej[dY_Wb'c[Z_Wdj[ bW\€hckbW5

(" ;CQJGPAF\IBC GJNAPCMKJNACGCNOCN"

=/ ,'-'.'

=ei Yk[hfei' Z[ cWiWiX* Q X+% iec[j_Zei Wik WjhWYY_€dckjkW' i[ck[l[d Z[ ceZe gk[ i[ Yedi[hl[ _dlWh_WXb[ik Z_ijWdY_W';& <WbYkbWh[bf[h~eZe Z[ h[lebkY_€d)

EWicW]d_jkZ[i WYedi_Z[hWhied5 [b f[h~eZe' bWicWiWi'bWZ_ijWdY_WobWYedijWdj[Z[ bW]hWl_jWY_€d)<ed [bbWifk[Z[ \ehcWhi[ kd \WYjehZ[\ehcW5b 7 X+(X*o IbWdj[WZeWi~[b fheXb[cW' ik h[iebkY_€di[ bb[lWWYWXeYedWhh[]beWbi_]k_[dj[ [igk[cW5

ZedZ[ **%*+ o bWied bWiYecfed[dj[i' Yedh[bWY_€dWbei [`[i p)' c+%PWZ[bW\k[hpW'gk[ WYj•WieXh[ bWcWiWX YebeYWZW[d [b fkdje Yedi_Z[hWZe)Bdj[]hWdZe[ijW [YkWY_€dWbe bWh]eZ[ kdWYkhlWYkWbgk_[hWgk[ lWoW

Z[iZ[ [b fkdje , Wbfkdje -' h[ikbjW5

>fej V DX%

cB 9 ]

6 H H . (= H ( ( , H; , H (- H

( ,*- ,*- ( .*-

L 7 .6 =7 ,

V)0\J"\#1Q( Q5

o [ij| _dZ_YWZe[b Z[\_d_hkdWdk[lW cW]d_jkZ' bW[d[h]~Wfej[dY_Wb'c[(

Z_Wdj[bW\€hckbW5

Yedbe YkWbi[h|5( e >fej / E%

gk[ _dZ_YWgk[ [b jhWXW`e[i _]kWbWbWZ_ic_dkY_€dZ[ bW[d[h]~Wfe(

j[dY_Wb)AWijWWgk~'WcXWi\ehcWi Z[ [d[h]~W'bWY_d}j_YWo bWfej[dY_Wb'WfW(

h[Y[d Yece cW]d_jkZ[i i[YkdZWh_Wi'Yed i[dZWi \€hckbWiZ[ Z[\_d_Y_€d'

o b_]WZWifeh kdWb[o5e >Y,d / %e >fej'

o [b :d|b_i_i Z_c[di_edWbf[hc_j[ fh[Z[Y_hgk[ bei YkWZhWZeiZ[ bei j_[c(fei Z[ h[lebkY_€died fhefehY_edWb[iWbei YkXeiZ[ bei hWZ_ei'Z[ WYk[h(Ze YedbWb[o Z[ D[fb[h) K[ikbjW'WZ[c|i' gk[ i_ jeZWibWicWiWiZ[ beiYk[hfei Y[b[ij[i i[ ckbj_fb_YWi[dfeh kd c_ice \WYjeh'Yedi[hl|dZei[_dlWh_WXb[iiki Z_ijWdY_Wi'bei f[h~eZei h[ikbjWh~WdZ_l_Z_Zeifeh bWhW~pYkWZhWZWZ[ Z_Y^e\WYjeh)?_dWbc[dj[' [d Zei kd_l[hiei Z_\[h[dj[i' [dbei gk[ \k[i[ Z_ij_djWbWYedijWdj[Z[ bW]hWl_jWY_€d'bei f[h~eZei Z[ h[(gk[ [nfh[iW bWfei_Xb[ jhWdi\ehcWY_€dZ[ kdW[d ejhW)

Page 50: Análisis dimensional

,++ :GyEBLBL =BF>GLBHG:EOBBB) =BGyFB<: => L{EB=HL Kz@B=HL ,+,

lebkY_€d'W_]kWbZWZZ[ ejhWiY_hYkdijWdY_Wi'i[h~Wd_dl[hiWc[dj[ fhefeh(Y_edWb[iWbWhW~pYkWZhWZWZ[ Z_Y^WYedijWdj[)

L_bWjhWo[Yjeh_W[i [b~fj_YW_dj[hl[dZh|d bei Zei i[c_[`[i' E o F$gk[eh_]_dWd[b \WYjehZ[ \ehcW FCE$o bWiebkY_€di[h|5

L, "X M#_+/ D0 V-V' V )

Q]4 Q] E

Yece bWilWh_WXb[iied bWic_icWi' h[ikbjW5

J / >]Xb+%

o iWble [b d•c[he fkhe 8$ h[ikbjWbWc_icW [nfh[i_€d gk[ fWhWbW\k[hpW)Y[d(jh~f[jW)

+" :YIBPGJ A\IFAJ"

<ece ^[cei Z_Y^e' Akdjb[o Z[iYedeY[ [b j[eh[cW Z[ f_' o Yh[[ gk[' i_ i[eXj_[d[d lWh_ei cedec_ei Z[ Z_c[di_€d dkbW' fheY[Z[ \ehcWh ik fheZkYje)=[ [ij[ ceZe' [ _djheZkY_[dZe[d bWXWi[bWcWiW]hWl_jWjeh_WWZ[c|i Z[ bW

_d[hY_Wb'bb[]WWbWiebkY_€d

WL "X#LV) / )&&&KK- '

Q(9 Q5

Nd f}dqqe i_cfb[' Z[ cWiWX o bed]_jkZ P$]_hWZ[ ceZe gk[ [b ^_beZ[ ikif[di_€d \ehc[ Yed bWl[hj_YWb[b |d]kbe YedijWdj[ +#' <WbYkbWh[bf[h~eZe Z[ h[lebkY_€d)

<ece bW•d_YW\k[hpWgk[ _dj[hl_[d[ [d [b cel_c_[dje [i [b f[ieX 7 QK$o ^Wokd \WYjehZ[ \ehcW b 7 BP' [b fheXb[cWi[ fbWdj[WF h[(ik[bl[ Yece _dZ_YW[b i_]k_[dj[ [igk[cW5

)" 2PCMT?ACIOMZKCO?"

X b

6 H , H ,7 H H , ,B , H H (-

$+$ , ( ,*- ( ,*- ,*-

S 7 .6 =7 (

. *"QP 5_ 7 (((5666N"BP$ 7 R N"BP$)

o de YW[[d bWYk[djWZ[ gk[ [i _dWZc_i_Xb['fehgk[ ^Wokd [nfed[dj[ gk[ de[i d•c[he \_`e) >ij[ [`[cfbe XWijWfWhWZ[ceijhWh gk[ de Z[X[d \_]khWh[d bW

XWi[bWiZei cWiWi' _d[hY_Wbo ]hWl_jWjeh_W)

_Jk} \k[hpW Wogk[ Wfb_YWhWkd Yk[hfe Z[ cWiWX fWhWgk[ Z[iYh_(XWkdWY_hYkd\[h[dY_WZ[ hWZ_e] YedbWl[beY_ZWZWd]kbWh;B G

IbWdj[Wc_[djeo iebkY_€d5

J T X Ye

6 , ( H H7 , H , HB (- H H %(

$+$ , (, %( (-

L 7 .6 q7 (

N0 1TQX+o

K[iqblWcei )[ij[ c_iqe fhe9b[cW Z_iYh_c_dWdZebWiYecfed[dj[i [ifWY_Wb[i)>b iqj[cW jj[d[ kd [`[ Z[ i_c[jh~W' gk[ [i l[hj_YWb'feh be gk[ bei [`[i c [ d

iqd [gN,lWbqdj[i) EW\ehcW Z[ cel_c_[dje gk[ZW Z[\_d_ZW)feh bWiZei fheo[Y(Yhed[i Zqb^_be5kdWWeieXh[ [b [`[ l[hj_YWb'o ejhW']%ieXh[ [b fbWde^eh_pedjWb)>ijW qjBcW Ye_dY_Z[Yed [b hWZ_eZ[ bW)Y_h[kd\[h[d[_WZ[iYh_jWfeh bWcWiWX'=[ bWb_ijWZ[ cW]d_jkZ[i Z[iWfWh[Y[[b |d]kbe Yn)

IbWdj[Wc_[dje o iebkY_€d5

*" =CINF\I JMFEFI?B?KJMPI HJQFHFCIOJAFMAPG?M"

_% X X ]

_'1655 H H H H ,6& H , H , H7 H H , , H; , H H (- H

$+ , ( ,*- ( ,*- ,*- H

S 7 /6 =7 ,

EWj[eh~WYecfb[jW ZW5 / b)

L[ ^WY[]_hWhkd lebWdj[ Z[ hWZ_e] o cWiWX YedbWl[beY_ZWZWd]k(bWhYe) <WbYkbWhbW\k[hpWjWd][dY_Wbgk[ be cWdj_[d[ j[die)

:kdgk[ bW\k[hpWgk[ i[ XkiYW[i Z_\[h[dj[ Z[ bWYedi_Z[hWZW[d [b fheXb[cW)Wdj[h_eh'Z[iZ[ [b fkdje Z[ l_ijW Z_c[di_edWbde i[ Z_ij_d]k[ kdW)Z[ ejhW' o

_2ZdX0 2Zdf'>d bWiebkY_€d[nWYjW[i > / %$+"

Page 51: Análisis dimensional

,+- :GyEBLBL =BF>GLBHG:E OBBB) =BGyFB<: => L{EB=HL Kz@B=HL ,+.

4) HiY_bWY_ed[if[h_€Z_YWi)

Nd i€b_Zegk[ fk[Z[ ]_hWh[d jehde Z[ kd [`[' i[ ^WbbWiec[j_Ze WkdfWh[b|ij_Ye OI$ ZedZ[ [ [i bW[bed]WY_€dWd]kbWho Okd \qYje5Z[ fhefeh(Y_edWb_ZWZ)L[ jhWjWZ[ YWbYkbWh[b f[h~eZe' ;Z% Z[ bWieie~bWY_ed[i)

E_ijWZ[ cW]d_jkZ[i5 <ece [d bei cel_c_[djei Z[ hejWY_€d_dj[hl_[(d[d bWicWiWifeh iki cec[djei Z[ _d[hY_WYedh[bWY_€dWb[`[' F bWi\k[h(pWifeh iki cec[djei' bWicW]d_jkZ[i WYedi_Z[hWh'WfWhj[Zqbf[h~eZeXkiYWZe'ied5 [b cec[dje Z[ _d[hY_W*%[b Ye[\_Y_[dj[V%gk[ LBhl[fWhWZ[\_d_h[b fWh[b|ij_Ye' o bWWcfb_jkZ' [e' gk[ i[h| kd \WYjehZ[ \ehcW)

5e * V

,,) HiY_bWY_ed[iWcehj_]kWZWi)

Nd i€b_Zei[ ck[l[ [d bWic_icWi YedZ_Y_ed[igk[ [d [b [`[h<B<BHZ[b s 4' f[he [n_ij[ kd fWh Wcehj_]kWZeh'LOP(O_%fhefehY_edWbWbWl[beY_ZWZWd]kbWh)L[ jhWjWZ[ Wl[h_]kWhY€ce Z[f[dZ[ bW[bed]WY_€d'[' Z[b j_[cfe)

EWicW]d_jkZ[i WYedi_Z[hWhied5 [' _%*%L%V%Z[ bWiYkWb[i[ [i kd\WYjehZ[ \ehcW)

6 H - -7 H , ,B , H (-

2j, , ( ,*- ,*-

S 7 -6 =7 (

( L V

6 H - - -7 H , , ,B , H ( , (-

2j, , ( ,*- H ,*-2j% H ( ,*- , ( ,*-

S / -6 T2+

;$ \ = \ q#3'$)

2jb7 _ ?'>7 -2j DVD7 -2j"j"D: Me

:b Z[iWhhebbWhbWj[eh~WZ[ ceZe Yecfb[je' i[ l[ gk[ [b f[h~eZe [i _dZ[(

f[dZ_[dj[ Z[ bWWcfb_jkZ' F h[ikbjW5

;$ \ )G Df!

L L2j- 7 (( 7 ( 7 [n

DV: We

1 / hf # 6+"q$ 7 hf#"j"' [n$)

Nd WbWcXh[ece]}d[e [ _d[nj[di_Xb[' Ykoe f[ie feh kd_ZWZZ[ bed]_jkZ[i b%^WZ[ WcWhhWhi[WZei fkdjei i_jkWZei W_]kWbWbjkhWo i[fWhWZeifeh bWZ_ijWdY_W)H&x<ed gk} \k[hpW'_'^WXh|gk[ j_hWhWbWcWhhWh[b WbWcXh[fWhWgk[

h[ikbj[ kdW\b[Y^WS3?WYjehZ[ \ehcW5 r6' / SWO%

>d [ij[ YWie'bW)iebkY_€d[i cko lW]W'fk[i bW\kdY_€d_dZ[j[hc_dWZW'hf' Yed(j_[d[ Zei cedec_ei Yece lWh_WXb[i): f[iWh Z[ [bbe' i[ fk[Z[ W\_hcWhgk[ Zeii_ij[cWi Z_\[h[dj[i [`[YkjWh|d [b c_ice cel_c_[dje Yed jWbZ[ gk[ bei cede(c_ei 2j, o 2j- \ehcWZei Yed bWicW]d_jkZ[i *%L' V%lWb]Wdbe c_ice [d kde gk[[d ejhe) >b i[kZef[h~eZe ;^ o [b Z[Yh[c[dje be]Wh~jc_Ye'3' ^WXh|d Z[ lWb[h5

,+) <Wj[dWh_W)

S b V

6 , H ,= H ( (B H (- (-

2jb , , ( ,

S 7 -6 =7 ,

XL2j7((

V

J / XL/S " \ # . e X_[d5L / HTSP" \H # &

Page 52: Análisis dimensional

<:I~MNEH BP

71/U85/- 01 <W6509< =>?HKF:;E> L

$" <FNOCH?BFHCINFJI?G"

>d bWj[eh~WZ[ bW>bWij_Y_ZWZde WfWh[Y[d_d]kdWdk[lW cW]d_jkZfh_cWh_W'o bWi[YkWY_ed[i\kdZWc[djWb[i' gk[ i[ W]h[]WdWbWiZ[ bWF[Y|d_YWZ[ i€b_Zei h~]_Zei' [ij|d jeZWi fhel_ijWi Z[ kdW YedijWdj[YWhWYj[h~ij_YWZ[b Yk[hfe Yed gk[ i[ ef[hW)=[ [ijWi Zei Y_hYkdijWdY_Wih[ikbjWgk[' fWhW\ehcWhbWXWi['XWijWh|djh[i cW]d_jkZ[i jWb[iYece bWbed]_jkZ' bWcWiWo [b j_[cfe' YedbWfei_X_b_ZWZZ[ Z_iYh_c_dWhbWiZ_(c[di_ed[i [ifWY_Wb[ii_ i[ Wj_[dZ[WbYWh|Yj[hl[Yjeh_WbZ[ bWi[YkWY_ed[i)

EWib[o[i \kdZWc[djWb[iZ[ bW>bWij_Y_ZWZi[ XWiWdjeZWi[d [b fei(jkbWZeZ[ Aeea[' [d YkoWl_hjkZ PcT^_P[]Z[Z]NTZYLWTOLOPY_]PWLOPQZ]XL&NTmY`Q]TOL[Z] PWN`P][Z d WL I`P]eLP \`P WLZ]TRTYLY'Ge [i _dYkcX[dY_WZ[b :d|b_i_i Z_c[di_edWbWl[h_]kWhWijWgk} b~c_j[i [i WY[fjWXb[[ij[feijkbWZe'feh be gk[ dei b_c_jWh[ceiWZ[Y_hgk[ [b [dkdY_WZeZ[ Aeea[jecW Z_ij_djei Wif[Yjei i[]•d i[W bWcWd[hWZ[ Wfb_YWhWbYk[hfe bWi\k[hpWiZ[\ehcWZehWi'be YkWbZWeh_][d WZ_l[hiWi[YkWY_ed[iYed ikih[if[Yj_lei Ye[\_Y_[dj[ie c€Zkbei [b|ij_Yei' YkoWi\€hckbWi Z_c[di_e(dWb[igk[ZWdZ[j[hc_dWZWifeh bWi\€hckbWi [d gk[ WfWh[Y[d)

)<edl_[d[ Z[\_d_h[d bWj[eh~WZ[ bW>bWij_Y_ZWZkdWdk[lW cW]d_jkZi[YkdZWh_W6bW[]P^TmY0

S D 6 7 V\VkV[VhpVWVA |h[W

YkoW\€hckbWZ_c[di_edWb[i5

BSC/ 6%57;%)&

Page 53: Análisis dimensional

,+1 :GyEBLBL =BF>GLBHG:E

<kWdZebW\k[hpWj_[dZ[ WYecfh_c_h [b Yk[hfe' i[ Wjh_Xko[WbWfh[(i_€d [b i_]de fei_j_le) >d YWieYedjhWh_e'bWfh[i_€d [i d[]Wj_lW'o i[Z[dec_dW _PY^TmY'

EWi Z_l[hiWi YedijWdj[i [b|ij_YWi[ij|d h[bWY_edWZWiZ[ ceZe gk[XWijWYedeY[hZei fWhWYWZWYk[hfe fWhWfeZ[h YWbYkbWhbWih[ijWdj[i)IWhWdk[ijhe fhef€i_je XWijWjecWh [d Yedi_Z[hWY_€dbWii_]k_[dj[i5

F€Zkbe Z[ Qekd]' 70 B2C/ 6%57;%)

F€Zkbe Z[ h_]_Z[p'S,)5_A

SS,)U/ 6%57;%)&

>b c€Zkbe Z[ Qekd] _dj[hl_[d[ [d jeZei bei fheY[iei Z[ WbWh]Wc_[dje'c_[djhWi gk[ [b c€Zkbe Z[ h_]_Z[pWjW•[WbZ[ib_pWc_[djeckjke Z[ ZeifehY_ed[i Yedj_]kWi)

%"2GCRF\IAFMAPG?MBCPI? @?MM?"

NdWXWhhW[ij| [cfejhWZWfeh kd [njh[ce) >d [b ejhe [njh[ce bb[lWkdWfbWYWh~]_ZW'f[hf[dZ_YkbWhWbWXWhhW'o i[ b[ Wfb_YWkd fWhZ[ \k[h(pWiYkoe cec[dje' 9$ [ij| i_jkWZe[d [b fbWdeZ[ bWfbWYW)>d [ijWiYedZ_Y_ed[i'bWj[eh~W[b[c[djWbf[hc_j[ fh[Z[Y_hgk[ bWi\_XhWibed]_jkZ_(dWb[iZ[ bWXWhhWi[ jhWdi\ehcWd[d WhYeiZ[ Y_hYkd\[h[dY_W'gk[ ik hWZ_ede Z[f[dZ[ Z[ bWbed]_jkZ Z[ bWXWhhWo gk[ de _d\bko[ [b c€Zkbe Z[h_]_Z[p)L[ jhWjWZ[ ^WbbWh[b hWZ_eZ[ YkhlWjkhW']%Z[ bW\_XhWd[kjhW)

EWcW]d_jkZ XkiYWZWi€be Z[f[dZ[h| Z[b cec[dje Z[b fWh' Z[b c€Zkbe Z[Qekd] o Z[ bW\ehcW Z[ bWi[YY_€djhWdil[hiWb)IWhWWjh_Xk_hZ_c[di_ed[i WbWiY_jWZWicW]d_jkZ[i' jecWdZe [d Yedi_Z[hWY_€dbWjh_Z_c[di_edWb_ZWZZ[b [ifW(Y_e'jec[cei [b [`[ c [d bWZ_h[YY_€dZ[ bWXWhhW'o [b d [d bWZ_h[YY_€dZ[b ce(c[dje Z[b fWh' Yed be gk[ [b [`[ p j[dZh|) bWZ_h[YY_€dZ[b hWZ_eZ[ YkhlWjkhW)EW\ehcW Z[ bWi[YY_€djhWdil[hiWb[ijWh| Z[\_d_ZWfeh bW[YkWY_€dZ[ ik f[h~c[(jhe' !G"d%p$ / H' bWYkWbfeZh|) [iYh_X_hi[Wi~5

!G"<%f# / H'GZ 7B

ZedZ[ GZ! 7B h[fh[i[djWd Z[j[hc_dWZei i[]c[djei Z[ Z_Y^Wi[YY_€d'feh [`[cfbe'iki Z_c[di_ed[i c|n_cWi fWhWb[bWiWbei [`[i d%p' h[if[Yj_lWc[dj[) EW_d\bk[d(Y_WZ[ bWi[YY_€djhWdil[hiWbi[ cWd_\[ijWh|' fk[i' feh \WYjeh[i Z[ \ehcW jWb[iYece GW(G>!G+(G>! oo' pj*pe' ))) R-*R+" ‚‚‚ )

BP) F><yGB<: => L{EB=HL =>?HKF:;E>L ,+2

EW\€hckbW Z_c[di_edWb Z[ 2 [d bWXWi[ 6Y$ 6d% 6e% 7$ ;$ i[ [ijWXb[Y[h|h[YehZWdZegk[' fWhWZ[\_d_hZ_Y^ec€Zkbe' i[ Yedi_Z[hWkdW\k[hpWgk[ j_[dZ[WWbWh]Whkd WbWcXh[o' [djedY[i' [d bW\€hckbW

B2C7 \k[hpW 7 bjE|h[W B:C

: h[fh[i[djW [b |h[W Z[ bWi[YY_€djhWdil[hiWb)>d dk[ijhe YWie'bWiZei \k[hpWiZ[bfWhj_[dZ[d' bWkdWW[ij_hWhbWXWhhW'o bWejhWWYecfh_c_hbW'feh be gk[ i[h|5

o : h[fh[i[djWh| [b |h[W Z[ kdWikf[h\_Y_[ i_jkWZW[d Z_Y^Wi[YY_€djhWdil[hiWb5B:C / 6Z6[! o h[ikbjW5

Eei cedec_ei f_ i[ eXj[dZh|d' feh jWdje' Yece _dZ_YW[b i_]k_[dj[ [igk[cW5

] ? 7

6!.J H ( (655 H H %(6I ( ( %(7 H ( (; H !% !%

GZ 7B

H H( HH (H HH H

H %(( -

2j, , H2j- H ( ,

3,

S 7 .6 T2+

]2jb /%-

7B

o bWiebkY_€d[i5

] / pe"I "7G8eZ)

$ C ))b))' ))) ' q' ))) $)? GZ 7B

>d be gk[ WjW•[WbW\kdY_€d kd_l[hiWb .C$ dWZWfk[Z[ Z[Y_hdei [b :d|b_i_iZ_c[di_edWb' f[he XWijWkd YedeY_c_[dje [b[c[djWb Z[ bWj[eh~WZ[ bW[bWij_Y_ZWZfWhWZ[`WhbWh[ZkY_ZWWkdW \kdY_€d Z[ bei \WYjeh[iZ[ \ehcW) >d [\[Yje' i_ i[jecW bWYkhlWjkhW#_dl[hiWZ[b hWZ_e$'Yece c[Z_ZW Z[ bWZ[\ehcWY_€d' bWb[oZ[ Aeea[ [n_][ gk[ ] [ij} [d hWp€d_dl[hiW Z[ 9$ fWhWbe YkWb[i fh[Y_ie gk[ i[W5

S-',U

o bW\kdY_€d "Ib Z[f[dZ[h| iebWc[dj[ Z[ bei \WYjeh[i Z[ \ehcW Z[ bWi[YY_€djhWdil[hiWb)

Page 54: Análisis dimensional

,+3 :GyEBLBL =BF>GLBHG:EBP) F><yGB<: => L{EB=HL =>?HKF:;E> L ,+4

L_de i[ ^kX_[hWdZ_iYh_c_dWZebWiZ_c[di_ed[i [ifWY_Wb[i'i[ ^kX_[hWbb[]WZeW5

S-'-C

: [ije i[ h[ZkY[ bW_d\ehcWY_€dgk[ ikc_d_ijhW [b :d|b_i_i Z_c[di_edWbgk['Yece i[ l[' [i ikcWc[dj[ lW]W'fk[i d_ i_gk_[hWf[hc_j[ Wl[h_]kWhY€ce Z[f[d(Z[ bW\b[Y^WZ[ bW\k[hpWWfb_YWZW)L_d [cXWh]e' XWijWdWb]kdei YedeY_c_[djeiiec[hei Z[ bWj[eh~WfWhWeXj[d[h kdW_d\ehcWY_€dckY^e c|i Yecfb[jW)

>d fh_c[h j}hc_de' bWb[o Z[ Aeea[ W\_hcWgk[ bW\b[Y^WWZ[ i[h fhefeh(Y_edWbWbW\k[hpW'be gk[ [n_][ gk[ i[W5

ZedZ[ ,,' (+% ooo % ied i[]c[djei gk[ YWhWYj[h_pWdbW\ehcW Z[ bWi[YY_€djhWdi(l[hiWb) >ijW \€hckbW de f[hc_j[ Wfb_YWh[b :d|b_i_i Z_c[di_edWbi_de WXWhhWiYkoWii[YY_ed[i jhWdil[hiWb[i i[Wd i[c[`Wdj[i) >d YWcX_e'bWS-',U ck[ijhWYece' W_]kWbZWZZ[ ejhWiY_hYkdijWdY_Wi'lWh~W[b hWZ_eZ[ YkhlWjkhWYkWdZei[Wbj[hWdfhefehY_edWbc[dj[ bWiZ_c[di_ed[i Z[ bWXWhhWWbe bWh]eZ[b [`[ d%e Wbe bWh]eZ[b [`[ p' feh i[fWhWZe)

>d kdWXWhhWZ[ i[YY_€dh[YjWd]kbWh'feh [`[cfbe' i_ iki Z_c[di_ed[i jhWdi(l[hiWb[i ied GZ / L%HZ/ M%jeZei bei \WYjeh[iZ[ \ehcW Z[ bWi[YY_€djhWdil[hiWblWb[d ,' o bW[YkWY_€dS-',U i[ Yedl_[hj[ [d5

S "L M#jf !! %(%jfr %(%!%(%. ( "L M#L / 2P jfb %(%!%(%&

Ieh ejhWfWhj[' fk[ije gk[ de ^Wo Z[ib_pWc_[djei' Zkfb_YWhbWWdY^khWL [gk_(lWb[ Wj[d[h gk[ ZeXbWhZei XWhhWi_]kWb[i' feh be gk[' fWhWbe]hWhbWc_icW\b[Y^W' Wh| \WbjWkdW \k[hpW ZeXb[' o ^WXh| Z[ i[h5

7] / )& LM,o

SS / D( jf- #() -)($ )

7L *

EWj[eh~WYecfb[jW ZW> / ,*,-)?_dWbc[dj[' feh bWc_icW j[eh~Wi[ iWX[gk[ [d jeZei bei fheXb[cWi Z[ \b[n_€dZ[ XWhhWiYkWb[igk_[hW'bWi[YY_€d_dj[hl_[d[ feh ik cec[dje Z[ _d[hY_W#][e(c}jh_Ye$ Yed h[bWY_€dWbfbWde ^eh_pedjWbgk[ fWiWfeh bW\_XhWd[kjhW) >d [bYWieZ[ kdW XWhhWh[YjWd]kbWh[i5 :R / LM^(*+%be YkWbbb[lWYedi_]e gk[ i[W5

&" 2GCRF\IBCPI? @?MM?NJHCOFB?? PI? NJG?DPCMT?"

Ee c_ice gk[ [d [b fheXb[cW Wdj[h_eh'[b [njh[ce b_Xh[i[ ikfed[fhel_ije Z[ kdWfbWYWh~]_ZWgk[ j_[d[ feh eX`[je Z_ijh_Xk_hbW\k[hpWJ o[l_jWhgk[ i[ fheZkpYWdZ[ib_pWc_[djei' Yed be gk[ jWcfeYe _dj[hl[d(Zh| [b c€Zkbe Z[ h_]_Z[p)>d [b YWieWYjkWb'bWiZ_ij_djWifehY_ed[i Z[ bWXWhhWde [ij|d oW[d bWic_icWi YedZ_Y_ed[i'Yece ikY[Z~W[d [b fheXb[(cW Wdj[h_eh'feh be gk[ bW\ehcW Z[ bWXWhhWZ[\ehcWZWde i[h| oWY_hYk(bWh'o' [d l[p Z[b hWZ_e' Wogk[ Z[j[hc_dWhbW\b[Y^W'S' ?_dWbc[dj['Yece bW\k[hpWWfb_YWZWde j_[dZ[ Z_h[YjWc[dj[WWbWh]Whe Yecfh_c_h bWXWhhW'de i[ fk[Z[ ^WbbWhbW\€hckbWZ_c[di_edWbZ[ 2 [d bWXWi[Z_iYh_(c_dWZW'feh be gk[ ^Wogk[ fheY[Z[h WbWcWd[hWYb|i_YW)

LebkY_€d5

S2>f7LM,

o i€be gk[ZWfeh Z[j[hc_dWh [b \WYjeh8$ gk[ ^WZ[ i[h kd d•c[he \_`e)L[ l[ \|Y_bc[dj[ gk[ [ijW \€hckbW[i Wfb_YWXb['Yed i€be YWcX_Wh8$ YkWdZe

bW\k[hpW i[ ^WbbWkd_\ehc[c[dj[ Z_ijh_Xk_ZWfeh jeZW bWXWhhW'o YkWdZei[jhWjWZ[ kdW XWhhW[cfejhWZW feh WcXei [njh[cei o YWh]WZW[d [b Y[djhe)>d [b YWie[d gk[ ^Wokd [njh[ce b_Xh[o bW\k[hpW i[ Wfb_YW[d }b [i > / /'c_[djhWi gk[ i_ bW\k[hpWi[ h[fWhj[ kd_\ehc[c[dj[' [i > / .*-)

'" :YIBPGJ CGXNOFAJ"

S J 7

6 , , ( ,7 e , ,; e (- (-

'10 , ( ,*- ,*-

S 7 -6 _7 ,

S+ 7 D(D jf #q L 2 7 W! A! ( &

=[b [njh[ce Z[ kd h[iehj[ l[hj_YWbf[dZ[ kdWcWiWX' L[ jhWjWZ[ Wl[h_]kWh[bf[h~eZe' _%Z[ bWieiY_bWY_ed[igk[ [`[YkjW[b Yk[hfe YkWdZei[ i[fWhWZ[ ik fei_(Y_€dZ[ [gk_b_Xh_e[d i[dj_Ze l[hj_YWb)L[ ikfed[ Z[ifh[Y_WXb[bWcWiWZ[b h[iehj[)

:Z[c|i Z[ X%_dj[hl[dZh| [b f[ie' >. bWWcfb_jkZ' 3' o bWfe dY_WZ[bh[iehj['c[Z_ZW feh [b \WYjehZ[ fhefehY_edWb_ZWZZ[ bWb[o Z[ Aeea[5 O / X',(&

LkfedZh[cei gk[ bWXWhhW[i h[YjWd]kbWhYedbei i_]k_[dj[i ZWjei5bed]_jkZ' *1WdY^khW'E. WbjkhW'M1c€Zkbe Z[ Qekd]' 7'

?WYjeh[i Z[ \ehcW5S(W%L(W%TY'

X X V 3

< H H , H ,7 H , , , H; , H (- (- H

'1$ , ( ,*- H ,*- H'1% H H ! , 9

L 7 .6 T2+

Page 55: Análisis dimensional

<IyGDNDN ?DH@INDJI<G

aY2 aY#!#. 3( 3((

e VP

@c<e|c`j`j [`d\ej`feXc gi\m} cXgfj`Yc\ `e]cl\eZ`X [\ cX ^iXm\[X[ p [\ cXXdgc`kl[ $&%'g\if cX*k\fi~X Zfdgc\kX dl\jkiX hl\' d`\ekiXj j\ ZldgcX cXc\p[\ Cffb\' cX]leZ`€e `e[\k\id`eX[X 2Qj\ i\[lZ\ Xce•d\if .'!'*

'! 8BMVJAJABPI MBNJMOBBI BNKFM>G>NJ@F>AJ> PI QJG>IOB!

* GXi\^lcXZ`€e [\ cfj i\cfa\j [\ Yfcj`ccfj\ cf^iX Zfe le mfcXek\hl\\a\ZlkX le dfm`d`\ekf [\ ifkXZ`€e^iXZ`XjXcXXZZ`€e[\ le i\jfik\ \e\jg`iXc*N\ kiXkX[\ ZXcZlcXi\c g\i~f[f [\ cXjfjZ`cXZ`fe\j*

* Gr c`jkX [\ dX^e`kl[\j \jkXi| ]fidX[X gfi \c g\i~f[f' [. \c dfd\ekf [\`e\iZ`X' ,& [\c mfcXek\7cXcfe^`kl[' Z&[\c i\jfik\7 \c d€[lcf [\ S fle^' 93 p \cdfd\ekf [\ `e\iZ`X' (P [\ cXj\ZZ`€e kiXejm\ijXc*

, 9 ,1

9 J . ) - - 0? J - - J JF , J ). J J

#!#- - ) -+. &%' (%' J! !) J J J 0 )-

3* () K 3 .

b- 3X2Q #X$9Z. ,1

Ll`\e \jk} ]Xd`c`Xi`qX[f Zfe cX k\fi~X [\ cfj dfm`d`\ekfj fjZ`cXek\j jXYi|hl\ \c g\i~f[f \jk| j`\dgi\ \e iXq€e `em\ijX [\ cXiX~qZlX[iX[X [\c gXi [`i\Zkfi[\ [fe[\ i\jlckX hl\' 'j` j\ ZfcfZXe [fj i\jfik\j \e gXiXc\cf jfYi\ \c d`jdf

mfcXek\' *Zfecf ZlXc j\ [lgc`ZX , U" \c g\i~f[f _XYi| [\ j\i B) m\Z\j d\efi* @jk\c#XTJeXDcc`\ekfYXjkXgXiX [\k\id`eXi cX]fidX [\ cX]leZ`€e 2Q'p i\jlckX6

b 3 +G ;Z,19"

kx&% =i~[^dXe $..%Zfdgc`ZX*\c \eleZ`X[f jlgfe`\e[f hl\ cXdXjX* d€m`c\j ZfrjkckP-[X gfi leX mXj`aX[\ mfcld\e G cc\eX [\ le c~hl`[f [\ [\ej`[X[ Qrfe cXc[rX [\ h6l\ le ]~j`Zf `e\og\ikf* `eZclpX G p Q \e cXc`jkX[\ dX^e`kl[\jr

e ZXdY`f' ef k`\e\ \e Zl\ekX cXXdgc`kl[' Xg\jXi [\ hl\ ef _Xp iXq€e O ^`W]`WgXiX [\jZXikX[X*

DR* H@>yID>< ?@ N{GD?JN ?@AJMH<=G@N ###

p' j` cXj\ZZ`€e [\c i\jfik\ \j i\ZkXe^lcXi6

-. R ;Zb- 3 +- ((((

9OP.

(! 0MB@PBI@F>ABG>NQF?M>@FJIBNCPIA>HBIO>GBNABPI> @PBMA>!

>XcZlcXicX]i\Zl\eZ`X [\ cXjm`YiXZ`fe\j[\ leX Zl\i[X hl\ j\ dXe)k`\e\ k\ejX d\[`Xek\ leX ]l\iqX [&GXcfe^`kl[ \j UWcXdXjX gfi le`[X[[\ cfe^`kl[ mXc\s*k 3 V8U&

@e cXk\fi~X \c\d\ekXc j\ jlgfe\e cXj fjZ`cXZ`fe\j [\ kXe g\hl\•X Xdgc`kl[hl\ cXk\ej`€e j\ dXek`\e\ ZfejkXek\* @e \jkXj Zfe[`Z`fe\j' ef \j gi\Z`jf k\e\i\e Zl\ekX' e` [`Z_X Xdgc`kl[ e` cXjgifg`\[X[\j \c|jk`ZXj [\ cXZl\i[X' p Zfe cXjdX^e`kl[\j d\eZ`feX[Xj j€cf i\jlckX le dfefd`f g`

m9 r Q]*@c]XZkfi A [\g\e[\ [\c fi[\e ^& [\c Xid€e`Zf* GXk\fi~X Zfdgc\kX [X A 3 ^,-)

)! /IBMDV>ABG>NQF?M>@FJIBNCPIA>HBIO>GBNABPI> @PBMA>!

@e cXd`jdX Zl\i[X [\c gifYc\dX Xek\i`fi' cXXdgc`kl[ [\ cXjfjZ`cX)Z`fe\j ZlXe[f \a\ZlkX jl m`YiXZ`€e]le[Xd\ekXc \j 2&>XcZlcXicX\e\i)^~X4&

Nlgfe`\e[f kXdY`}e hl\ cX Xdgc`kl[ \j cf jl]`Z`\ek\d\ek\ g\hl\•X gXiXhl\ ef `ek\im\e^Xe cXjgifg`\[X[\j \c|jk`ZXj' cX\e\i^~X j\i| [\Y`[X •e`ZXd\ek\X cfj dfm`d`\ekfj Xid€e`Zfj \a\ZlkX[fj gfi cXj [`m\ijXj gXik\j [\ cX Zl\i[X'cfj ZlXc\j hl\[Xe [\k\id`eX[fj gfi cXdXjX' cXXdgc`kl[ p cX*]i\Zl\eZ`X* KfikXekf' [`jZi`d`eXe[f cXj [`d\ej`fe\j \jgXZ`Xc\j' \c gifYc\dX j\ gcXek\Xp i\jl\c)m\ Zfdf j`^l\6

9 U [WZ 6

Gf6 J J - )- J>h . J J J -: - J J - JF ). )- J J J

#!#- - ). )- - ).

Q 3 07 K3 -

9 3 A[d-6-)

Page 56: Análisis dimensional

,,-<IyGDNDN ?DH@IN-,I<G

N`j\ _lY`\iX gifZ\[`[f XcXdXe\iX Zc|j`ZX'_lY`\j\ i\jlckX[f6

9 3 [Z-d-i #i$)

WcX]leZ`€e r _XYi~Xhl\[X[f `e[\k\id`eX[X*

4* Ofij`€e [\ leX YXiiX*

- eX YXiiX[\ cfe^`kl[ Up iX[`f Z j\ ]`aXgfi le \oki\df p j\ i\kl\ir\[`Xek\ le gr6 [\ ]l\iqXj' <$ Xgc`ZX[f\e \c fkif \oki\df* >XcZlcXi\cXe^lcf [\ kfij`€e' \*

* @e cXk\fi~X \c\d\ekXc j\ jlgfe\ hl\ cXj]`YiXjef j\ XcXi^Xegfi cf hl\ j€cfdk\im\e[i| \c r€[lcf [\ i`^`[\q* N` j\ kfdX \c \a\ F \e cX[`irZZ`€e [\c \`\ [\cX'YriiX' cfj \a\j D \ E j\i|e \hl`mXc\ek\j p eX[X el\mf j\ Zfej\^l`i'E [#ZiDdd|e[fcfj* 'X DN)

>fdf cXj ]l\iqXj j\ Xgc`ZXe\e \c gcXef I ` jl ]€iielc [` ' -# ' :' X Dd\eNcJeX j\i|6

WcX[\c gXi6LTM 3 >O3?F(-

G<I 3 >O3-?F(-)

E6#XiX_XccXicX]€idlcX [`d\ej`feXc [`jZi`d`eX[X [\c d€[lcfZliiqi\dfj X cX\ZlXZ`€e6 [\ i`^`[\q' i\)

[rO0"&9?%MW!

\e cXhlr O rj cX]l\rqX hlr _Xp hl\ Xgc`ZXikXe^\eZ`Xcd\ek\ X cXjlg\i]`Z`\ E676X grf P>DileX [`jcfZXZD€e'kXdY`}e kXe^\eZ`Xc' [r' \eki\ [fj glekfj hl\

Xe \ Xcf cXi^f [\ cXefidXc X [`Z_X jlg\i]`Z`\' @e el\jkif ZXjf j\i|6

GMWI3 >hp' \e Zfej\Zl\eZ`X6

L#)>M0>O3?F(- >h

>- (( 3 >(-> ?F(-> f h )f f

>fdf 2 \j [\ [`d\ej`€e elcX' j\ gifZ\[\i| Zfdf j`^l\6

B $*G ` (W)3>g . $) , 9

>h 9 , 9 ,? , , 9 9F $) $) 9 9

!- , (, $+ ,

2 3 X#0X$

DR* H@>yID>< ?@ N{GD?JN ?@AJMH<=G@N --/

p' k\e`\e[f \e Zl\ekX cXc\p [\ Cffb\6

/4Ai)"%3;+

N` ef j\ _lY`\iXe [`jZi`d`eX[f cXj [`d\ej`fe\j \jgXZ`Xc\j' _XYi~Xi\jlckX[f6

p' Zfe cXc\p [\ Cffb\6

hl\[Xe[f kf[Xm~XleX ]leZ`€e `e[\k\id`eX[X* N\i~Xe gi\Z`jfj el\mfj iXqfeX)d`\ekfj gXiX ZX\i \e cXZl\ekX [\ hl\' gfi jl]i`i cXd`jdX [\]fidXZ`€e kf[XjcXjgfiZ`fe\j [\ cXYXiiX' \c |e^lcf _X [\ j\i gifgfiZ`feXc XcXcfe^`kl[' Zfe cfhl\ j\ cc\^Xi~XXcd`jdf i\jlckX[f Xek\i`fi*

5* Nfc`[\q [\ cXj ZfejkilZZ`fe\j*

N\ hl`\i\ ZfdgXiXi cXjfc`[\q [\ [fj gl\ek\j' ^\fd}ki`ZXd\ek\ j\d\)aXek\j' \e cfj hl\ cXjgXik\j _fd€cf^Xj \jk|e Zfejkil`[Xj Zfe dXk\i`Xc\j`^lXc\j $cfi[ MXpc\`^_' 3' Y%*

GX dXpfi' O&[\ cXj k\ej`fe\j \e cXgXik\ d|j ZXjk`^X[X'[\g\e[\i| [\ cXj]l\iqXj' T# 3 GbBb P$ i\gXik`[Xj gfi cfj [`]\i\ek\j \c\d\ekfj [\ mfcld\e' p [\cXj [`d\ej`fe\j c`e\Xc\j' U8! hl\ [\k\id`eXe cX ]fidX [\c gl\ek\* >fe \jkXjdX^e`kl[\j' \c <e|c`j`j [`d\ej`feXc Zfe[lZ\ X6

, #( ($O4Z-ieW&HW3b)eW 3 B'B'(

[fe[\ cX]leZ`€e le`m\ijXc r kfdX \c d`jdf mXcfi \e kf[fj cfj gl\ek\j hl\ j\Zfej`[\iXe' p [ 3 B QI \j \c g\jf [\ leX gfiZ`€e _fdf^}e\X ZlXchl`\iX* @e [fjgl\ek\j j\d\aXek\j j\ Zldgc`i| hl\6

O GZ"-O" 3 G"Z- 3 a$!

p cXjk\ej`fe\j jfe gifgfiZ`feXc\j XcXiXq€e [\ j\d\aXeqX' gfi cf hl\ cfj gl\e)k\j ^iXe[\j j\ _le[`i|e Xek\j hl\ cfj g\hl\•fj* )

@c i\jlckX[f Xek\i`fi \j m|c`[f gXiX gl\ek\j Zfejkil`[fj gXiX jfgfikXij\X j~ d`jdfj* GXZfjX ZXdY`Xj`' Zfdf fZlii\ \e cXgi|Zk`ZX' j\ kiXkX[\ gl\ek\jhl\' X[\d|j' _Xe [\ jfgfikXi leX ZXi^XX[`Z`feXc*

<IyGDNDN ?DC@INDJI<G' ) 4

Page 57: Análisis dimensional

--0 <IyGDNDN ?DH@INDJI<G DR* H@>yID>< ?@ N{GD?JN ?@AJMH<=G@ N --1

@e kXcZXjf' j\ gl\[\ gi\jZ`e[`i [\ cfj g\jfj O[$W \c <e|c`j`j [`d\ej`feXc[X' gXiXcXk\ej`€e Zi gif[lZ`[X* gfi leX ZXi^XX[`Z`feXc'5 \c mXcfi6

Zi 3 X d$n#%Z- ; M"

p cX*jfclZ`€e [\c gifYc\dX j\ fYk`\e\ Zfdf j`^l\6

O U 4 b& s*i*

U"-

5! 3 5%&Z-

Gf6 J J (, * J

977 J J ( , , (,

9a , , , J J: , J , J ,F $) J $) J $)

, ) $* (, )

WcXZXi^X5! hl\ _Xp hl\ Xgc`ZXiX fkiX ZfejkilZZ`€e' j\d\aXek\ X*cXgi`d\iX'gXiXfYk\e\i cXd`jdX k\ej`€e O&j\i~X6

p' \e Zfej\Zl\eZ`X' S\ ^cS\bSa US][pb`WQO[S\bSaS[SXOacSa&ZOS]ZWRSkSa ^`]^]`(QW]\OZOZQcOR`OR]RS ZO`Ohr\ RS aS[SWO\hO)

b3 J 9.7Pf

Z-

GXk\fi~X Zfdgc\kX [X J 3 3k.‚

-,* KXe[\f* --* ?`XgXjfe\j*

@e [~XgXjfe\j [\ `^lXc]fidX' g\if [\ [`jk`ekf kXdX•f' \c g\i~f[f [\cXjm`YiXZ`fe\j[\g\e[\i| [\ cX[\ej`[X[' [\c d€[lcf [\ Sfle^ W[\ leX[`d\ej`€e c`e\Xc*>fe \jkfj [Xkfj' \c <e|c`j`j [`d\ej`feXc \o`^\ hl\ j\X6

PeX ZfcldeX [\ cfe^`kl[ U W j\ZZ`fe i\ZkXe^lcXi [\]`e`[X gfi \c\jg\jfi O p cXXeZ_liX P#O 2 P$&\jk| jfd\k`[f XleX ZXi^X[&N\ hl`\i\Xm\i`^lXi cXZXi^Xe\Z\jXi`X gXiXhl\ j\ `e`Z`\ \c gXe[\f' jXY`\e[f hl\cX j\ZZ`€e kiXejm\ijXc `ek\im`\e\ gfi jl [][S\b] RS W\S`QWOUS][pb`WQ];P 3 PO.SU!)&

@j `ek\i\jXek\ \e \jk\ ZXjf [`jZi`d`eXi cXj [`d\ej`fe\j \jgXZ`Xc\jgfihl\ ZX[XleX [\j\dg\•X le gXg\c [`]\i\ek\* OfdXi\dfj \c \a\ K XcfcXi^f [\ cXZfcldeX' \c \a\ D \e cX[`i\ZZ`€e [\c \jg\jfi p \c E \e cX[`i\ZZ`€e [\ cXXeZ_liX*

@e cXk\fi~X\c\d\ekXc j\ kfdX \e Zfej`[\iXZ`€e \c d€[lcf [\ Sfle^•e`ZXd\ek\' g\if Zfe cXjdX^e`kl[\j

LTM 3 >h?F(Z3

ef \j gfj`Yc\ ]fidXi le dfefd`f [\ [`d\ej`€e elcX' p ZXY\g\ejXi hl\j\ _Xmlce\iX[f cXi\^cX /*X*[\c t 0' ZXg~klcfQDD*@e \]\Zkf' \c ZfdgfikX)d`\ekf \c|jk`Zf \jk| [\]`e`[f gfi \c d€[lcf [\ Sfle^ p \c d€[lcf [\i`^`[\q* @jk\ •ck`df ef `e]clp\ d`\ekiXj ef _Xp gXe[\f' g\if \e ZlXekfj\ `e`Z`X\jkX [\]fidXZ`€e [\jc`qXe cXj ZXgXjgXiXc\cXjXcgcXef JK&ppX ef j\ gl\[\ gi\jZ`e[`i [\ }c*

MXqfeXe[f Zfdf \e \c t / j\ m\ hl\' \e \jk\ ZXjf6

Page 58: Análisis dimensional

><K~OPGJ R

5/-S62-+ ./ 04<2.7:

#! :FNOBH>AFHBINFJI>G!

@e cXk\fi~X[\ cfj c~hl`[fj p [\ cfj ^Xj\j' Zfej`[\iX[fj Zfdf d\[`fjZfek`elfj' ef j\ `ekif[lZ\e e` el\mXj dX^e`kl[\j gi`dXi`Xj' e` el\mXjc\p\j le`m\ijXc\j' gfi cf hl\ \c j`jk\dX [`d\ej`feXc j\i| \c d`jdf hl\_\dfj lk`c`qX[f _XjkXX_fiX*Kf[i|' gl\j' lk`c`qXij\ cXYXj\ "9$ :$ @#$[`jZi`d`eXe[f cXj[`d\ej`fe\j \jgXZ`Xc\jj`\dgi\ hl\ Zfem\e^X*

$! ->KFG>MFA>A!

@e cXjlg\i]`Z`\ [\ cfj c`hl`[fj j\ gif[lZ\e cfj ]\e€d\efj [\ ZXg`cX)i`[X[' cfj ZlXc\j \jk|e i\^`[fj gfi leX c\p ]le[Xd\ekXc hl\' gXiXcfj]`e\j [\c <e|c`j`j [`d\ej`feXc' gl\[\ \eleZ`Xij\ Xj~6

BO`O Oc[S\bO` ZOac^S`TWQWSRS c\ Zq_cWR]VOg _cS O^ZWQOO QOROSZS([S\b] RS ac Q]\b]`\] c\O TcS`hO ^`]^]`QW]\OZ O ZOZ]\UWbcRRSZ[Wa[]2

O3 Oa)

@c ]XZkfi [\ gifgfiZ`feXc`[X[' O&\j leX ZfejkXek\' ZXiXZk\i~jk`ZX[\ZX[Xc~hl`[f' hl\ j\ [\efd`eX bS\aWr\ ac^S`TWQWOZf Q]\abO\bSQO^WZO`)Nl]€idlcX [`d\ej`feXc \j6

%! +N@BINJABGVLPFAJNBI OP?JN@>KFG>MBN!

@e \jk\ ]\e€d\ef `ek\im\e[i| \c c~hl`[f gfi jl ZfejkXek\ ZXg`cXi'O&pgfi jl g\jf \jg\Z~]`Zf' g^' p \c ZXg`cXigfi jl iX[`f `) CXYi| hl\ kfdXi kXd)Y`}e\e Zfej`[\iXZ`€e \c |e^lcf [\ ZfealeZ`€e' $c'[\c d\e`jZf Zfe cXgXi\[*

Page 59: Análisis dimensional

--4 <IyGDNkN ?DH@INDJI<G

CXZ`\e[f Zf`eZ`[`i \c \a\ q Zfe \c \a\ [\c klYf' hl\ j\ jlgfe\ m\ik`ZXc'\c]\e€d\ef j\i| j`d}ki`Zf \e kfief [\c d`jdf' WcX ]€idlcX [`d\ej`feXc [\ QI

j\i|6@QIA3 9.!.%]:@%-t

Kfi fkiX gXik\' [\ cX]l\iqX [\Y`[X X cXk\ej`€e jlg\i]`Z`Xc' _XYi| hl\ kfdXi cXZfdgfe\ek\ m\ik`ZXcp [`m`[`icX gfi \c Zfekfief [\c d\e`jZf' hl\ j\ _XccX\e \cgcXef fg&gfi cf hl\ j\i|6

U,!V 3 U]l\iqXVUcfe^`kl[V

?\ \jk\ df[f' gf[i| i\jfcm\ij\ \c gifYc\dX [`jZi`d`eXe[f cXj [`d\ej`fe\j\jgXZ`Xc\j Zfdf j\ `e[`ZX X Zfek`elXZ`€e6

V 9! ` QI

f ) ,, ,4 (9 ( -

- ) .4 44 (J ) .

- ) - , ,!-V 3 /7 K3 -

9!Q 3 ( /Y"+#&

982

KXiX*[\k\id`eXi cX]fidX [\ cX]leZ`€e 2Q' YXjkXk\e\i \e Zl\ekX hl\' [\ cXj]l\iqXj [\Y`[Xj X cXk\ej`€e jlg\i]`Z`Xc' j€cf `ek\im`\e\ cXZfdgfe\ek\ m\ik`ZXc'[\ [fe[\ i\jlckX*

V 3 KB+!B EPS2*982

GX k\fi~X Zfdgc\kX [X K 3 .!*

N` ef j\ _lY`\iXe [`jZi`d`eX[f cXj [`d\ej`fe\j \jgXZ`Xc\j' _XYi~XXgXi\Z`[ffkif ]XZkfi [\ ]fidX }c%3 V*`&f' cf hl\ \j cf d`jdf' j\ _XYi~X\eZfekiX[f fkifdfefd`f6

& 9'82MT)9 )))77)9 ))

>D% Op cXjfclZ`€e _XYi~Xj`[f6

) O # `'82#V 3 (( 2Q 2' )) *982 0

&! :>GOJABKMBNFJIBNBI G>NPKBMCF@FBAB PI GVLPFAJ!

GX[`]\i\eZ`X YljZX[X' KY$\jkXi| [\k\id`eX[X gfi O p gfi cXZlimX)kliX [\ cXjlg\i]`Z`\ \e \c glekf Zfej`[\iX[f' f j\X gfi cfj iX[`fj [\ZlimXkliX'`, S `-& [\ cXjj\ZZ`fe\j gi`eZ`gXc\j' hl\ [Xe fi`^\e Xle ]XZkfi[\ ]fidX6 ^ 3 `-*`,t

o* H@>yID>< ?@ AGPD?JN --5

N`e e\Z\j`[X[ [\ [`jZi`d`eXi cXj [`d\ej`fe\j \jgXZ`Xc\j' j\ cc\^XX6

hl\ \jk| [\ XZl\i[f Zfe cX\ZlXZ`€e [\ GXgcXZ\6

'! =BGJ@FA>AABG>NJG>N!

@e cXgifgX^XZ`€e[\ cXjfcXj `ek\im\e[i| cX[\ej`[X[ [\c c~hl`[f' g'

i\gi\j\ekXk`mX [\ cX`e\iZ`X7\c g\jf \jg\Z~]`Zf' QI' gXiX kfdXi Zl\ekX[\ cXj]l\iqXj [\Y`[Xj XcX^iXm\[X[7cXcfe^`kl[ [\ fe[X' <7 cXgif]le[`)[X[' Q$[\c X^lX' Zfe \c ]`e [\ kfdXi \e Zfej`[\iXZ`€e cXdXjX X]\ZkX[Xgfi \c dfm`d`\ekf' p cXk\ej`€e jlg\i]`Z`Xc' O&

\ 6 : QI O

9 - - $* . J: J J - - -F )- J J . ).

MT, - ) -+. -+. ) -+. JMT) J ) . J ) - ,

VV4.3 K3 .7 e4(

6

\ 3 rr$WZiW' r%*QI6. 6

GX]€idlcX _XccX[Xk\€i`ZXd\ek\ gfi cfi[ F\cm`e \j6

6U # Zi% -,bVZ. 9 )) - & 0''. )) O_ ))f

.-k QIX 6

(! =F?M>@FJIBNAB leX) DJO>!

@jk\ gifYc\dX ]l\ gifgl\jkf gfi Gfi[ MXpc\`^_ Zfdf lef [\ cfjZXjfj \e hl\ \c <e|c`j`j [`d\ej`feXc Zfe[lZ\ `ed\[`XkXd\ek\ XleX jfcl)Z`€e hl\ j\i~X [`]~Z`c[\ _XccXiXgc`ZXe[fcXk\fi~X*

Page 60: Análisis dimensional

-., <IyGDNDN ?DH@INDJI<G

N\ jlgfe\ cX^fkXjljkiX~[X XcX]l\iqX [\ cX^iXm\[X[' Zfe cf hl\ ef_XYi| hl\ Zfej`[\iXi d|j ]l\iqXj hl\ cXj[\Y`[Xj XcXk\ej`€e jlg\i]`Z`Xc'p cX]fidX [\ \hl`c`Yi`f j\i| \j]}i`ZX*

GXj mXi`XYc\jX Zfej`[\iXi jfe6 b&&Zi Wg* N`e e\Z\j`[X[ [\ [`jZi`d`eXZ`€e

j\ cc\^XX6

p j\ gl\[\ X]`idXi hl\ \c ZlX[iX[f [\c g\i~f[f \j gifgfiZ`feXc Xc ZlYf [\ciX[`f' X cX[\ej`[X[ WXcX`em\ijX [\ cXk\ej`€e jlg\i]`Z`Xc*

N\ gl\[\ ^\e\iXc`qXi \c gifYc\dX gi\Z\[\ek\ kfdXe[f \e Zfej`[\iX)Z`€e cX]l\iqX [\ cX^iXm\[X[ p jlgfe`\e[f hl\ cX^fkX j\ _X ]fidX[fjfYi\ le gcXef _fi`qfekXc*Kfi iXq€e [\ j`d\ki~X jl jlg\i]`Z`\ j\i| [\i\mfclZ`€e' p YXjkXi|kfdXi \e Zfej`[\iXZ`€e \c iX[`f' `&[\ cXj\ZZ`€e_fi`qfekXc d|o`dX* GX ^iXm\[X[ `e]cl`i| jfYi\ \c g\jf \jg\Z~]`Zf' g^*

` Q QI ]

9 9 K $* ). 9? 9 9 c c cF K 9 9 ). ).

!&<1 - ) -+. ) -+. -+. 9!&<) 9 ( . 9 ) c -

b4ii#NQ` $U `-^U

f Y`\e' gl\jkf hl\6

' -B - Zi,TK9 ,TY!- 9 b ((

R/:

3* K\jf [\ cXj^fkXj [\jgi\e[`[Xj [\c \oki\df [\ le klYf ZXg`cXi*

N\ jlgfe\ hl\ \c ]\e€d\ef \j jl]`Z`\ek\d\ek\ c\ekf gXiX gf[\iX[d`k`i hl\' \e \c dfd\ekf [\ cXilgkliX' _Xp\hl`c`Yi`f \eki\ \c g\jf' e&[\ cX^fkX p cXj]l\iqXj [\Y`[Xj XcXk\ej`€e jlg\i]`Z`Xc*

o* H@>yID>< ?@ )AGPD?JN -.-

NfclZ`€e6

@e cXjZfe[`Z`fe\j [\c gifYc\dX' ef `ek\im\e[i| cX`e\iZ`X [\c ]cl`[f' hl\ \jk|i\gi\j\ekX[X gfi jl [\ej`[X[* GXj mXi`XYc\j e[\g\e[`\ek\j j\i|e' gl\j' \ciX[`f ` [\c ZXg`cXi'\c g\jf \jg\Z~]`Zf' g^' [\c c~hl`[f Wjl k\ej`€e jlg\i]`Z`Xc' O&>lXchl`\iX fkiX dX^e`kl[ j\i| ]leZ`€e [\ \jkXj ki\j mXi`XYc\j*OiXkXi\dfj [\

_XccXi\c mfcld\e' B$ [\ cX^fkX*

Z \ g^

9 K 9 ).: 9 c cF 9 ). ).

!&<1 . ) c c

BV 9 .7 `9 KC0%!

R"

Z)YPZi 9 Z)YPc " .#&,T",3((1

Zi

KXiXi\cXZ`feXi \jkX jfclZ`€e Zfe cX]€idlcX [\ OXk\' `ekif[lqZXdfj \c g\jf

[\ cX^fkX6

^ 3 BYP$

Zfe cf ZlXcj\i|6

`-e)O2 3 (('

GO

Wgf[\dfj fYk\e\i fkif dfefd`f g` hl\ ef Zfek\e^X G2

/ ."*T. 3 V"*Tc 3 ))f

`O

<j~ j\ k`\e\' \e [\]`e`k`mX6

]€idlcX hl\ ]l\ gifgl\jkX WZfdgifYX[X \og\i`d\ekXcd\ek\ $11 gfi CXib`ej

W=ifne $&%*

$&% Gf_ejk\`e $12%\jkl[`€ k\€i`ZXd\ek\ \jk\ gifYc\dX' g\if ef c;^i€ cXjfclZ`€e Zfdgc\kX' Wj€cf gl[f X]`idXi hl\ [\Y~Xj\i e 3 `Q`b*<#G;*.*O$& j`\e[f O\c XjZ\ejf ZXg`cXi[\c c`hl`[f \e \c klYf*

CXib`ej W=ifne i\\dgcXqXife' j`e aljk`]`ZXZ`€e'cXdX^e`kl[ O gfi uleX[`d\ej`€e c`e\Xc [\ cX^fkXwW[`\ife gfi jlgl\jkf hl\ [`Z_X [`d\ej`€e _XY~X[\ mXi`XiZfdf cXiX~qZ•Y`ZX[\c mfcld\e' ZfjX hl\ j\i~X Z`\ikX j` kf[Xj cXj^fkXj' \e \c dfd\ekf [\ cXilgkliX' ]l\j\e j\d\aXek\j*

@c<e|c`j`j [`d\ej`feXc' Zfdf j\ m\' Zfe[lZ\ `ed\[`XkXd\ek\ X cX]€idlcX[\ CXib`ej p =ifne j`e e\Z\j`[X[ [\ _`g€k\j`j \jg\Z`Xc\j*

Page 61: Análisis dimensional

()) <IyGDNDN ?DH@INDJI<G R* H@>yID>< ?@ AGPD?JN ()*

4* Q`jZfj`[X[* L# N\ kfdX \e Zfej`[\iXZ`€e cXm`jZfj`[X[*@cdfm`d`\ekf j\i| Xdfik`^lX[f' p ef gf[i| pX X[d`k`ij\ hl\ \c ]cl`[f j\

dl\m\ \e Ycfhl\' gfi cf hl\ cXjmXi`XYc\je[\g\e[`\ek\j j\i|e' cX[\ej`[X[' K'\c g\jf \jg\Z~]`Zf' g^' p cXk\ej`€e jlg\i]`Z`Xc' X[\d|j [\c kXdX•f p ]fidX [\cklYf' hl\ `e]cl`i|e gfi \c iX[`f' `&p cXjlg\i]`Z`\' ?$ [\ ZfekXZkfZfe \c c`hl`[f*@e \jkXj Zfe[`Z`fe\j' X[\d|j [\c dfefd`f g` \e hl\ ]`^liX F]& i\jlckX6

KXiX\jkl[`Xi \c dfm`d`\ekf [\ cfj ]cl`[fj' j\ X^i\^XXcXjc\p\j ]le)[Xd\ekXc\j [\ cXH\Z|e`ZX [\c glekf dXk\i`Xc \jkX fkiX6

9\ b]R] TZcWR]S\ []dW[WS\b]&QORO]`QW<[SXS`QSa]P`S ZOaQ]\bWUcOac\O TcS`hO bO\US\QWOZ]^]`QW]\OZ OZo`SO RS ZOac^S`TWQWSRS aS^O`OQWr\g O ZO^`]gSQQWr\RSZ U`ORWS\bSRS ZOdSZ]QWRORa]P`S ZO\]`[OZ O RWQVOac^S`TWQWS)

<c gXjXi [\ cXi\cXZ`€e [\ gifgfiZ`feXc`[X[ \eki\ ZXek`[X[\j X cX\ZlXZ`€e \eki\ d\[`[Xj' _Xp hl\ `ekif[lZ`i leX ZfejkXek\ ZXiXZk\i~j*k`ZXhl\ j\ [\efd`eX Q]STWQWS\bSRS dWaQ]aWROR&"

[mT4j3)E()

[e

` g g^ $G

9 - $* ). )-: J - - -F J J ). )-

3k- - -+/ -+/ ) .+/

`) ig.^%2m2 3k- 3((

$G.

p \c j\l[fg\i~f[f mXc[i|6

@jkX\ZlXZ`€e Zfe[lZ\ XcXj`^l`\ek\ ]€idlcX [`d\ej`feXc6

Us7*V3 9%7:@%U&-,* >X~[X[\ leX \j]\iX \e ! d\[`f m`jZfjf*

5* JjZ`cXZ`fe\j [\ ! c~hl`[f \e ! klYf \e P* PeX \j]\iX [\ iX[`f' `&p [\ej`[X[' -#'ZX\\e \c j\ef [\ le ]cl`[f [\[\ej`[X[ Kf S m`jZfj`[X[ s7**R>l|c j\i| cXm\cfZ`[X[ [\ ZX~[X'd&ZlXe[f\c dfm`d`\ekf j\X le`]fid\ Pe c~hl`[f j\ _XccXZfek\e`[f \e le klYf \e A [\ j\\Z`fe le`]fi)

d\* @e cXgfj`Z`€e [\ \hl`c`Yi`f XcZXeqXi|\c d`jdf e`m\c \e XdYXjiXdXj* N\ kiXkX[\ ZXcZlcXi\c g\i~f[f [\ cXjfjZ`cXZ`fe\j ZlXe[f j\ gif)[lZ\ leX g\hl\•X [\je`m\cXZ`€e p j\ [\aX cl\^f \c c~hl`[f XYXe[feX[fXj~ d`jdf*

NfclZ`€e6

GX jfclZ`€e Zfdgc\kX' k\e`\e[f \e Zl\ekX kf[Xj cXj Z`iZlejkXeZ`Xjhl\' \edXpfi f d\efi ^iX[f' gl\[\e `e]cl`i \e \c ]\e€d\ef' \j dlp Zfdgc`ZX[X' gficf hl\ Zfem`\e\ gifZ\[\i gfi Xgifo`dXZ`fe\j jlZ\j`mXj*

K# N\ jlgfe\e [\jgi\Z`XYc\j cXj ]l\iqXj [\Y`[Xj X cX m`jZfj`[X[ p X cXZXg`cXi`[X[*

GX `e\iZ`X \jkXi| i\gi'\j\ekX[X gfi cXdXjX' [& [\c c`hl`[f' p cX]l\iqX hl\fZXj`feX \c dfm`d`\ekf j\i| cX[\Y`[X X cX[\je`m\cXZ`€e -h& \o`jk\ek\ \e ZX[X`ejkXek\6

N` \j elcX cXXZ\c\iXZ`€e[\ cX\j]\iX' ef `ek\im\e[i| jl dXjX* @e \c ]cl`[f'gfi \c ZfekiXi`f' _X [\ _XY\i ]fiqfjXd\ek\ XZ\c\iXZ`fe\j' gfi cf hl\ _XYi|hl\ kfdXi \e Zfej`[\iXZ`€e jl [\ej`[X[' Kf# A`eXcd\ek\' X[\d|j [\ cXj ]l\iqXj[\Y`[Xj X cXm`jZfj`[X[' _X [\ ]`^liXi \c ^Sa] O^O`S\bS [\ cX\j]\iX6

.( 9 ) 3ki$g ) Kf%^*

/

d 9 Kf ( $G

> - - )/ - )-: J J - - -@ ) - J J ). ) -

3k, - - J )- -3k. - - - J ) -

Q 9 .7 W4-

d4 J( 2Q #X$)9"57$ "89

p kf[f gXjX Zfdf j` j\ kiXkXiX[\ le j€c`[f i~^`[f jfd\k`[f X leX ]l\iqX \c|j)k`ZX'Ta$ j`\e[f T 3 ;3ki.g^* N\^•e j\ m`f \e \c ZXg~klcfQDDD'\c g\i~f[f gifg`f[\c j`jk\dX mXc\6

Page 62: Análisis dimensional

-.0 < yGDNDN?DH@ NDJI<G

Nljk`klp\e[f Ogfi jl mXcfi j\ k`\e\6

d4

@jk\ i\jlckX[f \jk| [\ XZl\i[f Zfe cX]€idlcX [\ Jj\\e6

$- & / migf% W . . K ) KfTK ( (( ( ( ` ((( P&

4 ]G 5 ]G

>lXe[f j\X [\jgi\Z`XYc\ cXXZ\c\iXZ`€e[\ cXjgXik~ZlcXjc~hl`[Xj' gl\[\ gi\j)Z`e[`ij\ [\ cX[\ej`[X[ [\c c~hl`[f' Wi\jlckX cX]€idlcX* [\ Nkfb\j $&%*

##! /G IXHBMJAB 9BRIJGAN!

N\Xle dfm`d`\ekf \jkXZ`feXi`f\e \c hl\ `ek\im`\e\e le ]cl`[f Wlej€c`[f i~^`[f* N` \c i}^`d\e \j cXd`eXi' cXm\cfZ`[X[ \e ZX[Xglekf j\dXek\e[i| ZfejkXek\ p' j` \j kliYlc\ekf' ]clZklXi| \e kfief [\ Z`\ikfmXcfid\[`f* @e \c mXcfi[\ [`Z_X m\cfZ`[X[ `e]cl`i| \c j€c`[f gfi jl]fidX' i\gi\j\ekX[X gfi Z`\ikfj dfefd`fj ^\fd}ki`Zfj' e& p gfi jlkXdX•f' hl\ hl\[Xi| [\k\id`eX[f gfi leX [`d\ej`€e c`e\Xc'a) @cc~hl`)[f' gfi jl gXik\' `e]cl`i| gfi jl m`jZfj`[X[ p gfi jl `e\iZ`X' i\gi\j\ekX[Xgfi cX[\ej`[X[' g* @eki\ cXjdX^e`kl[\j d&S&g' p s*kgl\[\ ]fidXij\ ledfefd`f g`6

@d^a

>0%%$s*k

hl\ i\Z`Y\ \c efdYi\ [\ \s[S`] RS DSg\]ZRa&Zfe \c hl\ _XYi| hl\ ZfekXi\e kf[fj cfj gifYc\dXj i\]\i\ek\j Xc]\e€d\ef Zfej`[\iX[f* @e \c \a\i)Z`Z`fXek\i`fi _X XgXi\Z`[f pX [`Z_f dfefd`f Zfdf Xi^ld\ekf [\ cX]leZ`€e le`m\ijXc*

$r%*@rk\ gi;Yc\dX _X j`[f kiXrX[f gfi =i`[^dXe $..% gfi cfj d}kf[fj [\cr|c`jrj [`d\ej`feXc* rfi ef gXircc#[\c _\Z_f [\ hl\ cXj •e`ZXj ]l\iqXj hl\`ek\im`\e\e jfe cXj [\Y`[Xj X cXm`jZfj`[X[ p Xc\dgla\ _`[ifjk|k`Zf ef Zfej`)^l\ fYk\e\i cX]€irlcX Zfdgc\kX' j`ef kXe j€cf cX[\ Nkfb\j p' gXiX \ccf' Xdgc~XcXYX6j\[\ i\]\i\eZrX X^i\^Xe[f* cX]l\iqX Zfdf el\mX dX^e`kl[ Y|j`ZX** ND]l\iX e\r\jXicJ gifZ\[\i j`\dgi\ Zfdf _XZ\ =i`[^dXe' \c <e|c`j`j [`d\e)

j`feXc j\i~X*le djkild\rkf `e•k`c' gl\j \e \c gcXek\Xd`\ekf _XZ\ iXqfeXd`\ekfjkXe ZXjl~Xk`Zfjp XcXdY`ZX[fjhl\ [\jZfiXqfeXe X kf[f \c hl\ kiXk\ [\ `e`Z`Xij\\e \jk,*j Xjlekfj p' X[\d|j' xZ€df jXY\i Zl|e[f p Z€df j\ [\Y\ Xdgc`Xi cXYXj\;@rk\*\a\dgcf dl\jkiX hl\' \e H\Z|e`ZX' ef _Xp iXq€e e`e^leX gXiX kXcCN(gc`XZ`€e*

R* H@>yID>< ?@ AGPD?JN -.1

@c]cl`[f `ek\im`\e\ \e \c e•d\if [\ M\pefc[j gfi \c ZfZ`\ek\

d 3 )))) 0))'g

UmV3 B@%U$

hl\ i\Z`Y\ \c efdYi\ [\ dWa]]aWROR]W\S[obWQO)GXgi\j\eZ`X [\ cX[\ej`[X[ \j [\Y`[X XcXjXZ\c\iXZ`fe\j [\ cXdXjX

]cl`[X' gfi cf hl\ j\ gl\[\ X]`idXi hl\ \c e•d\if [\ M\pefc[j ]`^liXi|\e cXjfclZ`€e X d\efj [\ hl\ j\ kiXk\ [\ le dfm`d`\ekf i\Zk`c~e\f'

cXd`eXip \jkXZ`feXi`f*

#$! -FM@PG>@FWIABCGPFAJNKJMOP?BMV>N!

C$ DpUW[S\ ZO[W\O`)

@e cfj \oki\dfj [\ le klYf i\Zk`c~e\f [\ cfe^`kl[ Up iX[`f `&j\dXek`\e\ leX [`]\i\eZ`X [\ gi\j`€e ZfejkXek\' cY$ hl\ _XZ\ Z`iZlcXile]cl`[f* N\ jlgfe\ hl\ \c i}^`d\e \j cXd`eXip j\ kiXkX[\ ZXcZlcXicXm\cf)Z`[X[ d\[`X' B$ leX m\q \jkXYc\Z`[f \c i}^`d\e g\idXe\ek\*

NfclZ`€e6

Kl\jkf hl\ \c dfm`d`\ekf \j i\Zk`c~e\f p g\idXe\ek\' ef _XYi| XZ\c\iXZ`fe\j'p ef j\i| gi\Z`jf kfdXi \e Zfej`[\iXZ`€e cX[\ej`[X[ [\c ]cl`[f* OXdgfZf `ek\i)m\e[i| jl g\jf \jg\Z~]`Zf' gl\jkf hl\ cXj ]l\iqXj \ok\i`fi\j jfe kXe j€cf cXj

[\Y`[Xj X cX[`]\i\eZ`X [\ gi\j`€e*

G +&Y ` ]G

9 , (, , (,: J , J ,@ ( , $) J (,

-kc , (, , ,

J U^0%.

`BO9

-kc 3((Z+&Y

@c^Xjkf \e mfcld\e' =$ j\i|6

Page 63: Análisis dimensional

(), <IyGDNDN ?DH@INDJI<G

@c<e|c`j`j [`d\ej`feXc ef g\id`k\ _XccXicX]fidX [\ cX]leZ`€e le`m\ijXc 2Q'

g\if' j` j\ kiXkX[\ le ]cl`[f `eZfdgi\j`Yc\' YXjkXZfej`[\iXi hl\' Xc [lgc`ZXicXcfe^`kl[' j\i| gi\Z`jf [lgc`ZXi kXdY`}e cX[`]\i\eZ`X [\ gi\j`€e gXiXfYk\e\i\c d`jdf ^Xjkf' [\ [fe[\ i\jlckX hl\ \c ^Xjkf [\Y\ j\i gifgfiZ`feXc X cXZX~[X[\ gi\j`€e gfi le`[X[ [\ cfe^`kl[* M\jlckX Xj~cX]€idlcX [\ Kf`j\l`cc\6

C 3 A )R1;;^Y)R) U

A4i . %

D$ DpUW[S\ bc`PcZS\b]) Bp`RWRORS QO`UO)

zjk\ \j \c ZXjf[\ d|j `ek\i}j gi|Zk`Zf p' Zfdf \j `dgfj`Yc\ XYfi[Xicfk\€i`ZXd\ek\' j\ i\Zlii\ X ]€idlcXj \dg~i`ZXj* @c<e|c`j`j [`d\ej`feXc\j le `ejkild\ekf gi\Z`fjf gfihl\ j`im\ [\ ^l~X gXiX\eZfekiXicXj*

< cXjdX^e`kl[\j Zfej`[\iX[Xj \e \c i}^`d\e cXd`eXi _Xp hl\ X^i\)^Xi cX[\ej`[X[* Kfi fkiX gXik\' ZlXe[f \c ]cl`[f gl\[\ j\i kiXkX[fZfdf`eZfdgi\j`Yc\' ef \j gi\Z`jf Zfej`[\iXi cX[`]\i\eZ`X [\ gi\j`fe\j p cXcfe^`kl[ gfi j\gXiX[f' j`ef cXg}i[`[X [\ gi\j`€e gfi le`[X[ [\ cfe^`kl['6 3 [UY'U&?\ \jk\ df[f' XcXgc`ZXi\c <e|c`j`j [`d\ej`feXc' j\ fYk`\e\e[fj dfefd`fj [\ [`d\ej`€e elcX' XjXY\i6

J BO8&&,( Z-:"

) );D4 ]YZ 9r'

72% m

\c gi`d\if [\ cfj ZlXc\j gl\[\ jljk`kl`ij\ gfi6

p cXg}i[`[X [\ ZXi^Xgfi le`[X[ [\ cfe^`kl[ \jk| [X[X gfi6

GX]€idlcX \dg~i`ZX#[\ AXee`e^ \j6

@e i}^`d\e cXd`eXi' cX]€idlcX [\ Kf`j\l`cc\ [X6

:4 ,]O8& &

`-

o* H@>yID>< ?@ AGPD?JN ()-

Z% GSZ]QWRORS\ Tc\QWr\ RS ZORWabO\QWOO ZO^O`SR)

N\^•e cX_`g€k\j`j [\ KiXe[kc' Xgc`ZX[XXcZXjf hl\ efj fZlgX' j\]fidX \e cXZXiXek\ieX [\c klYf leX [\c^X[X ZXgX]cl`[X \e cXhl\ j\fi`^`eXe i\dfc`efj dlp `ek\ejfj' hl\ j\ [`]le[\e cl\^f \e \c i\jkf [\ cXdXjX ]cl`[X*@e \jkX QO^OZq[WbSmXi~Xi|g`[Xd\ek\ cXm\cfZ`[X[ XcgXjXi[\ le glekf X fkif' gfi cf hl\ \e \ccXj\ fi`^`eX cXdXpfi gXik\ [\ cXjXZZ`fe\j hl\' gfi \]\Zkf [\ cXm`jZfj`[X[' j\ \a\iZ\e \eki\ \c j€c`[f p \c

]cl`[f*Al\iX [\ cXZXgXc~d`k\' cXZfii`\ek\ j`^l\ j`\e[f kliYlc\ekX' g\if cXj

]clZklXZ`fe\j [\ cXm\cfZ`[X[' kXekf\e dX^e`kl[ Zfdf \e [`i\ZZ`€e' jfecf jl]`Z`\ek\d\ek\ g\hl\•Xj gXiXhl\ k\e^X j\ek`[f \c kiXkXi[\ Xm\i`)^lXi \c mXcfi'd&[\ cXm\cfZ`[X[ \e ZX[Xglekf*

GXj mXi`XYc\je[\g\e[`\ek\j \e \jk\ gifYc\dX jfe6 cX[`jkXeZ`X'g&) [\c glekf X cXgXi\[' cX[\ej`[X[' g' cXm`jZfj`[X[ Z`e\d|k`ZX' m' p cX

ZX~[X[\ gi\j`€e gfi le`[X[ [\ cfe^`kl[' 6& >fe \jkXj dX^e`kl[\j p cXm\cfZ`[X[' d&j\ fYk`\e\e cfj j`^l`\ek\ dfefd`fj g`6

:`!- 9 ))7

Y]-Z]

!. 9 ))7Q

J!/ 3()

`

>fem`\e\ X_fiX`ekif[lZ`i cX]l\iqX kXe^\eZ`Xc')i' hl\ \c ]cl`[f \a\iZ\jfYi\ cXle`[X[ [\ jlg\i]`Z`\ [\c klYf* >fdf \e i}^`d\e \jkXZ`feXi`f_X[\ j\i6

i\jlckX6

>fe Xlo`c`f [\ \jkXel\mX dX^e`kl[ j\ gl\[\ ]fidXi \jk\ fkif j`jk\dX[\ dfefd`fj g` `e[\g\e[`\ek\j6

' "T"

!-9)).7QU c!%>!c!‚‚ . ) '

: U

''#/ 3 -+ "T" \ 78'- g U

Wj\i|6

gXiX g5 ,&

Page 64: Análisis dimensional

<IyGDNDN ?DH@INDJ <G().

* * * *kiX\c <e|c`j`j [`d\ej`feXc* <_fiX \j gcXl)zjkX \j cX`e]fidXZ`€e hl\ Nrk id`eX[X gfi cXm\cfZ`[X[ d \e leX ZXgX

j`Yc\ X[d`k`i rl\ cX*]l\iqX !- hl\ X[

rJ\hl\ g\id`k\ X]`idXi hl\ DE`cef [\g\e[\j`klX[X X cX[`jkXe>DXS [\ X gXi\ '[\ `&p' \e Zfej\Zl\eZ`X' _XYi| [\ j\i6

d 3 Q7 r. $ r r% ‚

* Yc ` j\ fYk`\e\e [fj! [ cXZXgXc`d`k\ WcXjmXi`X \j !' g' U S

>fe \c \jg\jfi' ,' \dfefd`fj g`' W_XYi| [\ j\i6

+%9m$]r$rQ7%vl\ cX]l\iqX ! gifZ\[X \e jl dXpfi gXik\ [\

OXdY`}e \j iXqfeXYc\ jlgfe\i r `e]clpX j\ej`Yc\d\ek\ \c iX[`f Whl\cXZXgXc`d`k\' cf hl\ cc\mXZfej`^f hlr efcX]leZ`€e r j\ i\[lqZX Xle e•d\if ]`af6

j 9 N%Q r *| [ XZl\i[f Zfe cfj i\jlckX[fj fYk\e`[fj

GXj gi\m`j`fe\j gi\Z\[\ek\j \jk e \ F| |e% Wd\[`[Xj \og\i`d\ekXc\j*d\[`Xek\ [\jXiifccfj k\€i`Zfj $KiXe[kcp mfe [ ir c` #k\ j\ fYk`\e\ cX\o)KXiXcX[`jki`YlZ`€e [\ m\cfZ`[X[\j d|j Xcc| \ X ZXgX d`

gi\j`€e cf^Xi`kd`ZX6 - s))7 $ V` - s))7%d 3 1'31 G Kcf^ - & (U( G g '

* * [\c klYf @ce•d\if [ [\g\e[\ [\ cXil^fj`[X[hl\ \j m|c`[X _XjkX\c eljdf GLG ) ) [`d\ej`€e c`e\Xc'V)N\^•e KiXe[kc'[\ cXjgXi\[\j' cXZlXcj\ [\]`e\ d\[`Xek\ leX

d`\ekiXj j\X*

X

"T! VBB ((2.': U

cX jlg\i]`Z`\ gl\[\ ZXc`]`ZXij\[\ c`jX' W\j [ 3 5*

* k Y c`jfj j\ lk`c`qXcX]€idlcX*KXiXZXcZlcXi\c \jg\jri [\ cXZXgXc`d`k\ \e l fj

[\ KiXe[kc6

+%9 /U #H)

#%! 9JO>@FWIABPI> KG>@>BI PI> @JMMFBIOBCGPFA>!

< leX gcXZXi\ZkXe^lcXi' d€m`c \r kfief *[\ lef [6r6r6r\6 rrZrrd\ki~X $]~^*-%'j\ _XZ\cc\^XileX ZfiiD\ek\ ]cl`[X g\ig\ *# XcX\a\* >fe m\cfZ`[X[\j g\hl\•Xj' cXgcXZXj\ ZfcfZXg\ig\e[`ZlcXid\ek\

o* H@>yID>< ?@ AGPD?JN ()/

Zfii`\ek\' g\if ZlXe[f cXm\cfZ`[X[i\YXjXZ`\ikf c~d`k\' hl\ [\g\e[\ [\cXeXkliXc\qX[\c ]cl`[f' X[hl`\i\ le dfm`d`\ekf [\ ifkXZ`€ele`]fid\*WLl} gl\[\ gi\[\Z`ij\ i\jg\Zkf [\ cXm\cfZ`[X[Xe^lcXi 2)<5

q

ADB*-* ) MfkXZ`€e[\ leX gcXZXi\ZkXe^lcXi \e leX Zfii`\ek\ ]cl`[X

@jk\ gifYc\dX \j `eXYfi[XYc\ gfi m~Xk\€i`ZXp' gfi \jf' ]l\ gifgl\jkf gfiM`XYflZ_`ejbp Zfdf \a\dgcf k~g`Zf[\ Xgc`ZXZ`€e[\c <e|c`j`j [`d\ej`feXc*

GXj dX^e`kl[\j X Zfej`[\iXi jfe' [\j[\ cl\^f' cXj [`d\ej`fe\j O WP [\ cXgcXZX'cX[\ej`[X[ p cXm`jZfj`[X[ [\c ]cl`[f p cXm\cfZ`[X[' d&[\c d`jdf* >fdfj\ [`Z\ \e \c \eleZ`X[f hl\ cXgcXZXXZXYXgfi ^`iXi Zfe m\cfZ`[X[ ZfejkXek\'gf[i~X Zi\\ij\ hl\ ef `ek\im\e[i| jl dfd\ekf [\ `e\iZ`X*N`e \dYXi^f' \j [\k\e\i \e Zl\ekX hl\ cXjXZZ`fe\j [\ cXZfii`\ek\ ]cl`[X jfYi\ cXgcXZXjfe [`]\i\e)k\j \e cXj [`m\ijXj ]Xj\j [\c dfm`d`\ekf' gfi cf hl\' j` Y`\e }jk\ j\i| g\i`€[`Zf'ef gl\[\ j\i le`]fid\* >lXe[f cXgcXZX'gfi \a\dgcf' \j efidXc X cXZfii`\ek\'[`Z_Xj XZZ`fe\j j\ \hl`c`YiXe gfi iXq€e [\ j`d\ki~X' Wj\i| leX gfj`Z`€e [\ \hl`)c`Yi`f d|j f d\efj gi\ZXi`f* Gf d`jdf jlZ\[\ ZlXe[f \c gcXef [\ cXgcXZX\j'6:XiXc\cfX cX Zfii`\ek\* CXYi|' gl\j' XZ\c\iXZ`fe\j W j\i| gi\Z`jf kfdXi \eZfej`[\iXZ`€e \c dfd\ekf [\ `e\iZ`X*($ [\ cXgcXZXZfe i\cXZ`€e Xc\a\ [\ ifkX)Z`€e* >fe \jkXj dX^e`kl[\j' gifZ\[`\e[f X cXdXe\iX Zc|j`ZX' i\jlckX6

[fe[\ e 3 PMO)GXgi\j\eZ`X [\c ]XZkfi [\ ]fidX PZO_XZ\ hl\ \jkX ]€idlcX j€cf k\e^X lk`c`[X[

gXiXZfdgXiXi \c ZfdgfikXd`\ekf [\ gcXZXj[\ ]fidX j\d\aXek\* @j `e[l[XYc\'j`e \dYXi^f' hl\ cXj [`d\ej`fe\j O WL _Xe [\ `ek\im\e`i dlp [`]\i\ek\d\ek\\e \c ]\e€d\ef' ZfjX hl\ ef \j k\e`[X \e Zl\ekX XcXgc`ZXi\c <e|c`j`j [`d\ej`f)eXc*Kfi \jf' i\\dgcXq€ M`XYflZ_`ejbp \c dfefd`f Q[ \e hl\ ]`^liX ,&gfi fkiffYk\e`[f _XccXe[fcXiXq€e \eki\ \c dfd\ekf [\ `e\iZ`X [\ cXgcXZXp \c dfd\ekf

<IyGDNDN ?DH@INDJI<G* ) 5

Page 65: Análisis dimensional

(*' <IyGDNDN ?DH@INDJI<G

[\ `e\iZ`X [\c Z`c`e[if ]cl`[f hl\ fZlgX \c \jgXZ`f YXii`[f gfi Xhl}ccX'Zfe cfhl\ i\jlckX6

j`\e[f [\ efkXi hl\ \e cX\ogi\j`€e [\ ;D _X [\ ]`^liXi gi\Z`jXd\ek\ cX[`d\e)j`€e kiXejm\ijXc' O&[\ cXgcXZX*@jkX\ogi\j`€e \j lk`c`qXYc\Zfe gcXZXji\ZkXe)^lcXi\j ZlXc\jhl`\iX Wdl\jkiX cX\og\i`\eZ`X hl\' cf d`jdf Zfe X^lX hl\ >feX`i\' cXifkXZ`€e j\ `e`Z`XZlXe[f \c dfefd`f

mXc\.' S j\ \jkXY`c`qXZlXe[f -(0- 3 1*KXiXZfdgc\kXi cX`e]fidXZ`€e fYk\e`[X Zfe \c <e|c`j`j [`d\ej`feXc _X j`[f

gi\Z`jX leX ]\c`q `[\X* Q\Xdfj hl\ j\ cc\^X Xcd`jdf i\jlckX[f [`jZi`d`eXe[fcXj [`d\ej`fe\j \jgXZ`Xc\j*

OfdXe[f \a\j ]`afj' Zfdf `e[`ZX cX]`^liX' \c ]\e€d\ef \j j`d}ki`Zf i\jg\Zkf[\c gcXef fh) @jkXZfej`[\iXZ`€e YXjkXgXiX_XccXicX]€idlcX [`d\ej`feXc [\ ]G'gl\j cXj ]l\iqXj [\Y`[Xj X cXm`jZfj`[X[ _Xe [\ j\i j`d}ki`ZXj Zfe i\cXZ`€e X[`Z_f gcXef' gfi cf hl\ YXjkXkfdXi \e Zl\ekX cXj Zfdgfe\ek\j gXiXc\cXjXcd`jdf' W[\ cX \ogi\j`€e

[m[` 3 ]G (RE&

[e

i\jlckX6

Zfe cf ZlXc6

W\c Z|cZlcf j\ [`jgfe\ Zfdf j`^l\6

Zf d : H8 O P ,

>_a 9 , $) J , J )>g J J ( , ( , J , J: J J , , J J ,@ (, ( , J ( , J J J

-(0- , ( , J J , J J-(0) J , , ( , , J 9-(0* J J ( , J )0 ( , ,

V 9 07 W4.

d #d^O ,$Zf 9 r ZK (H8(" ^PO"

p j\ fYk`\e\ [`i\ZkXd\ek\ cX]€idlcX j`e ]XZkfi [\ ]fidX WZfe cX[`d\ej`€e O \e\c e•d\if [\ M\pefc[j*

(*(o* H@>yID>< ?@ AGPD?JN

0 Q\cfZ`[X[ [\ gifgX^XZ`€e[\c jfe`[f*- *

@e cfj ]cl`[fj' cXj g\ikliYXZ`fe\j cfZXc\jj\ gifgX^Xe \e ]fidX [\[Xj \e cXjhl\ cXjZfe[\ejXZ`fe\j Xck\ieXeZfe cXj[`cXkXZ`fe\j*@j [\

ORGUGRhl\ cXm\cfZ`[X[[\ gifgX^XZ`€e'd&[\ cXjfe[Xj gcXeXj'[\g\e[Xr\ cX[\ej`[X[' g' S [\c Zf\]`Z`\ek\ [\ Zfdgi\j`Y`c`[X[' T$ Zfe cf ZlXc\c<e|c`j`j [`d\ej`feXc Zfe[lZ\ X cX\ogi\j`€e6

d 9 Sd bcg *

GXk\fi~X Zfdgc\kX [X S 3 -*

-1* Je[Xj jlg\i]`Z`Xc\j \jkXZ`feXi`Xj*

CXccXi\c g\i~f[f [\ cXjm`YiXZ`fe\jjlg\i]`Z`Xc\j [\ le c~hl`[f Zfe)k\e`[f \e le mXjf Z`c~e[i`Zfgif]le[f* N\ jlgfe\ hl\ `ek\im`\e\e jfcX)d\ek\ cXjj`^l`\ek\j dX^e`kl[\j6 [\ej`[X[' g' p g\jf \jg\Z~]`Zf' e 3 g^'[\c c~hl`[f' p \c iX[`f' `&[\c mXjf*

NfclZ`€e6

-2* M\jfeX[fi\j [\ C\cd_fckq*

CXccXicX i\cXZ`€e \eki\ cfj *g\i~f[fj gifg`fj [\ [fj i\jfeX[fi\j^\fd}ki`ZXd\ek\ j\d\aXek\j*

GXjdX^e`kl[\j XZfej`[\iXi jfe6 cX[\ej`[X[' g' [\c X`i\' jl Zfdgi\)j`Y`c`[X['o' p leX [`d\ej`€e c`e\Xc'U&

NfclZ`€e6

"T! 3 SZGfB&

[fe[\ S \j leX ZfejkXek\ hl\ j€cf [\g\e[\ [\ cX]fidX [\c i\jfeX[fi*

-3* C`[i€d\kif [\ I`Z_fcjfe*

Pe _`[i€d\kif [\ I`Z_fcjfe' [\ dXjX [& ]cfkX\e le c~hl`[f [\[\ej`[X[ g* N\ [X Xc_`[i€d\kif le g\hl\•f \dgla€e _XZ`XXYXaf'p j\[\aX XYXe[feX[f Xj~d`jdf* N\ kiXkX[\ _XccXi\c g\i~f[f' b&[\ cXjfjZ`cX)Z`fe\j' jlgfe`\e[f hl\ ef `e]clp\ cXk\ej`€e jlg\i]`Z`Xc' hl\ \j [\jgi\Z`X)

Page 66: Análisis dimensional

-/. <IyGDNDN ?DH@INDJI<G

Yc\ cXm`jZfj`[X[ p hl\ cXmXj`aXhl\ Zfek`\e\ \c c~hl`[f \j [\ ^iXe[\j[`d\ej`fe\j' X ]`e [\ hl\ ef `e]clpX \c dfm`d`\ekf [\c c`hl`[f*

@c_`[i€d\kif `ek\im\e[i| gfi jl dXjX' [& gfi jl g\jf' H&Wgfi cXj\ZZ`€ekiXejm\ijXc' E&[\ jl m|jkX^f* @cc`hl`[f j€cf gl\[\ `e]cl`i gfi jl g\jf \jg\Z~)]`Zf' YP& A`eXcd\ek\' _XYi| hl\ kfdXi \e Zl\ekX cX gfj`Yc\ `e]cl\eZ`X [\ cXXdgc`kl[' O&[\ cXj fjZ`cXZ`fe\j*

>fdf cfj [fj m\Zkfi\j' H WYP$ hl\ ]`^liXe \e cXc`jkX[\ dX^e`kl[\j' k`\e\e`^lXc [`i\ZZ`€e hl\ cXj [~jcfZXZ`fe\j [\c m|jkX^f' eX[X j\ Zfej\^l`i| Xlehl\ j\[`jZi`d`e\e cXj Zfdgfe\ek\j' Wi\jlckXi|6

[ H QI ? O

9 9 9 - ). . -: 9 - - - 9 9F - 9 ). ). 9 9

(<8 - ) -+. 9 -+. -+. 9(<) 9 9 9 9 ) -+. -(<) 9 9 - )- ) /+. 9

V 3 /7 K3 /'

Zfe cf hl\' k\e`\e[f \e Zl\ekX hl\ H 3 VP$ cXjfclZ`€e \j6

><K~OPGJ RD

+/97.26S52-+

#! /G KMFI@FKFJABNFHFGFOPA" G>AFN@MFHFI>@FWIABG>NAFHBINFJIBNABGBNK>@FJ!

@c\jkl[`f [\c dfm`d`\ekf [\ le j€c`[f \e \c j\ef [\ le ]cl`[f k`\e\^iXe `ek\i}j gfi jl Xgc`ZXZ`€eXcfj YXiZfj p Xcfj Xm`fe\j*GXj[`]`ZlckX)[\j [\c Z|cZlcf k\€i`Zf jfe `ejlg\iXYc\j' gfi cf hl\ j\ lk`c`qXe]€idlcXj\dg~i`ZXj gXiX\jkXYc\Z\icXjZlXc\j j`im\ [\ ^l~X\c <e|c`j`j [`d\ej`feXc*<gXik\ [\ \jkX Xgc`ZXZ`€e'\c d`jdf Xe|c`j`j Zfe[lZ\ Xc `W\QW^W]RS aW([WZWbcR&hl\ [X cXgXlkXgXiXgXjXi[\ cXjd\[`[Xj _\Z_Xj \e cfj ZXeXc\j_`[i|lc`Zfj f \e cfj k•e\c\j X\if[`e|d`Zfj XcXjhl\ j\ fYk\e[i~Xe \e cXeXm\ [\ kXdX•f eXkliXc*@cd\eZ`feX[f gi`eZ`g`f \j Zfej\Zl\eZ`X `e)d\[`XkX [\c k\fi\dX [\ g`' p gl\[\ \eleZ`Xij\ Zfdf j`^l\6

>lXchl`\i \ZlXZ`€e hl\ i\cXZ`fe\ cXj dX^e`kl[\j hl\ `ek\im`\e\e\e le ]\e€d\ef gl\[\ kfdXi cX]fidX

\e cXhl\ 3ks' 3k.# #! jfe dfefd`fj [\ [`d\ej`€e elcX' p "-# ".# *'* jfe]XZkfi\j [\ ]fidX* @e Zfej\Zl\eZ`X' cfj mXcfi\j fYk\e`[fj gXiX3kc# ZfemXcfi\j [\k\id`eX[fj [\ 3k.' 3kX ‚‚‚ j\i|e Xgc`ZXYc\jX kf[fj cfj Zl\igfjj\d\aXek\j Xclk`c`qX[f \e cfj \ejXpfj*

GXXgc`ZXZ`€e[\c <e|c`j`j [`d\ej`feXc Xcfj gifYc\dXj [\ X\ifk\Ze`Xj€cf gl\[\ j\i i\Xc`qX[Xgfi cfj \jg\Z`Xc`jkXj\e cXdXk\i`X p ef efj fZl)gXi~Xdfj \e \ccf' Xef j\i gfihl\ cX[`jk`eZ`€e \eki\ cXjki\j [`d\ej`fe\j\jgXZ`Xc\jZfejk`klp\ leX `eefmXZ`€ehl\ gl\[\ j\i dlp ]\Zle[X' gl\jj\ jljk`klp\ cXi\cXZ`€e[\ j\d\aXeqX gfi cXi\cXZ`€e[\ X]`e`[X[*

Page 67: Análisis dimensional

-/0 <IyGDNDN ?DH@INDJI<G

@c\jkl[`f [\ cXifkXZ`€e[\ leX gcXZX\e leX Zfii`\ek\ ]cl`[X' hl\_\dfj i\Xc`qX[f\e \c ZXg`klcfXek\i`fi' dl\jkiX hl\' XcXdgc`XicXYXj\`ekif[lZ`\e[f \e \ccXcXj ki\j [`d\ej`fe\j [\c \jgXZ`f' \e m\q [\ leXjfcX' \c <e|c`j`j [`d\ej`feXc i\jl\cm\ \c gifYc\dX [\ _XZ\i lk`c`qXYc\jcXjd\[`[Xj _\Z_Xj \e leX gcXZXi\ZkXe^lcXi' ef j€cf XcXjgcXZXjj\d\)aXek\j' j`ef XgcXZXji\ZkXe^lcXi\j ZlXc\jhl`\iX* @jkf efj gXi\Z\ iXq€eYXjkXek\gXiX\ejXpXi \c el\mf d}kf[f \e Xc^lefj gifYc\dXj [\ X\ifk\Z)e`X*<j~ cf _X_\Z_f pX Clekc\p $1-%'g\if ef gXi\Z\ _XY\i i\gXiX[f \ehl\ jlj i\jlckX[fj jfe' \m`[\ek\d\ek\' `eXZ\gkXYc\jp hl\' gfi kXekf'j€cf j`im\e gXiX[\jXZi\[`kXi jl `eefmXZ`€e*Ifj gifgfe\dfj _XZ\i m\ihl\ \c ]iXZXjfj\ [\Y\ X _XY\i lk`c`qX[f leX ]€idlcX [`d\ej`feXc `eZf)ii\ZkX gXiXcXm`jZfj`[X[ p hl\7 j` j\ gifZ\[\ [\Y`[Xd\ek\' j\ cc\^XX]€idlcXj hl\' j` Y`\e _Xe [\ XZf^\ij\ Zfe cX[\Y`[X i\j\imX' d\i\Z\e pXj\i jfd\k`[Xj XcXZfdgifYXZ`€e \og\i`d\ekXc*

.* ?`d\ej`fe\j [\ cXm`jZfj`[X[*

GX gi`d\iX [`]`ZlckX[Zfe hl\ j\ kifg`\qX XcXdgc`XicXYXj\ Zfej`jk\\e _XccXicX]€idlcX [`d\ej`feXc [\ cXm`jZfj`[X[*OiXj [\ dlZ_fj \ejX)pfj Zi\\dfj gf[\i i\jfcm\icX Zfdf j`^l\*

>X[X \c\d\ekf' [@' [\ cXjlg\i]`Z`\ [\ le j€c`[f jld\i^`[f \e le]cl`[f Zfe dfm`d`\ekf cXd`eXi \jk| jfd\k`[f X leX ]l\iqX kXe^\eZ`Xc[X[X gfi6

RW3 Rd [@H8 16 ! U.'-V

[fe[\ m\j cXm\cfZ`[X[p \ cXefidXc XM?&N\ kiXkX[\ leX \ZlXZ`€em\f)kfi`Xc'p gXiXgfe\icf [\ dXe`]`\jkf' i\gi\j\ekXi\dfj M? gfi le m\Zkfi[`i`^`[f j\^•e jl efidXc p Zfe le j\ek`[f \c\^`[f Zfem\eZ`feXcd\ek\*N`\e[f [N p FTm\Zkfi\j cfZXc`qX[fj\e le d`jdf glekf [\c \jgXZ`f' \jjXY`[f $&%hl\ \o`jk\ le k\ejfi' O' kXchl\' [X[f le \c\d\ekf [\ jlg\i]`)Z`\' [N' gifgfiZ`fe\ cX]l\iqX Zfii\jgfe[`\ek\ d\[`Xek\ cXfg\iXZ`€e6

FH9 O[N U.'.V

f Y`\e' Zfe i\cXZ`€eXle j`jk\dX [\ \a\j i\ZkXe^lcXi\j' DU1 D)$ >j6

`' S 3 -' .' /* U.'/V

$&% Q}Xj\' gfi \a\dgcf' \c c`Yif [\c Xlkfi $13%*

RD* <@MJ?DIyHD>< -/1

GfN\c\d\ekfj [`X^feXc\j [\c k\ejfi' O' [Xe cXj]l\iqXj efidXc\j hl\[\g\e[\e [\ cXm`jZfj`[X[*

ef Gfj \c\d\ekfj ef [`X^feXc\j [Xe cXj]l\iqXj kXe^\eZ`Xc\jf \j]l\iqfj

k k\X Kfi \a \dgcf ' j` [N \j efidXc Xc\a\ D*$ cXZfdgfe\ek\ []s [\Zfi Xe *cX]l\iqX j\i|6

U.'0V

p ZfdfU.'1V

i\jlckX cX]€idlcX [`d\ej`feXc6

G@;.M3 9%,:@%-

.U.'2V

p' \e ^\e\iXc'

`' W&Y 3 -' .' /* U.'3V

Kfi fkiX gXik\' cX\ZlXZ`€e U.'-V' ZlXe[f [N \j efidXc XD* [X6

p [\ cXZfdgXiXZ`€eZfe U.'0Vi\jlckX6

KXiXhl\ \jkX \ogi\j`fe j\X [`d\ej`feXcd\ek\ Zfii\ZkX' \j gi\Z`jfhl\ H8j\X le k\ejfi' p \jZi`Y`i6

AGW@[S3 O9RS%%$

AIX

Zfe cf hl\ U.'/V j\ Zfem`\ik\ \e6

AGb[`' 3 6@O9RS%M4S, AIX

p' k\e`\e[f gi\j\ek\ U.'3V' i\jlckXe cXj j`^l`\ek\j ]€idlcXj [`d\ej`f)eXc\j6

U.'4V

N\ m\ ]|Z`cd\ek\ hl\ cX]€idlcX [`d\ej`feXc [\ H8 fYk\e`[X \e \c ZX)g~klcf R' t -/' Zfii\jgfe[\ X ]GDN9 ]GNc# \e \c ZXjf \e hl\ GD 3 >Ol

Page 68: Análisis dimensional

-/2 <IyGDNDN ?DH@INDJI<G

%! +G>NAB>QFWI!

@cXcX[\ Xm`€ej\ [\]`e\ gfi jl g\i]`c $&%'gfi jl ]fidX \e gcXekXpgfi jl \em\i^X[liX' P) OfdXi\dfj \c \a\ Rc \e cX[`i\ZZ`€e [\ XmXeZ\p \e \c gcXef [\ j`d\ki~X [\c XcX'p \c \a\ D) \e cX[`i\ZZ`€e [\ cX\em\i^X)[liX* Nlgfe`\e[f hl\ \c g\i]`c j\ Zfej\imX Xcf cXi^f [\ kf[X cX\em\i^X)[liX' gf[i| j\i [\k\id`eX[f gfi Z`\ikf e•d\if [\ glekfj Zfe cXj Zffi)[\eX[Xj #Z"Y' Z".$&#Z!c#Z!.$))) &Zfe cf ZlXccfj ]XZkfi\j [\ ]fidX j\i|e [\[fj ZcXj\j' ZZ*Sp Z.*O&[fe[\ \ p O jfe [fj d€[lcfj ZXiXZk\i~jk`ZfjZfii\j)gfe[`\ek\j X cXj [`i\ZZ`fe\j [\ Rc p f.& i\jg\Zk`mXd\ek\* N`' gXiX j`d)gc`]`ZXicXZl\jk`€e' j\ jlgfe\ hl\ \c |e^lcf [\ XkXhl\ \j elcf' \ gl\[\j\i cXZl\i[X p K \c \jg\jfi d|o`df [\c XcX*

@c ]cl`[f `ek\im\e[i| gfi jl [\ej`[X[' gfi jl m`jZfj`[X[ p gfi cXm\cfZ`[X[' d&[\c m`\ekf i\cXk`mf*

>lXe[f j\X gi\Z`jf kfdXi \e Zfej`[\iXZ`€e cX[\ej`[X[ [\c ]cl`[f'_Xp hl\ \dg\qXi gfi _XccXijl ]€idlcX [`d\ej`feXc \e cXYXj\ Zfdgc\kX*KXiXj`dgc`]`ZXicXZl\jk`€e' jlgfe[i\dfj hl\ \c i}^`d\e \j Y`[`d\ej`f)eXc'\jkf \j' hl\ cXjc~e\Xj[\ Zfii`\ek\ j\ _XccXe\e gcXefj gXiXc\cfjXcRc I.)

KXiX\c Z|cZlcf [\ cX`SaWabS\QWOOZOdO\QS&3$ _Xp hl\ gifp\ZkXi cXj]l\iqXj jfYi\ \c \a\ Dd$ p cX[\Y`[X Xc\c\d\ekf [@ j\i|6

[` ) - )M? XB( XBU- ) ) gQc - & ]*G-.)) M?- & ]*GcN)) M?.t

- XD) XD*

?\ \jkX \ZlXZ`€e j\ [\[lZ\' \e gi`d\i k}id`ef' hl\ cX]€idlcX [`d\ej`f)eXc [\ cX[\ej`[X[ \j6 UgV9 Gc)cG.)cG/)cH* <[\d|j' j` \c i}^`d\e \jY`[`d\ej`feXc' QDj\i| `e[\g\e[`\ek\ [\ I-& S cXm`jZfj`[X[ `ek\im\e[i| gfi\c \c\d\ekf ]*G-/#ZlpX ]€idlcX [`d\ej`feXc \j6 U]*GcNV3 >Z(Z>-(Z>.?F(Z)

@cZ|cZlcf j\ cc\mXX ZXYfZfdf j`^l\6

!3 d Q S P O ]E*-/

>Z - - ) - - J J ) -Gq J J ) - J - J ) ->. J J ) - J J - ,: - J - J J J -F $) ) - J J J J ) -

W7 - $) (, J ) - (, J+, J (, ( , , J $) -

$&% KXiXcXj [\]`e`Z`fe\j' m}Xj\ \c c`Yif [\ A* GX]`kX*$14%*

RD* <@MJ?DIyHD>< -/3

U/'-V

N` ef j\ _lY`\j\ [`jk`e^l`[f \eki\ cXj [`d\ej`fe\j [\c \jgXZ`f j\ _XYi~X

fYk\e`[f6U/'.V

p ef _XYi~Xhl\[X[f [\ dXe`]`\jkf Zl|c _X [\ j\i cXjlg\i]`Z`\ E&e` cXcfe^`kl[hl\ _X [\ ]`^liXi \e \c e•d\if [\ M\pefc[j' e` \c d€[lcf hl\ _X [\ j\im`i gXiX_XccXicfj ]XZkfi\j [\ ]fidX e) Kfi \jkXj iXqfe\j' cfj i\jlckX[fj fYk\e`[fj \ecfj \ejXpfj j€cf jfe Xgc`ZXYc\jX Zl\igfj j\d\aXek\j Xcdf[\cf' d`\ekiXj hl\ cX]€idlcX U/'-Vg\id`k\ _XZ\icfj \ok\ej`mfj X kf[fj jlj X]`e\j' j\^•e mXdfj X m\i*

?\ cX\ogi\j`€e U/'-E j\ [\[lZ\ hl\' j` j\ dlck`gc`ZXecXjki\j [`d\e)j`fe\j [\c XcXgfi j\e[fj ]XZkfi\j' Yj&Y-& bj' \jkf \j' j`

cX]leZ`€e Q^8 Zfej\imXi| \c d`jdf mXcfi j` ef j\ Xck\iX\c e•d\if [\M\pefc[j' f j\X ZlXe[f

Yd" 9 W-WB

4-/

p cXel\mX i\j`jk\eZ`X XcXmXeZ\j\i|6

8" 3 Y,-Y- 8

Y X #/

XZfe[`Z`€e' [\j[\ cl\^f' [\ hl\ \c \jg\jfi d|o`df j\X g\hl\•f \e Zfd)gXiX*Z`€eZfe cX\em\i^X[liX' gXiX hl\ \c i}^`d\e j`^X j`\e[f Y`[`d\e)j`feXc*

*<[\d|j [\ cXi\j`jk\eZ`X XcXmXeZ\p [\ cX]l\iqX jljk\ekX[fiX `ek\)i\jXe cXj Zfdgfe\ek\j' 9$: p ;$ [\c gXi [\ ]l\iqXj* @c<e|c`j`j [`d\e)j`feXc' Zfe cXYXj\ \jgXZ`XcZfdgc\kX' Zfe[lZ\ X6

[fe[\ QB9$ QB: S QB; jfe ]leZ`fe\j [\c e•d\if [\ M\pefc[j W[\ cfj ]XZkf)i\j [\ ]fidX*

Page 69: Análisis dimensional

(*. <IyGDNDN ?DH@INDJI<G

Clekc\p' j`e aljk`]`ZXicf' Xki`Ylp\ X @)8 cX]€idlcX [`d\ej`feXc

Zfe cf hl\ cc\^XX cX\ZlXZ`€e

8 3 ^d-POi # g6rX%p gi\k\e[\ hl\ k`\e\ mXc`[\q ^\e\iXc* N\ m\ ]|Z`cd\ek\ hl\ \jkX jfclZ`€e \j`eXZ\gkXYc\'gl\j \e \c ZXjf [\ le XcX[\ ^iXe \em\i^X[liX 8 [\Y\ j\i gifr fi)Z`feXcX P&gXiXcf ZlXc\j gi\Z`jf hl\ r ef [\g\e[X [\ [`Z_X [`d\ej`€e' cf hl\'[\ j\i Z`\ikXcX]€idlcX [\ Clekc\p' cc\mXi~XZfej`^f cXef `e]cl\eZ`X [\ cXm`jZf)

j`[X[ jfYi\ cXi\j`jk\eZ`X XcXmXeZ\*

>fe cXYXj\ \jgXZ`Xcdlk`cX[X p gXiXcfj ]`e\j [\c <e|c`j`j [`d\e)j`feXc' eX[X [`jk`e^l\ cX TcS`hO acabS\bOR]`O&>& [\ cX i\j`jk\eZ`X XcXmXeZ\'gfi cf hl\ cXd`jdX ]€idlcX U/'.V' Zfe fkiX ]leZ`€e le`m\ijXc[\ cfj d`jdfj gXi|d\kifj' j\im`i| gXiX\c Z|cZlcf [\ >) @e cXYXj\ Xd)gc`X[X'gfi \c ZfekiXi`f' cX]€idlcX hl\ [X cX`e]cl\eZ`X [\ cXm`jZf)j`[X[ \j6

p Zfdf' j` cX\em\i^X[liX \j ^iXe[\ \e ZfdgXiXZ`€e Zfe cXj [`d\e)j`fe\j kiXejm\ijXc\j' j\ gl\[\ X[d`k`i hl\ =C ef [\g\e[\ [\ I-& YXjkXkfdXi \e Zfej`[\iXZ`€e \c \c\d\ekf H8C 4 ZlpX ]€idlcX [`d\ej`feXc \j69H9-%(9O%U:@%US j\ cc\^XX cXjfclZ`€e6

> 3 gm. POh

7T5> #^dS& Z&i$S HM S O

U/'/V

p X_fiX \c e•d\if [\ M\pefc[j i\jlckX j\i6

@& N ^dSD( ((&

HM

?\ cX\ZlXZ`€e U/'/Vj\ [\jgi\e[\ hl\ 7T5> ef ZXdY`Xi|[\ mXcfiXle)hl\ j\ dlck`gc`hl\e cXj[`d\ej`fe\j cc# Z- S cXgfi j\e[fj ]XZkfi\j b-' Y-

S bj' Zfe kXc[\ hl\ cXm\cfZ`[X[ j\ _X^Xb- m\Z\j d\efi* >fe \ccf' cXel\mX ]l\iqX jljk\ekX[fiX j\ Zfem\ik`i| \e6

>" 3 YKYh

. >)4.

-

RD* <@MJ?DIyHD>< (*/

KXiXg\i]`c\j dlp [\c^X[fj' Zfe `^lXc ]fidX \e gcXekX'j\ lk`c`qXcX]€idlcX6

> 3 =^d-PO U/'0V

d`\ekiXj hl\' j\^•e U/'/V [\Y\ j\i6

PO- $gmZ%9 3 gm.)Z) e[- ))))ss*) ‚ U/'1V

N\i~X`ek\i\jXek\ _XZ\i \ejXpfj gXiX gfe\i X gil\YX cXmXc`[\q[\ \jkXj ]€idl)

cXj' ZlpX `eZfdgXk`Y`c`[X[ \j dXe`]`\jkX*

&! ;MTINFOJABGMUDFHBIG>HFI>M>GMUDFHBIOPM?PGBIOJ!

>lXe[f cXm\cfZ`[X[ \j i\cXk`mXd\ek\ ^iXe[\' \c i}^`d\e j\ _XZ\‚ kliYlc\ekf' p cXjXZ\c\iXZ`fe\j [\ cXdXjX ^Xj\fjX jfe kXc\jhl\ gi\[f)

d`eX \c \]\Zkf [\ cX`e\iZ`X jfYi\ cXj ]l\iqXj [\Y`[Xj X cXm`jZfj`[X[*

@ekfeZ\j' cXj]€idlcXj j\ i\[lZ\e X

U0'-V

p cXj]leZ`fe\j O8 S O> ef ZXdY`Xi|e[\ mXcfiXlehl\ j\ dlck`gc`hl\e cXj

[`d\ej`fe\j W&p cj gfi ]XZkfi\j b- p m3>lXe[f j\ gifZ\[\ X cXdXe\iX Zc|j`ZX'i\jlckX le jfcf e•d\i*f [*\

M\pefc[j' ]YU'OU$p gXiXcXcfe^`kl[ Ujl\c\ kfdXij\ cXZl\i[X* <c [`j\i`)d`eXi cXj [`d\ej`fe\j \jgXZ`Xc\j efj _Xe i\jlckX[f [fj e•d\ifj [\M\pefc[j6 lef' ;D& gXiXcXi\j`jk\eZ`X XcXmXeZ\'p fkif' ;! D& gXiXcX

jljk\ekXZ`€e6

@"D4im

ZX[Xlef [\ cfj ZlXc\j Zfe[lZ\ XleX m\cfZ`[X[ZXiXZk\i~jk`ZX6

UGdQ0 %%.

O-

7 QBQ0%!

N

>fdf d\[`[X [\ cXkliYlc\eZ`X \e le glekf gl\[\ kfdXij\ cXiX~qZlX[iX[X [\c mXcfid\[`f [\ cXj]clZklXZ`fe\j [\ cXm\cfZ`[X[ \c\mX[Xj

Page 70: Análisis dimensional

-0, <IyGDNDN ?DH@INDJI<G

XcZlX[iX[f* ?`m`[`\e[f gfi cXm\cfZ`[X[ d\[`X j\ k\e[i| leX dX^e`kl[[\ [`d\ej`€e elcX' p _XYi| [\ j\i6

CXjkXX_fiX' gfi ef Zfej`[\iXi d|j hl\ leX [`d\ej`€e \jgXZ`Xc'j\fg\iX Zfe le jfcf e•d\if [\ M\pefc[j' p j\ gi\k\e[\ hl\ \c ki|ej`kf [\ci}^`d\e cXd`eXiXckliYlc\ekf _X [\ gif[lZ`ij\ gXiXZ`\ikf mXcfi>i~kD>J[\c d`jdf* GXgi\Z`j`€e hl\ j\ cf^iX \e cXjd\[`[Xj [\ [`Z_f mXcfiZi~k`Zf\j dlp d\[`fZi\' p ZXY\g\ejXi hl\ \ccf j\X [\Y`[f X hl\' Xle \e \cZXjf [\ le gifYc\dX \e [fj [`d\ej`fe\j' `ek\im`\e\e [fj e•d\ifj [\M\pefc[j hl\' dlp gifYXYc\d\ek\' _Xe [\ `e]cl`i [\ [`jk`ekf df[f jfYi\cXkliYlc\eZ`X*@e le j`jk\dX [\ \a\j' Zfe @D p @"D Zfdf Zffi[\eX[XjrZlir #

`^#@D&@"D$ 3 Zi\gi\j\ekX \c ki|ej`kf [\ cXi\^`€e \e hl\ \c i}^`d\e \j cXd`eXi XcX[\kliYlc\eZ`X*

'! 9BHJGFIJNAB 3TMHTI!

?\ki|j [\ le Z`c`e[if YX•X[f gfi PeX Zfii`\ek\ kiXejm\ijXcj\ ]fidXleX \jk\cX [\ i\dfc`efj Xck\ieX[fj hl\ j\ jlZ\[\e g\i`€[`ZXd\ek\* GX]i\Zl\eZ`X' ;$ [\c ]\e€d\ef [\g\e[\i| [\ cXm\cfZ`[X[' c&[\ cX[\ej`)[X[' g' [\c ]c•`[f' p [\ jl m`jZfj`[X[ Z`e\d|k`ZX' d&@cZ`c`e[if `ek\im\e)[i| gfi jl iX[`f' `&)>fe cXjdX^e`kl[\j \e Zl\jk`€e j\ ]fidXe [fj df)efd`fj g`6

I•d\if [\ M\pefc[j6

\Z@D4(()

d

I•d\if [\ Nkil_Xc6

@`@a0%%

\

p \c <e|c`j`j [`d\ej`feXc X]`idX hl\ [\Y\ j\i6

RD* <@MJ?DIyHD>< -0-

4> \og\i`\eZ`X dl\jkiX hl\ \c ifjXi`f [\ i\dfc`efj j\ ]fidX Zfec!@#^lcXi`[X[gXiXmXcfi\j [\ ;D Zfdgi\e[`[fj \eki\

1, 8 @D 8 0,,*,,,'

p hl\' XgXik`i [\ @D 3 /,,' cXj]l\iqXj [\Y`[Xj XcXm`jZfj`[X[ jfe [\j)gi\Z`XYc\j\e ZfdgXiXZ`€e Zfe cXj ]l\iqXj [\ `e\iZ`X' gfi cf hl\ \c e•)d\if [\ Nkil_Xc j\ dXek`\e\ j\ej`Yc\d\ek\ ZfejkXek\ p mXc\6

@a &)))&,'-5*

(! 2ICGPBI@F>ABG>@JHKMBNF?FGFA>A!/G IXHBMJAB5>@E!

KXiXcXjm\cfZ`[X[\j dlp ^iXe[\j' cfj ZXdY`fj [\ [\ej`[X[ gif[lZ`)[fj \e \c ]cl`[f gfi cfj ZXdY`fj [\ gi\j`€e jfe kXeZfej`[\iXYc\j hl\ j\fi`^`eXe fe[Xj jfefiXj' Zfe cX Zfej`^l`\ek\ [`j`gXZ`€e [\ \e\i^~X* @jgi\Z`jf' gfi kXekf' kfdXi \e Zfej`[\iXZ`€e cXZfdgi\j`Y`c`[X[ [\c ]cl`[fp' \m\eklXcd\ek\' Xki`Yl`ic\ cX ]€idlcX [`d\ej`feXc X[\ZlX[X* N` \c]cl`[f \j `j€kifgf' cXj fe[Xj \c\d\ekXc\j k\e[i|e j`d\ki~X \j]}i`ZX' pkf[Xj cXj [`i\ZZ`fe\j j\i|e \hl`mXc\ek\j' gfi cf hl\ cX]€idlcX [`d\e)j`feXc [\ cXZfdgi\j`Y`c`[X[ j\i|6

GX`ek\im\eZ`€e [\ cXZfdgi\j`Y`c`[X[ _XZ\ hl\' kXekf\e cXi\j`jk\e)Z`XXcXmXeZ\Zfdf \e cXjljk\ekXZ`€e' XgXi\qZXle el\mf e•d\if g`' \ce•d\if [\ HXZ_' ]fidX[f Zfe d&g' Wo6

Kfi fkiX gXik\' \j jXY`[f hl\ cXm\cfZ`[X[ [\ cXj fe[Xj jfefiXj \jk|[X[X gfi6

,da4((&QoK

cl\^f6

@e \c ZXjf [\ le XcXdlp XcXi^X[X'hl\ XmXeqXZfe m\cfZ`[X[\jgi€o`dXj XcX[\c jfe`[f' cXj]l\iqXj [\Y`[Xj XcXm`jZfj`[X[ jfe [\jgi\)

Page 71: Análisis dimensional

-0. <IyGDNDN ?DH@INDJI<G RD* <@MJ?DIyHD>< -0/

Z`XYc\j'p cXj]€idlcXj jfe6

8 3 ^d)PO7B8 ";:! rc' r%

> 3 ^d- P2-

QB> ";:! c$ c#&

@jkXj\ogi\j`fe\j g\id`k\e Xm\i`^lXicf hl\ jlZ\[\ ZlXe[f kf[Xj cXj[`d\ej`fe\j gXiXc\cXjX ZX[Xlef [\ cfj \a\j j\ dlck`gc`ZXegfi le ]XZ)kfi ZlXchl`\iX*

*! ,JH?>N " QBIOFG>AJMBN!

)! 1UGF@B!

GXj YfdYXj p cfj m\ek`cX[fi\j k`\e\e gfi fYa\kf gif[lZ`i leX Zf)ii`\ek\ ]cl`[X*<c [\jXiifccXi jl k\fi~Xj\ gi\jZ`e[\ [\ cXjXZZ`fe\j [\Y`)[Xj XcXm`jZfj`[X[' gfi j\i [\jgi\Z`XYc\j \e ZfdgXiXZ`€eZfe cXjfZXj`f)eX[Xj gfi cX`e\iZ`X [\c ]cl`[f* <[\d|j [\ cfj ]XZkfi\j [\ ]fidX' j\i|emXi`XYc\je[\g\e[`\ek\j \c iX[`f' `&[\c ifkfi' jl m\cfZ`[X[ Xe^lcXi' Zf'

p cX[\ej`[X[' g' [\c ]cl`[f* OXdY`}e \j mXi`XYc\e[\g\e[`\ek\ \c ^Xjkf\e mfcld\e' _&gl\j j`\dgi\ j\ gl\[\ i\^lcXi cXj\ZZ`€e [\ jXc`[X*>fe\jkfj [Xkfj' \c <e|c`j`j [`d\ej`feXc Xgc`ZX[fX cXdXe\iX Zc|j`ZXZfe)[lZ\ X cXj`^l`\ek\ \ogi\j`€e gXiXcXjfYi\gi\j`€e6

<gXik\ [\ cfj ]XZkfi\j [\ ]fidX' cXjmXi`XYc\je[\g\e[`\ek\j j\i|e6leX [`d\ej`€e c`e\Xc'gfi \a\dgcf' \c iX[`f' `&[\ cXgXcX'cXm\cfZ`[X[[\XmXeZ\'d&p cXm\cfZ`[X[ Xe^lcXi' Zf* ?\c ]cl`[f `ek\i\jX kXej€cf cX[\e)j`[X[' gl\j cXj]l\iqXj [\Y`[Xj XcXjXZ\c\iXZ`fe\j [\c ]cl`[f gi\[fd`eXeZfej`[\iXYc\d\ek\ jfYi\ cXjfZXj`feX[Xjgfi cXm`jZfj`[X[*@e \jkXj Zfe)[`Z`fe\j' \c <e|c`j`j [`d\ej`feXc' ZlXe[f ef j\ [`jk`e^l\ \eki\ cXj ki\j[`d\ej`fe\j [\c \jgXZ`f' Zfe[lZ\ X cXj j`^l`\ek\j \ZlXZ`fe\j6

Kfk\eZ`X6 Y J / 1 #`7WZ ( $) g>`c ` QBY (d(&Zf' ***

< W .. #_ ( $lg ) g>`c Z QB ((& Zf' * ** *#7WZ`.

OiXZZ`€e6 @% .W0 #`7WZ ( $) g>`c)i 7BF (d(&>`cs' ‚‚‚

>fe cXYXj\ Zfdgc\kX' j` j\ gi\jZ`e[\ [\ cX]fidX [\ cfj |cXY\j' _XYi|hl\ `ekif[lZ`i [fj d€[lcfj' hl\ gl\[\e j\i \c iX[`f' `&p \c \jg\jfi' Q$[\c ifkfi* CXZ`\e[f Zf`eZ`[`i \c \a\ Rc Zfe \c \a\ [\ ifkXZ`€e'i\jlckX6

M\e[`d`\ekf6 Fd B 7BF"?L3(3(()

B >`ci 7B^

[8&Y Zf ` _ g V

9U 9 9 9 ( , ) - ,9-& / ( , 9 , ) $) 9: , "+ 9 9 , 9F $) (, 9 (, 9 9

-<( , $) ( , 9 ( , ( ,-<) 9 (, $) , 9 (,

8)) 3 ^7WZ-`VQ^ #(_(& X X$7WZ`-V W3" ` )

@j [\ \jg\iXi hl\ cX`e]fidXZ`€e j\X dXpfi j` j\ lk`c`qXcXYXj\ Zfd)gc\kX*rfdri\dfj \a\j Zffi[\eX[fj jfc`[Xi`fj Zfe cXgXcX7\c \a\ Rc j\i|\c gifg`f \a\ [\ cX_}c`Z\' p \c \a\ D) cX\em\i^X[liX' `&[\ cXgXcX*Gfj]XZkfi\j [\ ]fidX j\i|e [\ ki\j ZcXj\j U8Q U8Q p U8Q [fe[\ Q % `' ' - c# . . / /# . ) '

p cfj d€[lcfj Qbp V. jfe' i\jg\Zk`mXd\ek\' cXjgifp\ZZ`fe\j jfYi\ Rc p RX

[\ le j\^d\ekf Zfem\e`\ek\d\ek\ \c\^`[f' gfi \a\dgcf' cXZl\i[X d\[`X*>fe \jkf i\jlckX6

Kfk\eZ`X6 < 3 ^7WZ.`V,.V.7B ^ # Vi7WZ &

@3 g>`c.i_-.JX

?\ \jkX \ogi\j`€e i\jlckX hl\ j` ` j\ ZXdY`X\e `" 3 T-` p Q j\ Zfe)m`\ik\ \e V"3 Y-V&cXiXq€e [\c ^Xjkf XcXm\cfZ`[X[Xe^lcXi_XYi| [\ j\i

OiXZZ`€e6 _" N - _(( 4Y(2 Y-(l

e" Zf

M\e[`d`\ekf6 Fd G 7BF"?L3(3((

B eVZ 7BB

Page 72: Análisis dimensional

-00 <IyGDNDN ?DH@INDJI<G

/% ;PM?FI>N!

Kfi cXj kXe irg\k*`[Xj*irqfe\j' j\ gl\[\ gi\jZ`e[`i [\ cXm`jZfj`[X['gfi -, hl\ \c ]cl`[f `e]cl`i| gfi jl [\ej`[X[ p gfi cXm\cfZ`[X[

kiX \e DXd| * ' d&Zfehl\ g\e\ iX \e X dXhrX* ?\ cXkliY`eX gifg`Xd\ek\ [`Z_X _XYi| hl\kfdXi \e Zl\ekX \c iX[`f' `&p \c \jg\jfi O [\c ifkfi >fe \jk [ k* ** * # ' * fj X fj'NDj\ lk`c`qXcXYXj\ dlk`cX[X' \c <e|c`j`j [`d\ej`feXc Zfe[lZ\ XcX *

) ' , ) d`jdX\ogi\j`fe gXiX Xgfk\eZ`X hl\ \e \c ZXjf [\ cX_}c`Z\6

@e ZrdY`f' Zfe*rXYXj\ Zfdgc\kX' ZfcfZXe[f \c \a\ Rc \e Zf`eZ`[\eZ`XZfe \c \a\ [\ ifkXZ`€e' j\ cc\^XX6

rf Xek\i`fi \j m|c`[f gXiXcXjkliY`eXj _`[i|lc`ZXj p gXiXcfj dfc`efj[\ QDrekf*@e \c ZXjf [\ cXj kliY`eXj [\ mXgfi _Xp hl\ kfdXi efk`Z`XX[\7eXjr [\ cXj\ekXcg~Xj'VSp Va&hl\ gfj\\ ZX[Xle`[X[ [\ dXjX Xc\ekiX7pX jXc`i [\ cXkliY`eX*>fdf \jkXj dX^dvkl[\j k`\e\e cXd`jdX [**' - #* r cd\e)

jcre hr\ X \e\i^~X gfi le`[X[ [\ mfcld\e' i\jlckXe [fj el\mfj dfef)D?DJN gc7

VS!/ 3 ((1Y]-

GX `e]fidXZ`€e jld`e`jkiX[X gfi \c <e|c`j`j [` * -Zfd c\k k\e~ d\ej`fe\ j\ gl\[\

[ [g Xi 7l\e[f \e Zl\ekX hl\ cXgfk\eZ`X \j gifgfiZ`feXc XcXg}i[`)

X \ \ekXcg~XVS ( V0)

><K~OPGJ RDD

O @H K @M< O P M< #%$

#! 4>N BN@>G>N@JIQBI@FJI>GBN!

?\j[\ cfj k`\dgfj [\ BXc`c\f kiXkXife cfj ]~j`Zfj [\ Zfejkil`i k\id€)d\kifj' f j\X XgXiXkfjhl\ g\id`k`\j\e Xki`Yl`ile e•d\if $^iX[f [\ ZXcfi%X ZX[X\jkX[f k}id`Zf* @jkf YXjkXgXiXi\gif[lZ`i cfj i\]\i`[fj \jkX[fjj`\dgi\ hl\ j\ [\j\\' p gXiXd\[`i \dg~i`ZXd\ek\ kf[Xj Xhl\ccXjdX^e`)kl[\j \e ZlpX [\]`e`Z`€e `ek\im`\e\e `ek\imXcfj [\ k\dg\iXkliX' gfi \a\d)gcf' Zf\]`Z`\ek\j [\ [`cXkXZ`€ek}id`ZX' ZXcfi\j \jg\Z~]`Zfj' \kZ*K\if \jkXjd\[`[Xj X[fc\Z~Xe[\ mXi`fj `eZfem\e`\ek\j* @e gi`d\i k}id`ef fZlii~Xhl\ cXgfj`Z`€e [\c Z\if \e cX\jZXcX\iX XiY`kiXi`X'gfi cf hl\ cXj\jZXcXjef \iXe XYjfclkXjp \e e`e^leX ]€idlcX gf[~X `ek\im\e`i cXk\dg\iXkliX'j`ef jlj [`]\i\eZ`Xj $&&%*

$&% N\^•e j\ m\i| \e \jk\ ZXg`klcf' cX k\dg\iXkliX \j' `e[l[XYc\d\ek\'leX dX^e`kl[ ]~j`ZX*K\if cXZfjX \j [`jZlk`[X p' d`\ekiXj lefj ]~j`Zfj X]`idXehl\ ef [\Y\ j\i Zfej`[\iX[X Zfdf kXc' fkifj [`Z\e hl\ ZX[XdXe\iX [\ \jkX)Yc\Z\i leX \jZXcX\dg~i`ZX [\ k\dg\iXkliXj [\]`e\ leX dX^e`kl[ [`jk`ekX*Q}Xj\cfj kiXYXafj[\ DjeXi[` $15%'Gf\[\c $0.%'Gf\[\c p N|YXkf $2,%p M\p KXjkfi $0r%*

$&&%@j \jkX fZXj`€e [\ [\Z`i \ogi\jXd\ek\ hl\ kf[Xj cXj\jZXcXjffem\eZ`f)eXc\j _Xe [\ jXk`j]XZ\i leX Zfe[`Z`€e gXiX hl\ gl\[Xe Zfem\ik`ij\ \e \jZXcXjXY)jfclkXj* >fej`jk\ \e hl\' XckfdXi Zfdf fi`^\e \c Z\if XYjfclkf' ef [\Y\e i\jlckXimXcfi\j `e]`e`kfj gXiX cXjd\[`[Xj [\ cXj [\d|j k\dg\iXkliXj* Kfi \jkX iXq€e' cX\jZXcXcf^Xi`kd`ZX [\ ?Xckfe ef j`im\ gXiX \c ZXjf' gl\j \c `ek\imXcf \eki\ \cZ\if XYjfclkf p ZlXchl`\i fkif glekf ]`af X[hl`\i\ le mXcfi`e]`e`kXd\ek\ ^iXe[\*Kfi \a\dgcf' j` j\ `dgfe\ cXZfe[`Z`€e [\ hl\ cX\jZXcX[\ ?Xckfe Zf`eZ`[X686fecX \jZXcXXYjfclkX Z\ek~^iX[X \e cfj glekfj [\ ]lj`€e [\c _`\cf p [\ \Ylcc`>D€e[\c X^lX' cXj d\[`[Xj ; p F [\ ZlXchl`\i fkiX k\dg\iXkliX \e leX p fkiX \jZXcX*\jk|e i\cXZ`feX[Xj gfi cX \ogi\j`€e6

7W@%UW@X; 3 @]& -,, ))))))###))

7W@,++( Z\*;"nhl\ [X O 3 ( 66-, gXiX F 3 f*

+6S42:F: .25/6:276+4! #"

Page 73: Análisis dimensional

-02 <IyGDNDN ?DH@INDJI<G

Kfi fkiX gXik\' Xlehl\ j\ kfdXj\ gXiX kf[fj cfj k\id€d\kifj \cd`jdf Z\if Zfem\eZ`feXc'p Xlehl\ j\ Xki`Ylp\j\ j`\dgi\ \c d`jdf mXcfiXc`ek\imXcf \eki\ [fj glekfj ]`afj Zfem\eZ`feXcd\ek\ \c\^`[fj' jlZ\[~Xhl\ ZlXchl`\i fkif `ek\imXcf X[hl`i~X mXcfi\j [`]\i\ek\j j\^•e ]l\j\ \ck`gf [\ k\id€d\kif f cXjljkXeZ`X lk`c`qX[X\e jl ZfejkilZZ`€e* <j~' \c`ek\imXcf\eki\ cfj glekfj [\ ]lj`€e [\c d\iZli`f p [\c _`\cf [XYXd\[`[Xj[`]\i\ek\j Zfe \c k\id€d\kif [\ d\iZli`f hl\ Zfe cfj k\id€d\kifj [\^Xj\j f Zfe cfj k\id€d\kifj [\ i\j`jk\eZ`X \c}Zki`ZX'Xlehl\ \jklm`\j\e^iX[lX[fj [\c d`jdf df[f' gfi \a\dgcf' Zfe cX\jZXcX[\ >\cj`lj f ZfecX[\ AX_i\e_\`k* ?\ \ccf i\jlckXYX hl\ cfj Zf\]`Z`\ek\j [\ [`cXkXZ`€e'cXZfe[lZk`m`[X[ k}id`ZX' cfj ZXcfi\j \jg\Z~]`Zfj' \kZ*' X[hl`i~Xe mXcfi\j[`]\i\ek\j j\^•e ]l\j\ \c k\id€d\kif lk`c`qX[f*

>fe cXj \jZXcXjZfem\eZ`feXc\j' _lY`\iX j`[f `dgfj`Yc\ \cXYfiXi cXjk\fi~Xj \e hl\ `ek\im`\e\ cXk\dg\iXkliX XYjfclkXf ZlXchl`\iX [\ cXjdX^e`kl[\j Zfe \ccXi\cXZ`feX[Xj*@e gXik`ZlcXi'cXj k\fi~Xj ZlXek`jkXj[\ cXiX[`XZ`€ep [\ cfj ZXcfi\j \jg\Z~]`Zfj \jkXi~Xegfi _XZ\i*

@e [\]\ejX [\ cXj\jZXcXjef XYjfclkXjgf[i| X[l\`ij\ \c _\Z_f [\ hl\kf[Xm~Xj\ _Xcc\e \e ljf cX[\ >\cj`lj p cX[\ AX_i\e_\`k' p [\ hl\ j\lk`c`Z\e k\id€d\kifj [\ k`gfj dlp [`m\ijfj* K\if fZlii\ hl\ cfj k\id€)d\kifj \e ljf [Xe `e[`ZXZ`fe\j hl\' jXcmfleX ZfejkXek\ X[`k`mX'[`]`\)i\e dlp gfZf [\ cXj d\[`[Xj hl\ j\ fYk\e[i~Xe Zfe cX k\dg\iXkliXk\idf[`e|d`ZX' p \o`jk\e kXYcXjgXiX \]\ZklXi cXZfii\ZZ`€e fgfikleX*Gfj k\id€d\kifj ZlpXj `e[`ZXZ`fe\j [`]`\i\e dlZ_f [\ cXjfYk\e`[Xj ZfecX\jZXcXk\idf[`e|d`ZX _Xe j`[f [\j\Z_X[fj*

$! 4> BN@>G>AB+ QJD>AMJ!

N\^•e el\jkiXj efidXj' gXiXhl\ cXk\dg\iXkliX j\X dX^e`kl[ ]~j`ZX\j gi\Z`jf _XccXile Zi`k\i`f hl\ g\id`kX [\]`e`i cXiXq€e \eki\ ZX[X[fj\jkX[fj k}id`Zfj* OXcZi`k\i`f _X [\ j\i le`m\ijXc' \jkf \j' `e[\g\e[`\ek\[\ cXeXkliXc\qX[\ cfj Zl\igfj hl\ j\ lk`c`Z\e gXiXXgc`ZXicf*

>fdf cXk\dg\iXkliX ef \j leX dX^e`kl[ X[`k`mXgfi XZldlcXZ`€e' Xcdf[f [\ cXdXjX f \c mfcld\e' \c i\]\i`[f Zi`k\i`f _X [\ [\i`mXi [\ legfjklcX[f ZfdgifYXYc\ \og\i`d\ekXcd\ek\* 9Z RSQWRW`aWZObS[^S`Obc`OSa ] \] c\O [OU\WbcR TqaWQO\] Sa `SacZbOR]RS c\ Q]\dS\W]&aW\] T`cb] RSc\ RSaQcP`W[WS\b])

Kfi [fj ZXd`efj j\ _X cc\^X[f X \jkXYc\Z\i \c i\]\i`[f Zi`k\i`f' XjXY\i6gfi \c \jkl[`f [\ cXjgifg`\[X[\j [\ cfj ^Xj\j p gfi \c j\^le[f gi`e)Z`g`f [\ O\idf[`e|d`ZX*

RDD* O@HK@M<OPM< -03

@c\jkl[`f \og\i`d\ekXc [\ cXZfdgi\j`Y`c`[X[ [\ cfj ^Xj\j X[`]\i\ek\j\iXkliXj _X g\id`k`[f \jkXYc\Z\i cX\jZXcX[\ <mf^X[if' f \jZXcX

k\ifg ' - [ `j`k [[ cfj ^Xj\j g\i]\Zkfj' hl\ i\le\ fj fj i\hl`j` fj \ j\i XYjfclkXW\ *m\ijXc*@e jl ]fidX d|j \jZl\kX p gi\jZ`e[`\e[f [\ gfid\efi\j [\

Pccc' k\i _`jk€i`Zf jl [\]`e`Z`€e fg\iXZ`feXc \j cXj`^l`\ek\6 jlg€e^Xj\ZXiXZ #

l\ j\ kiXkX[\ _XccXicXiXq€e \eki\ [fj k\dg\iXkliXj' "@#W"@]$& gfih* dgcf \eki\ [fj glekfj ]`afj*HXek\e`\e[f ZfejkXek\ cXgi\j`€e' _|ccX)\E\ '\ cXiXq€e \eki\ cfj mfc•d\e\j' "B# p $mf%'hl\ fZlgX leX dXjX ^Xj\fjX6- j\i jfd\k`[X XcXjk\dg\iXkliXj "@#W"@]$l M\g~kXj\cXfg\iXZ`€e Zfei\j`fe\j ZX[Xm\qd|j g\hl\•Xj* @cc~d`k\Xhl\ k`\e[\ cXiXq€e "B# - "B]$&

rlXe[f Y [`jd`elp\ `e[\]`e`[Xd\ek\' i\jlckX j\i' Zfe kf[X cXgi\Z`j`€e[\j\XYc\' `e[\g\e[`\ek\ [\ cXeXkliXc\qX[\c ^Xj' WcXiXq€e YljZX[XmXc\6

$\eki\ ZXek`[X[\j%* 5)#(6

KXiXXgc`ZXi\jkX i\cXZ`€e ef \j gi\Z`jf \c\^`i le`[X[\j e` gXiXcXjk\dg\iXkliXj e` gXiXcfj mfc•d\e\j' j`ef jXY\i ZfdgXiXi \jkfj •ck`dfj\eki\ j~*@e cXZfdgXiXZ`€e [\ cXjk\dg\iXkliXj' gfi kXekf' ef _Xp eX[Xhl\ j\X XiY`kiXi`ff Zfem\eZ`feXc'e` \e cX\c\ZZ`€e [\c ^Xj' hl\ gl\[\ j\iZlXchl`\iX' e` \e cXX[fgZ`€e [\ le`[X[\j' hl\ \j `ee\Z\jXi`X* N\ kiXkX'gfi kXekf' [\ le Zi`k\i`f le`m\ijXc*

<ek\ kf[f' jXckXXcXm`jkXhl\ kf[Xj cXjk\dg\iXkliXj k`\e\e \c d`j)df j`^ef' gl\j ef _Xp mfc•d\e\j e\^Xk`mfj' p YXjkXXki`Yl`i Zfem\eZ`f)eXcd\ek\ le mXcfield}i`Zf Xc`ek\imXcf \eki\ [fj glekfj ]`afj ZlXc\j)hl`\iX gXiX hl\ i\jlck\ [\k\id`eX[X cX gfj`Z`€e [\c Z\if XYjfclkf*Nlg€e^Xj\' gfi \a\dgcf' hl\ j\ kiXkX[\ Zfejkil`i leX \jZXcXZ\ek~^iX[X*N`@

,++? @]jfe' i\jg\Zk`mXd\ek\' cXjd\[`[Xj [\ cfj glekfj [\ \Ylcc`Z`€e

p [\ Zfe^\cXZ`€e [\c X^lX X cXgi\j`€e [\ leX Xkd€j]\iX' _XYi| [\ j\i6

F -,, 3 c~d G-,, $\eki\ d\[`[Xj%*`& B]

GX\c`d`eXZ`€e [\ @-,, Zfe[lZ\ X6

-]@]3 -,, R c~d 'B,]]( B]

5)#)6

Page 74: Análisis dimensional

,/3 :GyEBLBL =BbT"b>LBHG:E

Z[ ZedZ[ h[ikbjWgk[ bWc[Z_ZW[d lWbehWXiebkjeZ[bfkdje Z[ \ki_€d Z[b^_[befk[Z[ h[Wb_pWhi[i_d c|i gk[ c[Z_h bWZ_bWjWY_€dh[bWj_lWZ[ kd ]WiYkWbgk_[hW[djh[ Z_Y^ei fkdjei \_`ei o [njhWfebWdZebWic[Z_ZWi fWhW^WbbWh[b lWbehYehh[ifedZ_[dj[ W\ 3 e) :i~ [i Yece i[ ^WWl[h_]kWZe[nf[h_c[djWbc[dj[ gk[ [b Y[heWXiebkjei[ ^WbbW-2.',0 ]hWZeiY[dj~]hWZeifeh Z[XW`eZ[b fkdje Z[ \ki_€d Z[b ^_[be)

>i Z[ dejWh gk[ bWZ[j[hc_dWY_€dZ[b Y[he WXiebkjee dWjkhWbZ[j[cf[hWjkhW i[ ^W be]hWZei_d d[Y[i_ZWZZ[ h[Wb_pWhbe[nf[h_c[djWb(c[dj[' fk[ije gk[ XWijWYecfWhWhbei leb•c[d[i Z[ kdWcWiW]Wi[eiW[d bei Zei fkdjei \_`ei [b[]_Zei) G_ i_gk_[hWi[ [n_][ gk[ bW\€hckbW[cfb[WZWi[W Wfb_YWXb[YkWdZebWj[cf[hWjkhW [i cko XW`W'YeiWgk['feh ejhWfWhj[' [i _cfei_Xb[ Z[ YecfheXWh[nf[h_c[djWbc[dj[' fehgk[de ^Wod_d]•d Yk[hfe [d [b gk[ fk[ZWd ^WY[hi[c[Z_ZWiZ[ Yecfh[i_X_(b_ZWZ[d [ijWZe ]Wi[eie YkWdZebWj[cf[hWjkhW Z[iY_[dZ[ feh Z[XW`eZ[ Y_[hjeb~c_j[)

EWkd_l[hiWb_ZWZZ[ bW[iYWbWZ[ : le]WZhe ^Wi_Ze Yed\_hcWZW'YedjeZWbWfh[Y_i_€dWf[j[Y_Xb[' WijWbWij[cf[hWjkhWi fWhWbWiYkWb[i[b^[b_e i[ YecfehjW jeZWl~WYece kd ]Wi) <ed j[cf[hWjkhWi cko fh€n_(cWi WbY[he WXiebkje[i _d•j_bbW[YkWY_€dZ[ bei ]Wi[i f[h\[Yjei' f[he[bbede eXijWfWhWgk[' Yedik Wkn_b_eo fh[l_WbW[b[YY_€dZ[b]hWZe'gk[Z[Z[j[hc_dWZWbWfei_Y_€d Z[b Y[he)

.) ejhWi [iYWbWikd_l[hiWb[iV WXiebkjWi)

EW[iYWbWZ[ : le]WZhe [i WXiebkjWo kd_l[hiWbfeh [b ^[Y^e Z[ gk[ bWhWp€d[djh[ bei Zei lWbeh[igk[ bWcW]d_jkZ XG WZgk_[h[[d Zei h[Y_djei_iej[hcei' i€be Z[f[dZ[ Z[ bWj[cf[hWjkhW Z[ WcXei o de Z[ bWdWjkhW(b[pWZ[b ]Wi) Ieh jWdje' i[ fk[Z[ W\_hcWhgk[ YkWbgk_[hejhWcW]d_jkZgk[ i[ Yecfehj[ Z[bc_ice ceZe feZh| kj_b_pWhi[fWhWZ[\_d_hkdW[iYWbWWXiebkjW)MWb[i [b YWie'feh [`[cfbe' Yed YkWbgk_[hWZ[ bWicW]d_jkZ[ieXi[hlWXb[i [d bW5hWZ_WY_€dZ[b Yk[hfe d[]he' Yece bW[d[h]~W jejWb[c_j_ZW [d kd j_[cfe Z[j[hc_dWZe' bWfh[i_€d Z[ bWhWZ_WY_€d'[jY)<ece [i iWX_Ze'[d [ijW fhef_[ZWZi[ XWiWbWc[Z_ZW Z[ j[cf[hWjkhWi[b[lWZWi)

F[h[Y[ [if[Y_Wbc[dY_€d bWgk[ Z[X_[hWbbWcWhi[Q_OMXMPQ8a^UQfehgk[i[ \kdZW[d bWb[o i_]k_[dj[' Z[iYkX_[hjWfeh I_[hh[ <kh_[)=M^MfmZQZ`^QXM_\Q^YQMNUXUPMPQ_]aQ MP]aUQ^QaZ OaQ^\[ \M^MYMSZk`UO[\Q^RQO`[QZP[_`QY\Q^M`a^M_Q_UZPQ\QZPUQZ`QPQ_a ZM`a^MXQfM'

@hWY_WiW[ijW b[o ^W i_Ze fei_Xb[ bWc[Z_ZW Z[ j[cf[hWjkhWi jWdXW`Wigk[ [b j[hc€c[jhe Z[ ]Wi[i Z[`WZ[ i[h kj_b_pWXb[)

nd) M>FI>K:MNK: ,/4

! [iYWbWj[hceZ_d|c_YW))#>b i[]kdZe fh_dY_f_eZ[ bWMrhc)eZ_d|c_rWd_[]W'Yec)e)[i iWX_Ze'rW)X_b_ZWZZ[ Yedijhk_hkdW cWgkcW j}hc_YWgk[ ikc_d_ijh[ jhWXW`e

fe LB )C5< j j[ =) i[ Z_ifed[ Z[ Zei Yk[hfei gk[ j[d]Wd kk[h[d [ cf[hWjkhW) [3, j[

de) Y_f_ei[ Z[ZkY[ bW[iYWbWj[hceZ_d|c_YW e Z[ behZD[bl_d' Z[ bW[i fhc

k[Z[ Z[Y_hi[gk[ ]epWW•d Z[ cWoeh kd_l[hiWb_ZWZgk[ bW[iYWbWZ[gk[ f , ) "bwZ j_ wZ:le]WZhe fehgk[ [i h[Wb_pWXb[YedYk[hfei YkW[igk_[hW'3+, ei' gk_ +3

e ]Wi[i) ))Ge [i }ijW eYWi_€dZ[ [nfed[h [b dWZWi[dY_bbehWpedWc_[djegk['

fWhj_[dZeZ[b h[\[h_ZefeijkbWZe' YedZkY[Yed jeZe h_]Hb5"r ir d[r[i_ZWZZ[ dk[lWi ^_f€j[i_i WbW[n_ij[dY_WZ[ bW[iYWbWj[hceZ_d|c_YW # $)Geib_c_jWh[cei WZ[Y_hgk[ [d [ijW [iYWbWbWhWp€d[djh[ Zei j[cf[hWjkhWi

YkWb[igk_[hW[ij| Z[\_d_ZWfeh bW\€hckbW5

W 3 ( :-; #[djh[ YWdj_ZWZ[i$"B[# "B[#

[d bWgk[ ? o B[ ied Zei YWdj_ZWZ[iZ[ YWbehd[Y[iWh_Wc[dj[Z[ i_]reYedjhWh_e)>ijW \€hckbW f[hc_j[ bWYecfWhWY_€dZ[ j[cf[hWjkhWi i_dd[Y[i_ZWZZ[ _djheZkY_hd_d]•d [b[c[dje WhX_jhWh_e'feh [`[cfbe' kdi_ij[cW Z[ kd_ZWZ[i)=[iZ[ bk[]e' XWijWWZefjWhYedl[dY_edWbc[dj[fWhW[b lWbehZ[b ]hWZe[b _dj[hlWbe[djh[ Zei j[cf[hWjkhWi \_`Wi'fWhWgk[ gk[Z[d Z[j[hc_dWZWiWcXWi[d lWbehWXiebkje'be gk[ fhk[XWbW[n_ij[dY_WZ[b Y[he WXiebkjee dWjkhWb)?_dWbc[dj[' jeZWi bWij[cf[hW(jkhWi^WdZ[ j[d[h [b c_ice i_]de' o XWijWYedl[d_h [d gk[ jeZWii[Wdfei_j_lWi fWhWfeZ[h W\_hcWhgk[ QXOQ^[MN_[Xa`[O[Z_`U`aeQQXXlYU`Q

UZRQ^U[PQ`[PM_XM_QY\Q^M`a^M_'

0) K[bWY_€d[djh[ bWiZ_l[hiWi[iYWbWikd_l[hiWb[i)

EWj[cf[hWjkhW i[ cWd_\_[ijW[d bW?~i_YWYece kdWlWh_WXb[Z[ bWgk[' [d cWoeh e c[deh ]hWZe'Z[f[dZ[d jeZWibWicW]d_jkZ[i \~i_YWi#%%$)MeZWcW]d_jkZ' ;% gk[ Z[f[dZW Z[ bWj[cf[hWjkhW i[hl_h| fWhW[ijWXb[(Y[hkdW[iYWbWkd_l[hiWbYedjWbZ[ gk[ bWhWp€d";#O";[# [djh[ bei lWbeh[i

#%$ O}Wi[ [b jhWXW`eZ[ <WhWj^}eZeho#1,$ o ik h[ikc[d [d [b b_XheZ[bWkjeh#/1$) ) )

#%%$ :b [iYh_X_h[ijW \hWi[ l_[d[ WbWc[dj[ bW_Z[WZ[ [nYb)8 [b j_[cfe'feh Wgk[bbeZ[ gk[ [i bWlWh_WXb[_dZ[f[dZ_[dj[ feh WdjedecWi_W)I[he) [d :6?~i_YWde i[ ef[hW Yed j_[cfei' i_de Yed ZkhWY_ed[i'bWiYkWb[iied \kd<_€d [Z_l[hiWicW]d_jkZ[i gk[' Wik l[p' ik[b[d Z[f[dZ[h Z[ bWj[cf[hWjkhW)

Page 75: Análisis dimensional

,0+ :GyEBLBL =BF>GLBHG:E nd) M>FI>K:MNK: #'#

gk[ jecW [d Zei fkdjei \_`ei YkWb[igk_[hWi[W_dZ[f[dZ_[dj[ Z[ bWdWjk(hWb[pWZ[ bei Yk[hfei gk[ b[ i_hl[d Z[ iefehj[' fk[i XWijWh|Yedl[d_h[d gk[ i[W

[bfheXb[cWZ[ :d|b_i_i Z_c[di_edWbfbWdj[WZefeh bW[YkWY_€dS0'.Ui[V !\ehckbWhWWi_5

E A W

8! : 3 ";# #[djh[ YWdj_ZWZ[i$)"B[# ";[#

E ,>

>,

MN

,72 J8K , ( XXN

EW[b[YY_€dZ[b]hWZegk[ZWWhX_jhWh_Wo' feh jWdje' i_[cfh[ i[ fk[Z[_cfed[h bWYedZ_Y_€dZ[ gk[ h[ikbj[ kdW[iYWbWY[dj~]hWZW'o Wi~gk[ZWh|Z[\_d_ZWbWc[Z_ZWZ[ YkWbgk_[hj[cf[hWjkhW Yedh[bWY_€dWbY[he\~i_Yeh[if[Yj_le) L_bWcW]d_jkZ Yedi_Z[hWZWde YWcX_WZ[ i_]de' de ^WXh|j[cf[hWjkhWi d[]Wj_lWi

<ece i[ l[' [n_ij[ bWfei_X_b_ZWZZ[ Z[\_d_hZ_l[hiWi[iYWbWikd_l[hiW(b[i Y[dj~]hWZWi'o i[ fbWdj[WbWYk[ij_€dZ[ Wl[h_]kWhbWh[bWY_€dgk[ ^WZ[ [n_ij_h [djh[ bWic_icWi) EWiebkY_€d WZ[ ^WbbWhi[[d YWZWYWiefWhj_YkbWh'i[W [cf~h_YWc[dj[' i[W Yed Wkn_b_eZ[ bWij[eh~Wil_][dj[i'YeiWgk[ oW[ij| ^[Y^W[d bei YWieigk[ c|i _cfehjWd) I[he [b :d|b_i_iZ_c[di_edWbYedZkY[Wkd h[ikbjWZeYkh_eie'i[]•d lWcei Wl[h)

L[Wd; o < Zei cW]d_jkZ[i WfjWifWhWZ[\_d_hi[dZWi [iYWbWikd_(l[hiWb[i c[Z_Wdj[ bWi_]kWbZWZ[i5

o h[ikbjWkd iebe cedec_e Z[ Z_c[di_€d dkbW5

2j, 3 EM(N W&T(N

e X_[d5 ''8 2BZ7'%

S0',U

ZedZ[ 5 [i kdWdk[lW YedijWdj[kd_l[hiWbo 5;' 3 ( MVN%=M_YQPUPM_[N`QZUPM_O[Z P[_ Q_OMXM_aZUbQ^_MXQ_PURQ^QZ`Q_Q_`jZ XUSM&

PM_\[^ aZM RaZOUmZY[Z[YUM'>ij[ h[ikbjWZebb[lWYedi_]ebei i_]k_[dj[i YehebWh_ei5,)+ L_ 5;' 4 H' i[h|! 8 v YkWdZeB 8 +' [ije [i' bei Y[hei Z[ Wc(

XWi[iYWbWiYe_dY_Z[d) )-)+ ) L_5;' 2 +' i[h|! 3 ++ YkWdZeB 3 +' [ije [i' kdWZ[ bWi[iYWbWi

[ij| _dl[hj_ZWYedh[bWY_€dWbWejhW).)+ ;WijWgk[ [d kdW[iYWbWkd_l[hiWbde fk[ZW^WX[hj[cf[hWjkhWi

d[]Wj_lWifWhWgk[ ikY[ZWbe c_ice [d jeZWibWiZ[c|i) MeZWii[h|d

[iYWbWiWXiebkjWi)"%%# "<#

((3((" [# "?![#

S0'-UIWhWYecfheXWh bWifh[Y[Z[dj[i Yedi[Yk[dY_Wi'Yedi_Z[hWh[cei bWi[iYWbWi

kd_l[hiWb[i gk[ ^[cei c[dY_edWZe Wdj[h_ehc[dj[)>iYWbWj[hceZ_d|c_YW Z[ behZ D[bl_d5<ed ik Wkn_b_e'o fh[l_WbW[b[YY_€dZ[b ]hWZe[d YWZWkdW'i[h| fei_Xb[

Wjh_Xk_hWYWZWfkdje \_`e Zei d•c[hei' B o (h' [djh[ bei gk[ ^WXh|Z[[n_ij_hkdWh[bWY_€d\kdY_edWb5

"B 3 YWdj_ZWZZ[ YWbehjecWZWZ[b h[Y_dje _iej}h(c_Ye E [d kd Y_YbeZ[ <Whdej$

''8 O"B%S#' S0'.U >iYWbWZ[ :le]WZhe5

Ieh ^_f€j[i_i' WcXWi[iYWbWiied kd_l[hiWb[i'be gk[ bb[lWYedi_]e [bgk[ [d S0'.Ude fk[ZW \_]khWhd_d]kdWYedijWdj[YWhWYj[h~ij_YW):Zc_(jWcei' i_d [cXWh]e' gk[ \_]kh[ kdWYedijWdj[kd_l[hiWb'S' Ik[ije gk[Wb[ijWXb[Y[hbWi[iYWbWiS0',Uo S0'-Ude ^Wi_Ze fh[Y_ie \_`WhbWikd_ZW(Z[i [d gk[ i[ ^WdZ[ c[Z_h ";# o "<#%Z_Y^WYedijWdj[i€be feZh| Z[(f[dZ[h Z[ bWikd_ZWZ[igk[ i[ WZefj[d fWhWc[Z_h B o (h' feh be gk[ik \€hckbWZ_c[di_edWb WXh|Z[ i[h6

"B3# "XD#

"B1#W 3 "XD#W

>iYWbWZ[ Lj[\Wd5

"B_# "*#

"B[#W 8r#, 3 _dj[di_ZWZZ[ bWhWZ_WY_€djejWb[c_j_ZW feh

kd Yk[hfe d[]he$

>iYWbWZ[ <kh_[5

#\b)3 f[hc[WX_b_ZWZZ[ kd Yk[hfe fWhWcW]d}j_Yef[h\[Yje$

Page 76: Análisis dimensional

,0- :GyEBLBL =BF>GLBHG:E

>nf[h_c[djWbc[dj[ i[ ^W YecfheXWZe gk[ bW[iYWbWZ[ :le]WZhe Ye_dY_Z[Yed bWZ[ behZD[bl_d' bk[]e5

E'3 3 Em [n 3 C€ )2 ,)

>d YWcX_e'bWb[o Z[ Lj[\Wd' ^WbbWZWfh_c[he [cf~h_YWc[dj[ o Z[ZkY_ZWbk[]e Yece Yedi[Yk[dY_WZ[b i[]kdZe fh_dY_f_e Z[ M[hceZ_d|c_YW' Z_Y[ gk[5

* 3 ME-

o' feh jWdje' Z[X[ i[h5

[n8/

o' [d bWi[iYWbWiY[dj~]hWZWi5

>b YWiec|i Ykh_eie[i [b Z[ bWgk[ ^[cei bbWcWZe[iYWbWZ[ <kh_[6fk[i Yece

YedijK; 3 (((

Eh[ikbjW5

e i[W [n 8 ( , R )2 , i_ "E@#X@@& "E[#[ 8 ( ,++'

[i Z[Y_h5

,E[0&

B

i_ WcXWi[iYWbWiied Y[dj~]hWZWi)K[ikbjW' feh jWdje' kdW [iYWbW_dl[hj_ZWgk[feZh~WbbWcWhi[Q_OMXMPQR^l[' :b WYjkWbY[he WXiebkjeYehh[ifedZ[ kd \h~e _d\_(d_je' [b cWoeh Z[ jeZei bei \h~ei fei_Xb[i) IWhWbe]hWhkd \h~e dkbe ^WXh~Wgk[h[Wb_pWhkdW j[cf[hWjkhW _d\_d_jWc[dj[ ]hWdZ[) >djh[ E 3 v o E 3 ,' [b \h~efWiWZ[ ee W,' o bk[]e [i i_[cfh[ c[deh gk[ bWkd_ZWZ)>d [b WcX_[dj[ [d gk[dei Z[i[dlebl[cei' jeZei bei \h~ei j_[d[d c[Z_ZWi f[gk[•~i_cWi i_ i[ kj_b_pWbW[iYWbWY[dj~]hWZW)

<:I~MNEH QBBB

.65/;.:2<2/,/ :U842.,

#! 3ARALBNG@=FAGM=EAL!

>d bWj[eh~WZ[ bWYedZkYY_€dZ[b YWbeh'gk[' Yece iWX[cei' i_hl_€W?ekh_[h fWhWi[djWh bWiXWi[i Z[b :d|b_i_i Z_c[di_edWb'_dj[hl_[d[d'WZ[c|i Z[ bWbed]_jkZ o [b j_[cfe' bWj[cf[hWjkhW' [' o [b YWbeh'?' =[bYWbehj[d~W?ekh_[h _Z[Wi[gk_leYWZWi'f[he [ijWXb[Y_€Yehh[YjWc[dj[ikc[Z_ZWh[Ykhh_[dZeWbYWbeh~c[jheZ[ ^_[be' o [ije XWijWfWhWYedi_Z[hWh[b YWbehYece cW]d_jkZ \~i_YWfh_cWh_W)=[ bWj[cf[hWjkhW dWZWZ_Y[?ekh_[h6ikfed[ gk[ [bb[YjehiWX[cWd[`Whj[hc€c[jhei o ZWfeh ikfk[i(je gk[ i[ jhWjWjWcX_}dZ[ kdWcW]d_jkZ \~i_YWfh_cWh_W)EW?~i_YWce(Z[hdW^WYed\_hcWZe[ijW fh[ikdY_€d' i[]•d i[ ^Wl_ije [d [b YWf~jkbefh[Y[Z[dj[)

EWib[o[i [d gk[ ?ekh_[h XWiWik j[eh~W'gk[ fk[Z[d i[h [dkdY_WZWiYece h[bWY_ed[iZ[ fhefehY_edWb_ZWZ[djh[ YWdj_ZWZ[i'ied5

,)+ EWYWdj_ZWZZ[ YWbehgk[ \bko[ WjhWl}i Z[ kd [b[c[dje Z[ ik(f[h\_Y_[ZL' i_jkWZe[d [b i[de Z[b i€b_Ze'[d [b j_[cfe M\%[ij| ZWZWfehbW[nfh[i_€d l[Yjeh_Wb5

ZJ 3 ( D#]hWZ[wZL$Zj' S,',U

ZedZ[ 9 [i kd Ye[\_Y_[dj[YWhWYj[h~ij_YeZ[b i€b_Ze' gk[ i[ Z[dec_dWO[ZPaO`UY!PMP`k^YUOM'

-)+ L_[b Yk[hfe [ij| ikc[h]_Ze [d kd c[Z_e \bk_Ze'o i[ [l_jWdbWiYehh_[dj[iZ[ Yedl[YY_€d'[b YWbehgk[ i[ f_[hZ[ WjhWl}i Z[ bWikf[h\_(Y_[ZL [d [b j_[cfe M\lWb[5

ZJ 3 6"N& [e$" MA!M\% S,'-C

Page 77: Análisis dimensional

,0/ :GyEBLBL =BF>GLBHG:Enc) <HG=N<MBOB=:= MzKFB<: ,00

ZedZ[ 6 [i ejhe Ye[\_Y_[dj[gk[ Z[f[dZ[ Z[b i€b_Zeo Z[b c[Z_e [d gk[[ij| ikc[h]_Ze' o i[ Z[dec_dW Q[ZPaQ`UbUPMP_a\Q^RUOUMX'' '

.)+ L_kd [b[c[dje Z[ lebkc[d' ZD%Z[b Yk[hfe YediBZ[hWZe'h[Y_X[kdW YWdj_ZWZZ[ YWbeh'PB%[nf[h_c[djW kd Wkc[dje Z[ j[cf[hWjkhWZWZWfeh5

IhefW]WY_€dZ[b YWbeh[d kd c[Z_e _dZ[\_d_Ze)(#

RJ 3 W PBQ! Wh"

S,'.U

>d kdWfehY_€d[i\}h_YWZ[ hWZ_e'[% i[ Z[iWhhebbWXhkiYWc[dj[ Y_[hjW[Wdj_ZWZZ[ YWbeh'gk[ eh_]_dW[d bWc_icW kdW[b[lWY_€di•X_jW'[

e' Z[

\W)j[cf[hWjkhW) >b c[Z_e i[ ^WbbWXW_d_Y_Wbc[dj[W++' o i[ jhWjWZ[Wl[h_]kWhYk|b [i bWj[cf[hWjkhW' [' WbYWXeZ[ kd j_[cfe' `%[d kd fkdje(gk[ Z_ijWd 3 ^ & ^[ Z[ bWikf[h\_Y_[Z[ bW[i\[hW [d gk[ i[ fheZk`e bWf[hjkhXWY_€d_d_Y_Wb)

EWicW]d_jkZ[i WYedi_Z[hWhied5 [' [e' d%^[% %9%Q!o h[ikbjW5ZedZ[ Q! [i ejhWYedijWdj[ YWhWYj[h~ij_YWZ[b Yk[hfe' gk[ i[ Z[dec_dWOMX[Q_\QOlRUO[PQXMaZUPMPPQb[XaYQZ'

/) X IWhWbei [\[Yjei Z[ ik fhefW]WY_€d'[b YWbehi[ YecfehjW Yece kd\bk_Ze_dZ[ijhkYj_Xb['feh be gk[ i[ Ykcfb[ bW[YkWY_€dZ[ Yedj_dk_ZWZ5

S,'/U

[ d < ["

: H , H ( , "(E H H , ( , H[ , H H (, ( ,B H H H , ,

H , ( ,*- ( ,*- ,*-

[ 3 [er "d G [" ' r$<` ^[

e X_[d5

1r 1)&G h`! !' G h` #'

-) L_ij[cW Z_c[di_edWb)

>d bWi[YkWY_ed[i\kdZWc[djWb[i S,',U' S,'-U' S,'.U R S,'/U' \_]khWd'WZ[c|i Z[ bed]_jkZ[i o j_[cfei' Zei dk[lWi cW]d_jkZ[i fh_cWh_Wi'gk[ied bWj[cf[hWjkhWo bWYWdj_ZWZZ[ YWbeh)Ieh ejhWfWhj[' Z_Y^Wi[YkWY_e(d[i Yedj_[d[d i[dZWi YedijWdj[i Z_c[di_edWZWi'9%6 R Q!%Z[ ZedZ[ i[Z[ZkY[ gk[ fk[Z[d Yedijhk_hi[i_ij[cWi Ye^[h[dj[i Z[ kd_ZWZ[i[b_]_[dZeWhX_jhWh_Wc[dj[bWikd_ZWZ[iZ[ bed]_jkZ' j_[cfe' YWbeho j[cf[hWjkhW)>ijWi cW]d_jkZ[i ied' fk[i' Z_c[di_edWbc[dj[ _dZ[f[dZ_[dj[i o \ehcWdkdWXWi[j[jhWZ_c[di_edWb'gk[ [i bW_dZ_YWZWfWhW[b jhWjWc_[djeZ[ beifheXb[cWi Z[ YedZkYY_€dZ[bYWbeh)>d [ijW XWi['bWi\€hckbWi Z_c[di_e(dWb[iZ[ 9%6 R Q!%ied5

/) IhefW]WY_€dZ[b YWbeh[d kdWXWhhW)

G9I 3 =&:E&*Q&*B

G6I 8 =&+E&*Q&*B

GN!I 8 :&,Q&*?'

V NdWXWhhW_b_c_jWZW[d WcXei i[dj_Zei' i[ [dYk[djhWW++ o' [d [b"BdijWdj[ 3 H' h[Y_X[Y_[hjWYWdj_ZWZZ[ YWbeh[d kd jhepe Z[ bed]_jkZ K%(Z[ jWbceZe gk[ jeZe }bgk[ZWWkdWj[cf[hWjkhW [) L[ ikfed[ gk[ de^Wof}hZ_ZWibWj[hWb[i'o i[ jhWjWZ[ YWbYkbWhbWZ_ijh_XkY_€dZ[ j[cf[hW(jkhWiWbYWXeZ[b j_[cfe `'

) Bdj[hl_[d[d [d [ij[ fheXb[cWbWic_icWi cW]d_jkZ[i gk[ [d [b Wdj[(hBHh'iWble[b hWZ_e[ gk[ W^ehW[i ikij_jk_Ze feh [b i[]c[dje N' >d Yed(i[Yk[dY_Wi[h|5

>d bWfhefW]WY_€dZ[b YWbeh[d c[Z_ei i€b_Zeide ^Wocel_c_[dje Z[Yk[hfei cWj[h_Wb[i'o feh [ie de _dj[hl_[d[d d_ cWiWi d_ Z[di_ZWZ[i)MWdjebWj[eh~WYece [b :d|b_i_i Z_c[di_edWbfk[Z[d i[h Z[iWhhebbWZei_]dehWdZebWh[bWY_€dZ_c[di_edWb[djh[ [b YWbeho bWicW]d_jkZ[i c[Y|(d_YWi:%;% B%WYedZ_Y_€dZ[ h[[cfbWpWh; feh ? [d bWXWi[)

>d h}]_c[d [ijWY_edWh_e'bWj[cf[hWjkhW de Z[f[dZ[ Z[b j_[cfe oi[h| HJ 8 H [d bW[YkWY_€dS,'.U o :HN 8 H [d bWS,'/U be gk[ ck[ijhWgk[ [" de _dj[hl_[d[ [d [b \[d€c[de)

S/',U

L_ ^kX_[i[ f}hZ_ZWibWj[hWb[i'WXh~Wgk[ W•WZ_hbWYedZkYj_l_ZWZikf[h\_Y_Wb'6%o h[ikbjWh~Wkd dk[le cedec_e f_ o bW\€hckbWi[h~W5

##K)G&

[" [" NQ!Q2Q[R d &%N &%L#'

<` <` 9`

Page 78: Análisis dimensional

,01 :GyEBLBL =BF>GLBHG:E

0) O[beY_ZWZZ[ fhefW]WY_€dZ[bYWbeh)

L_[b YWbehi[ fhefW]Wi[YedkdWl[beY_ZWZYedijWdj['b%YWhWYj[h~ij_YW)Z[b c[Z_e' o bWi•d_YWicW]d_jkZ[i gk[ _dj[hl_d_[i[d [d [b \[d€c[de\k[i[d < o Q!%Z[X_[hWfeZ[h \ehcWhi[ kd cedec_e f_ Yedb%< o Q!'I[he)WbjhWjWhZ[ eXj[d[hbe' h[ikbjWkd i_ij[cW Z[ [YkWY_ed[i_dYecfWj_Xb[i'be gk[ h[l[bWgk[ bWl[beY_ZWZZ[ fhefW]WY_€dWZ[ Z[f[dZ[h Z[ Wb]kdW)ejhWcW]d_jkZ) :]h[]k[cei' feh l~WZ[ [diWoe' bWZ_ijWdY_W'd%WbWh[(]_€d f[hjkhXWZW_d_Y_Wbc[dj[5

b d < ["

: , , (, "(E ( , > (, >1 > > (, ( ,B > > , ,

,,!, , , (, ,

b2h("h#'O!d d

>b :d|b_i_i Z_c[di_edWbdWZWfk[Z[ Z[Y_hdeiWY[hYWZ[ bW\kdY_€dkd_l[hiWb*%f[he' Wik\_Y_[dj[ Z_ijWdY_WZ[ bWf[hjkhXWY_€d'fk[Z[ [i(Yh_X_hi[5

9b2?&&%O!d

S0',q

ZedZ[ < 3 *")# [i kd d•c[he \_`e)

:b c_ice h[ikbjWZei[ ^WXh~Wbb[]WZe[d [b YWieZ[ kd c[Z_e _dZ[\_(d_Ze' o h[ikbjW gk[ XM_\Q^`a^NMOU[ZQ_k^YUOM__Q \^[\MSMZ O[Z aZM'bQX[OUPMPUZbQ^_MYQZ`Q\^[\[^OU[ZMXM XMPU_`MZOUM^QO[^^UPM'

=ei l[beY_ZWZ[iYWX[Yedi_Z[hWh[d bWfhefW]WY_€dZ[ kdW f[hjkhXWY_€d)j}hc_YW5bWZ[b \h[dj[ Z[ bWedZWV bWZ[b c|n_ce #e c~d_ce$) IWhWWcXWiZ[X_[(hWi[h l|b_ZWbW\€hckbW S0',U Yed Z_ij_dje lWbehZ[b \WYjeh<' I[he [d be gk[ W)bWl[beY_ZWZZ[b \h[dj[ i[ h[\_[h[' bWh[Wb_ZWZ[ij| [d YedjhWZ_YY_€djWdje Yed bWifh[l_i_ed[i j[€h_YWiYece Yed [b :d|b_i_i Z_c[di_edWb)>d [\[Yje' bWfhefW]WY_€dZ[b YWbehWbe bWh]eZ[ kdW XWhhW\k[ [ijkZ_WZWfeh ?ekh_[h' gk_[d eXjkle bW)[YkWY_€d

" RN18 VV+V [G^^W` e

#2U(U$"

/ W` M`% S0'-,

QB=) <HG=N<MBOB=:= MzKFB<: ,02

Z IWhWWXh[l_WhbW[iYh_jkhW'i[ ^W ^[Y^e W3 <(O' >ijW [YkWY_€d[ij|)eed [' ) , ) I

B[hZe Yed S/',U o ZWfWhWbWl[beY_ZWZZ[ c|n_ce [ 1 #%$e[ i[

gk[' fWhWd 4 4 K%i[ Yedl_[hj[ [d5

GY2h 8-r'F Q!d

gk[ [ij| Yed\ehc[ Yed S0',$)EWZ_\_YkbjWZikh][ YkWdZei[ jhWjWZ[ YWbYkbWhbWl[beY_ZWZ'G:%Z[b \h[dj['

fk[i bW\€hckbW S0'-U ZW1 "%"H fWhW "%"H' YkWbgk_[hWgk[ i[W d%be gk[ i_]d_(\_YWgk[ [b \h[dj[ Z[ bWf[hjkhXWY_€dZ[X_[hWfhefW]Whi[ Yed l[beY_ZWZ_d\_d_jW'7YeiWgk[' [l_Z[dj[c[dj[' de Yehh[ifedZ[ WbWh[Wb_ZWZ)>ije h[l[bW kdW_dik\_(([_[dY_W[d bWj[eh~WZ[ ?ekh_[h' _dik\_Y_[dY_Wgk[ fk[Z[ ikXiWdWhi[j[d_[dZe [d7Yk[djWgk[' i[]•d be gk[ WYjkWbc[dj[i[ iWX[WY[hYWZ[ bWj[cf[hWjkhW' QXR^QZ`QPQ XM[ZPM `k^YUOMPQNQ\^[\M]M^_Q O[Z XMbQX[OUPMPPQX_[ZUP[%[ije [i' Yed bWl[beY_ZWZZ[ bWiedZWibed]_jkZ_dWb[i'gk[ ied bWigk[ lWd c|i Z[ fh_iW)

EWedZWj}hc_YWi[ Z[\ehcW' fk[i ik \h[dj[ WlWdpWYed l[beY_ZWZYedijWdj['c_[djhWi gk[ [b c|n_ce i[ ck[l[ YWZWl[p c|i b[djWc[dj[ ^WijWgk[ i[ Z[i(lWd[Y[)

"1) MhWdic_i_€dZ[b YWbehfeh jkX[h~Wi)

Ieh kd jkXe Z[ Z_|c[jhe 6 Y_hYkbWkd \bk_ZeYedbWl[beY_ZWZc[Z_Wb%o i[ jhWjWZ[ Wl[h_]kWh[b Ye[\_Y_[dj[Z[ jhWdic_i_€dZ[b YWbeh'(h'[ije [i'bWYWdj_ZWZZ[ YWbehgk[ fWiWYWZWkd_ZWZZ[ j_[cfe WjhWl}i Z[ bWkd_(ZWZZ[ ikf[h\_Y_['YkWdZe[djh[ [b \bk_Zeo [b c[Z_e [nj[h_eh [n_ij[ kdWZ_\[h[dY_WZ[ j[cf[hWjkhW Z[ b+)

>d h}]_c[d bWc_dWh'WZ[c|i Z[ bWicW]d_jkZ[i Y_jWZWi'_dj[hl[dZh|[b b~gk_Zefeh ik YedZkYj_l_ZWZj}hc_YW'feh ik YWbeh[if[Y~\_Yeh[\[h_Ze)WbWkd_ZWZZ[ cWiW'[' o feh ik Ye[\_Y_[dj[Z[ l_iYei_ZWZ)IWhWi_cfb~\_(YWhbWYk[ij_€d WZc_j_h[cei gk[ [b jkXe [i cko Xk[d YedZkYjeh'o gk[d_ ik dWjkhWb[pWd_ [b [ijWZe Z[ ik ikf[h\_Y_[_d\bko[d [d [b \[d€c[de)

#%$ Nd eXi[hlWZeh YebeYWZe[d kd fkdje Z[ WXiY_iWd%eXi[hlWh| bWj[cf[(b"WjkhWc|n_cW [d kd _dijWdj[ ZWZefeh bWYedZ_Y_€d

Page 79: Análisis dimensional

)-0 6?c=<C<C 8< !S9?C<@?6=

=I ZVS\KQiUMZ2#",! " ? M a3'

$ !" ( ( %( @ % (

% @ @ @ @ % ( (

, % ( @ % ( %( @ % (

. %( @ @ % ( % ( @

* ( @ @ ( ( @

$%& ( ( @ % ( @ @

@ @ @ %( ( ($%"

+* # $&

9S TVUVTQV23(5' ZMLMUVTQUIUjTMYVLMAYIUL[S'=V YMWYMZMUb

[ITVZ WVY) !CQMSYfOQTMUMZ[\YJ\SMU[V%PIJYe X\MQU[YVL\KQY%ILMTeZ%MSUjTMYV5

LMBM_UVSLZ%_ ZMYe2

=I NiYT\SIMTWgYQKIWYVW\MZ[IWVY>K'eLITZ% MZ2

FMYMTVZMUMSKIWg[\SVWYi^QTVX\MSI JIZMX\MPMTVZ\[QSQ`ILVISYMZVS]MYMZ[MWYVJSMTIMZZ\WMYIJ\ULIU[MWVYX\MMSKISVYMZPVTVOfUMV5KVUSI MUMYOgI'AMYVZM]MNeKQSTMU[MX\MSI ZVS\KQiUMZKVYYMK[I'

! "+'.(#*(&+0, %&1+ /3)(%, &+ 1+# $,..(&+0&)2-1(%#"$#'

7VUVKQLIZSIZLQTMUZQVUMZLMSIZTIOUQ[\LMZX\MQU[MY]QMUMUMUSI'KVUL\KKQiULMSKISVY%MS6UeSQZQZLQTMUZQVUISWMYTQ[MIJVYLIYWYVJSMTIZX\M%WVYZ\ KVTWSMRQLIL%ZMYgIUWYeK[QKITMU[MQUZVS\JSMZWVYIWSQKIKQiULQYMK[ILMSI [MVYgILM:V\YQMY';M IX\g \U MRMTWSV%KVUVKQLVKVUMSUVTJYMLM:<90627/ 12 &9>==482=;#X\MZMPI PMKPVNITVZVWVYSI WVSfb

TQKIX\MPI Z\ZKQ[ILV".*#'

"$# AIYI SIZ IWSQKIKQVUMZLMS6UeSQZQZLQTMUZQVUISIS [YIUZWVY[M MSK SVYbWVYKVU]MKKQiU%]fIZM MSIY[QK\SVLM>' AISVTIYMZ%MUSI +29$ 12 6/ -<44>2<=41/112 )/1<41# ]VS' F<%WeO' +(/% )1-/'

)')

G<<<' 7@?8E7D<F<868 DdB><76 )-1

EU ZiSQLVYNOQLVVK\WI\UI WVZQKQiUNQRIMUMSZMUVLM\UI KVYYQMU[MSQX\QLI%_ MZTIU[MUQLVI \UI [MTWMYI[\YIKVUZ[IU[MX\MM^KMLMMU.( ISI X\M[QMUMMSSQX\QLVI OYIULQZ[IUKQILMSZiSQLV'7ISK\SIYMSKISVYX\MWQMYLMMSZiSQLVKILI \UQLILLM[QMTWV'

9Z[MWYVJSMTI%X\MMUMSNVULVKVQUKQLMKVUMSMZ[\LQILVMUMSIWIYb[ILV IU[MYQVY%N\M[YI[ILVWVYSVYLBI_SMQOP"/ J#%ILTQ[QMULVX\MMUMSNMUiTMUVMUK\MZ[QiUQU[MY]QMUMUSIZZQO\QMU[MZTIOUQ[\LMZ2

AfYLQLILMKISVYWVY\UQLIL LM[QMTWV'' ' ' ' ' ' ' ' ' ' ' ' '' ;8QTMUZQiUSQUMISLMSZiSQLV''''''' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' '' /FMSVKQLILLMSSQX\QLV'' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' '' ?9^KMZVLM[MTWMYI[\YI'' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' '' .7ISVYMZWMKgNQKVLMSSQX\QLVWVY\UQLILLM]VS\TMU'' ' ' ' 2 7VUL\K[Q]QLIL[fYTQKILMSSgX\QLV'' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' '' #

9S WYVJSMTILM6UeSQZQZLQTMUZQVUISZMWSIU[MIKVTVZQO\M2

; / ? ) 2 #

( @ ) ( @ !# %(, %( @ %( @ @ %()" @ @ @ ( %( %(& ( @ @ @ ( (

$%& ( %( @ %( @ %($%" @ ( ( @ ( %(

=I KIYIK[MYgZ[QKILMSI TI[YQ`NVYTILIKVUSVZM^WVUMU[MZLQTMUZQVbUISMZMZ' * ,%H W\MLMUNVYTIYZMQUNQUQLILLMWIYMRIZLMTVUVTQVZWQQULMWMULQMU[MZ'AVYSIUI[\YISM`ILMSWYVJSMTI%LMJMKVUZQLMYIYZM; KVTVN\UKQiULMSIZYMZ[IU[MZTIOUQ[\LMZ%WVYSVX\MKVU]QMUMPIKMYZ\KMZQ]IbTMU[M%*( 4 )% *( 4 @' CQT\S[eUMITMU[M%W\MLMMSMOQYZMIYJQ[YIYQIbTMU[MMSM^WVUMU[MLMV[YITIOUQ[\L%X\MW\MLMZMYK\ISX\QMYIKVU[ISX\MMSLM[MYTQUIU[MNVYTILVWVYSIZK\I[YVKVS\TUIZMUKIJM`ILIZWVYSIZTIOUQ[\LMZYMZ[IU[MZZMILQNMYMU[MLMKMYV'9U MZ[MKIZVZMMUK\MUb[YIUSIZWIYMRIZ;# ? _ ;# 2 $ 7VUSI WYQTMYIWIYMRIYMZ\S[I2

!/2 ? "; * /'%@ bbbbaab%.# $$$ $

9Z[I NiYT\SI Z\TQUQZ[YIQUNVYTIKQVUMZWYMKQZIZ%I ZIJMY2)'( =I WfYLQLILMKISVYMZWYVWVYKQVUISIS M^KMZVLM[MTWMYI[\YI'*'' CQZMKITJQI MS[ITIhV LMSZiSQLV_ SI UI[\YISM`I_ SI ]MSVKQLIL

LMSNS\QLVLMTVLVX\MMSTVUVTQV/2 ?5' KVUZMY]MZ\ ]ISVY%SI WfYLQLILMKISVYMZWYVWVYKQVUISI SI KVUL\K[Q]QLILKISVYgNQKILMSSgX\QLV_ I SILQTMUZQiUSQUMISLMSZiSQLV'

! !!!!! !!!!!!!!!!!!

Page 80: Análisis dimensional

&+% : yEBLBL =BF>GLBHG:E

>b c}jeZe i[]k_Ze feh behZKWob[_] [i [b fhef_e Z[ bei j_[cfei Z[?ekh_[h' YkWdZe'feh de ^WX[hi_Ze Z[iYkX_[hje[b fh_dY_f_eZ[ bW[gk_(lWb[dY_W[djh[ [b YWbeho [b jhWXW`e'^WX~Wgk[ Yedi_Z[hWh[b YWbehYececW]d_jkZ _dZ[f[dZ_[dj[ Z[ bWicW]d_jkZ[i c[Y|d_YWi#%$)IeZh~Wf[d(iWhi[ gk[' WbWjh_Xk_hWbYWbehbWc_icW Z_c[di_€d gk[ WbjhWXW`e'[b j[e(h[cW Z[ f_ ikc_d_ijhWi[ c|i _d\ehcWY_€dgk[ bWYedi[]k_ZWfeh behZKWob[_]^)Ge eYkhh[Wi~'i_d [cXWh]e' fehgk[ bWh[fh[i[djWY_€dZ_c[d(i_edWbZ[ bWicW]d_jkZ[i gk[ _dj[hl_[d[d [d [b fheXb[cWZ[ ;ekii_d[igh[gk_[h[ kdWXWi[Z[ YkWjhe'o [i _dZ_\[h[dj[ kj_b_pWhbW=%E%?%[' e bWi=%>%E%[' i[]•d i[ Yecfhk[XW\|Y_bc[dj[)

>d [b fh€n_ce YWf~jkbelebl[h[cei WeYkfWhdei[d [ij[ fheXb[cW)

*! ,GAFXFAMKH@A=E=F>KA?=EDAGMA!

>ij[ WfWhWjei[ XWiW[d [b [d\h_Wc_[djeZ[ kd WbWcXh[YebeYWZejhWdi(l[hiWbc[dj[ [d kdWYehh_[dj[\bk_ZW)L[ WZc_j[ gk[ [b [d\h_Wc_[dje [ifhefehY_edWbWbWbed]_jkZ o gk[' WZ[c|i Z[ bWicW]d_jkZ[i Yedi_Z[hWZWifeh behZKWob[_] [d [b fheXb[cWWdj[h_eh'_d\bko[bWl_iYei_ZWZY_d[c|(j_YWZ[b \bk_Ze'feh Z[f[dZ[h Z[ [bbWbWjkhXkb[dY_W)

K[fh[i[djWdZe feh Z [b hWZ_eZ[bWbWcXh['o feh P bWf}hZ_ZWZ[ YWbehfeh kd_ZWZZ[ bed]_jkZ o feh kd_ZWZZ[ j_[cfe' h[ikbjW[b i_]k_[dj[YkWZheZ[ [nfed[dj[i Z_c[di_edWb[i5

T b [ ^ < [" T

: ( , , H , ( , "( -E ( , ( , H H ( , H ( ,[ H H , H ( , (, HB , H H H , , H

,7& , H ( , H (, H H,7' H H H H ( , , ,$% H , H , H H ( ,

R bWiebkY_€dfk[Z[ [iYh_X_hi[Wi~5

# ["l $T 8 <QO\ F! ?C '

>d bei ]Wi[i f[h\[Yjei' i[]•d i[ l[h| [d [b YWf~jkbeQO' bWl_iYei_ZWZ[i fhefehY_edWbWbWYedZkYj_l_ZWZj}hc_YW'feh be gk[ [b cedec~e Q!bV<

#%$ <h[~W?ekh_[h gk[ [b YWbehl[d~WZ[b Lebo gk[' Yece bW]hWl[ZWZ'WjhW(l[iWXWjeZei bei Yk[hfei)

QBBB) Ye =N<MbOB=:= MzKbB\_<:&+&

j_[d[ gk[ i[h kd d•c[he \_`e [b c_ice fWhWjeZ ,) " ei ei ]Wi[i >d Yedi[Yk[d<bW'WZ[ i[h5 ) (

T 8 <Q^\X"?C#%

e X_[d5

]0^O"^#^ _Q_!

gk[ fed[ Z[ cWd_\_[ijebWfei_X_b_ZWZZ[ c[Z_h bW\b j )) i kY kWY_ed[iZ[ b [dkdW Yehh_[dj[jkhXkb[djWfeh bei YWcX_eigk[w )j[ PRN' [nf[h_c[djW [b YeY_[d(

:GyEBLBL =BF>GLBHG:E) ( ,,

Page 81: Análisis dimensional

<:I~MNEH QBO

:0846/25T42.,

#! .=EHK!

>bWXeh€?ekh_[h ik j[eh~WWdWb~j_YWZ[b YWbehYkWdZede i[ ^WX~WZ[iYkX_[hjebW[gk_lWb[dY_W[djh[ [b YWbehV [b jhWXW`e'[ije [i' YkWdZebWM[hceZ_d|c_YW[ijWXWfeh Yh[Wh)IheY[Z[' fk[i' h[l_iWhbWiceZ_\_YWY_e(d[i gk[ [ij[ dk[le YWf~jkbeZ[ bW?~i_YW_djheZkY[[d bW[ijhkYjkhWZ_(c[di_edWb)

>d fh_c[h bk]Wh'bWM[hceZ_d|c_YW^Wfh[Y_iWZe[b YedY[fje Z[YWbeh)5MX[^Q_X[]aQ \M_MPQaZ OaQ^\[ OMXUQZ`QM [`^[ R^l[ OaMZP[Q_`jZQZ O[Z`MO`[%Q_ PQOU^%XMOMa_MPQ]aQ _Q Q_`MNXQfOMQXQ]aUXUN^U[`k^YUO[QZ`^QMYN[_' L[ jhWjW'Z[iZ[ bk[]e' Z[ kdWcW]d_jkZfh_cWh_W)IWhWbe]hWhik Z[\_d_Y_€d_djh~di[YWYedl_[d[ dejWh' Wdj[ jeZe' gk[ [b YWbehde [i\kdY_€dZ[ [ijWZe' fk[i i€be fk[Z[ ^WXbWhi[Z[bgk[ WXiehX[e Z[ifh[dZ[kd Yk[hfe YkWdZe[nf[h_c[djW Z[j[hc_dWZWjhWdi\ehcWY_€d)<kWbgk_[hWZ[ bei c}jeZei YWbeh_c}jh_Yeii_hl[ fWhWYecfWhWhYWdj_ZWZ[iZ[ YWbehfeh l~Wef[hWY_edWbo kd_l[hiWb)

>b fh_dY_f_eZ[ bW[gk_lWb[dY_Wb_]W[b YWbehYed [b jhWXW`ec[Z_Wdj[kdWh[bWY_€dZ[ fhefehY_edWb_ZWZ5_UQY\^Q]aQ aZ _U_`QYMQO[^^QaZ OUOX[%TMe \^[\[^OU[ZMXUPMPQZ`^QQXOMX[MN_[^NUP[%J' e QX^MNMV[QMXUfMP[%P)

:b fWiWhWbW[YkWY_€d[djh[ c[Z_ZWi' i[ fk[Z[ _djheZkY_hkdWYedi(jWdj[ kd_l[hiWbV [iYh_X_hgk[' [d jeZWjhWdi\ehcWY_€dY~Yb_YW5

;B!2 H' S,',U

@hWY_WiWbWYedijWdj[' 8%[b YWbehYedi[hl€ ik YWh|Yj[hZ[ cW]d_jkZ_dZ[f[dZ_[dj[ Z[ bWicW]d_jkZ[i c[Y|d_YWi' o fkZe i[h c[Z_Ze [d

Page 82: Análisis dimensional

S-',U

QBO) M>KFH=BGyFB<:,1/ :GyEBLBL =BF>GLBHG:E ,10

kd_ZWZ[iWhX_jhWh_Wi):^ehW' feh WYk[hZe_dj[hdWY_edWb'i[ Z[X[ [nfh[iWh[b YWbeh[d kd_ZWZ[ic[Y|d_YWi'be gk[ [gk_lWb[Wikfh_c_h bWYedijWdj[kd_l[hiWb[d S,',U) >bbe de lW [d Z[jh_c[dje Z[b :d|b_i_i Z_c[di_edWb'fk[ije gk[' feh i[h S,',U kdWb[o \kdZWc[djWbWfb_YWXb[i_d [nY[fY_€dWjeZei Wgk[bbei\[d€c[dei [d gk[ _dj[hl_[d[ [b YWbeh'bei i~cXebei 8 o ?!_h|d i_[cfh[ kd_Zei' jWdje [d [b fbWdj[Wc_[djeZ[ YkWbgk_[hfheXb[cWYece [d ik iebkY_€d'feh be gk[ fk[Z[ h[[cfbWpWhi[[b fheZkYje ;B!feh ?% Yed bWYedi_]k_[dj[ i_cfb_\_YWY_€dZ[ bWi\€hckbWi)

=[ WYk[hZeYed be gk[ fh[Y[Z[' dk[ijhe i[]kdZe feijkbWZe W\_hcWgk[ bWYedijWdj[ ; [i ikf[h\bkW'fk[i bWicW]d_jkZ[i B o H de ied_di[fWhWXb[i'i_de jhWdi\ehcWXb[ikdW[d ejhWo gk[ZWYed\_hcWZWkdWl[p c|i bWlWb_Z[pZ[b c_ice)

>d h[ikc[d5 ]hWY_WiWbfh_c[h fh_dY_f_eZ[ M[hceZ_d|c_YW'[b YWbehi[ Yedl_[hj[ [d kdWcW]d_jkZ ^ece]}d[W YedbW[d[h]~Wc[Y|d_YW'o de[i fh[Y_ie Wkc[djWh[b i_ij[cW Z_c[di_edWb)

%! 9DLMAF=@DFAGLDHG=E!

EWi[YkWY_ed[iS-',U R S-'-U fk[Z[d Yedi_Z[hWhi[Yece bei feijkbW(Zei Z[ [n_ij[dY_WZ[ bW[d[h]~W_dj[hdWo Z[ bW[djhef~W'h[if[Yj_lWc[dj[)<ece jWb[i [YkWY_ed[ide h[fh[i[djWd h[bWY_ed[iZ[ fhefehY_edWb_ZWZ[djh[ cW]d_jkZ[i Ye[n_ij[dj[i' ^k[b]W' [d l_hjkZ Z[ dk[ijhe i[]kdZefeijkbWZe' bW_djheZkYY_€dZ[ YedijWdj[i kd_l[hiWb[i' feh be gk[ bWikd_ZWZ[iYe^[h[dj[i Z[ [d[h]~W_dj[hdWo Z[ [djhef~Wgk[ZWdZ[j[hc_dW(ZWi[d YkWdjei[ [b_`WdbWikd_ZWZ[iZ[ YWbeho Z[ j[cf[hWjkhW)L[ feZh|'fk[i' i[]k_h kiWdZekdWXWi[Z[ YkWjhe'gk[ feZh| i[h bW=%E%[' ?%ebW=%>%E%[) EWidk[lWi \€hckbWiZ_c[di_edWb[i'[d [ijW•bj_cW'i[h|d5

GCI 3 =+>E&+

GAI 3 =+>E&+Q&*b

&! <=KD=>EALDG@AIAG@DAGMAL" ?HGLM=GMAL?=K=?MAKWLMD?=L!$! 0GAKCW=DGMAKG=R [djhe f~W)

sr8e8 [ "

:b fbWdj[Whkd fheXb[cWYkWbgk_[hWZ[ :d|b_i_i Z_c[di_edWb'[i fh[Y_ieiWX[hYk|b[i ied bWilWh_WXb[i_dZ[f[dZ_[dj[i Ykoei lWbeh[iZ[j[hc_dWd[b [ijWZe Z[b i_ij[cW) >d M[hceZ_d|c_YWi[ WZc_j[ gk[ [b [ijWZe Z[kd i_ij[cW YkWbgk_[hWgk[ZWZ[\_d_Zefeh [b lebkc[d o bWj[cf[hWjkhW'Z[ jWbcWd[hWgk[' [d [b [ijWZeZ[ [gk_b_Xh_e'ejhWcW]d_jkZ YkWbgk_[hWi[h| \kdY_€dZ[ Z_Y^WilWh_WXb[io Z[ bWYecfei_Y_€dZ[b i_ij[cW)

MhWj|dZei[Z[ Yk[hfei fkhei' [ije [i' Z[ i_ij[cWi \ehcWZei feh kdiebe Yecfed[dj[' i[ Z[ck[ijhW gk[ ik YecfehjWc_[dje j[hceZ_d|c_Yegk[ZWZ[\_d_Zefeh bWcWiWo feh bei i_]k_[dj[i fWh|c[jhei' gk[ [d ][(d[hWbied \kdY_ed[i Z[ lebkc[d o Z[ bWj[cf[hWjkhW5

2] 3W#M?# YWbeh[if[Y~\_YefWhWlebkc[d YedijWdj[Y MN b

S/',U

>b fh_c[h fh_dY_f_eZ[ M[hceZ_d|c_YW'WbfeijkbWhgk[ [b YWbeh[ikdW\ehcWZ[ bW[d[h]~W'_cfb_YW'[d l_hjkZ Z[bfh_dY_f_eZ[ Yedi[hlWY_€dZ[ [ijW •bj_cW'bW[n_ij[dY_WZ[ kdWcW]d_jkZ Z[ [ijWZeZ[\_d_ZWfeh bWi_]k_[dj[ [nfh[i_€d' l|b_ZW[d kdWjhWdi\ehcWY_€dYkWbgk_[hW5

=[b i[]kdZe fh_dY_f_e'i[]•d i[ l_e [d [b YWf~jkbeQBB'i[ Z[ZkY[gk[bWj[cf[hWjkhW [i kdWcW]d_jkZ Z[ bWigk[ ^[cei bbWcWZefh_cWh_Wi):Z[c|i' Z_Y^efh_dY_f_ebb[lWYedi_]e[b gk[' [d jeZe Y_Ybeh[Yehh_Zefehl~Wh[l[hi_Xb[' i[W5

S-'-U

, #3 D # \_ j Z Z_bj )' ) XQd' & & && YW[b<B[d[ [ WW<BedBLHWhWD /J \

n ( ( r # 3D # Yecfh[i_X_b_ZWZ_iej}hc_YW)D -X [

S/'-Uo' [d Yedi[Yk[dY_W'[d kdWjhWdi\ehcWY_€dh[l[hi_Xb[YkWbgk_[hWZ[X[h|ikY[Z[h gk[5

S/'.U

ZedZ[ D [i kdWdk[lW cW]d_jkZ Z[ [ijWZe gk[ i[ Z[dec_dW [djhef~W)

<edl_[d[ [d jeZei bei fheXb[cWi Z[ M[hceZ_d|c_YWh[[cfbWpWhbWcWiW'Y%feh [b ZnYQ^[ PQY[XQ_%Z[\_d_Zefeh5

Z &Y(>^ S/'/U

Page 83: Análisis dimensional

S/'0U

QBO) M>KFH=BGyFB<: ,12,11 :GyEBLBL =BF> LBHG:E

gk[ [i Z_h[YjWc[dj[Wfb_YWXb[WjeZe Yk[hfe \ehcWZe feh kdWiebW[if[(Y_[Z[ fWhj~YkbWi)>d [ijW \€hckbW'Y [i bWcWiWYed gk[ i[ ef[hW o;Z [i bWhWp€d5

EWi\€hckbWiZ_c[di_edWb[iZ[ Qe%[0 o n i[ Z[ZkY[d_dc[Z_WjWc[dj[ Z[

iki \€hckbWiZ[ Z[\_d_Y_€d5JQeK3 :+B&+M&*

E#"*))F3 W(,Sn)U3 :;&7B+'

[djh[ bWcWiW'YY% Z[ YWZWfWhj~YkbW#ceb}YkbW'|jece' _€d' [b[Yjh€d'[jY}j[hW$o bWZepWlW)fWhj[' Ya% Z[ bWcWiWZ[b |jece d[kjhe Z[b d•[b_(Ze ,-<5

MeZWl~Wi[ kj_b_pWd[d M[hceZ_d|c_YWejhWicW]d_jkZ[i i[YkdZWh_Wi'

WiWX[h5Ua! ,'11+.2 Q ,+(-/ ] 92 F$\G

40 F&ED

50 F$\G&ED

[djWbf~W

[d[h]~Wb_Xh[

[djWbf~Wb_Xh['<ece ;^ j_[d[ Z_c[di_€d dkbWfeh i[h bWhWp€d[djh[ Zei cWiWi'i[Z[ZkY[ Z[ S/'/U gk[

NVI 3 F(b) jeZWibWiYkWb[iied ^ece]}d[Wi YedbW[d[h]~W)

EWkd_ZWZYe^[h[dj[ Yed S/'/U [i [b Y[X' >i Wgk[bbWcWiWYkoWc[(Z_ZW'U% [i _]kWbWbWcWiWceb[YkbWhh[bWj_lW';Z% Z[b Yk[hfe gk[ i[Yedi_Z[h[)>i' fk[i' kdWkd_ZWZZ[h_lWZW'gk[ Z[f[dZ[ Z[b Yk[hfe Yedgk[ i[ ef[hWo Z[b i_ij[cW Z[ kd_ZWZ[igk[ i[ WZefj[) Ieh [ie ^Wogk[Z_ij_d]k_h[djh[ [b ceb(]hWce #ceb(]$ o [b ceb(a_be]hWce #ceb(a]$ gk[[i bWkd_ZWZ[d [b i_ij[cW Z[ @_eh]_#%$)

'! .HGLM=GMA@AEHLC=LALIAKBA?MHL!

L[ ikfed[ [d M[hceZ_d|c_YWgk[ WjeZe Yk[hfe \~i_YWc[dj[^ece(]}d[e Yehh[ifedZ[ kdW[YkWY_€dZ[ [ijWZe' O"X%D%H$3 +' gk[ b_]WbWfh[i_€d' [b lebkc[d o bWj[cf[hWjkhW`kdjWc[dj[ YedY_[hjWiYedijWdj[iYWhWYj[h~ij_YWiZ[b Yk[hfe gk[ i[ Yedi_Z[h[)GWZWi[ fh[`kp]W WY[hYWZ[Z_Y^W\kdY_€do' Yed bei c}jeZei fkhWc[dj[ j[hceZ_d|c_Yei' de i[

fk[Z[ Z[ZkY_hbW\ehcW Z[ bWc_icW)I[he ^Wokd ]hkfe Z[ Yk[hfei' Yedij_jk_Zefeh bei i_ij[cWi ]Wi[eiei

o bWiZ_iebkY_ed[iZ_bk_ZWi'YkoW[YkWY_€dZ[ [ijWZe' Yed Y_[hjWWfhen_(

cWY_€d'jecW bW\ehcW5\G 3 ZCM% S0',U

) #%$ L[ dri fh[i[djW W^ehWbWeYWi_€dZ[ Yec[djWh be gk[ bWNd_€d Bdj[hdW(Y_edWbZ[) ?"~i_YWIkhW o :fb_YWZWW Z[Y_Z_ZeWY[hYWZ[ bWZ[\_d_Y_€dZ[b ceb)>d bW•bjbcW)h[Yef_bWY_€dZ[) iki Z[Y_i_ed[i #reY) L) N) <'. )1,(//$ i[ Z_Y[gk[5

uL[ h[Yec_[dZW gk[ bWkd_ZWZUWT i[W Yedi_Z[hWZW[d ?~i_YWYece bWkd_ZWZZ[ OMZ`UPMPPQ_a_`MZOUM#_dZ_YWZWfeh [b i~cXebe J$) EWZ[\_d_Y_€dZ[b ceb Z[X[i[h5 , ceb #i~cXebe ce)b$ [i bWYWdj_ZWZZ[ ikijWdY_Wgk[ Yedj_[d[ [b c_ice d•(c[he Z[ ceb}YkbWi#e _ed[i' |jecei' [b[Yjhed[i' i[]•d bei YWiei$Yece |jecei^Wo' rnWYjWc)[dj[' [d ,1 ]hWcei Z[b _i€jefe fkhe ,1+) >ijW cW]d_jkZ o ik Yehh[i(fedZ_rdj[ kd_ZWZZ[X[d i[h Yedi_Z[hWZWi'Wbb~ZedZ[ i[ kj_b_Y[d'Yece kdWdk[lWcW]hkjkZ \kdrW)c[djWbo Yece kdWdk[lW kd_ZWZ\kdZWc[djWb' h[if[Yj_lWc[dj[)[

) >rjb6T'Z[\_hd<b€dZ[b ceb' j[d_[dZe fh[i[dj[ bWikij_jkY_€d Z[b ,1+ feh [b ,-<'

Ye_dY_Z_h~WY)edbWgk[ i[ eXj_[d[ feh Ye^[h[dY_WYed bW[YkWY_€dS/'/U Wde i[hfehgk[ i[ \_`W[b ]hWce Yece kd_ZWZZ[ cWiW)>ijW WhX_jhWh_Wh[ijh_YY_€d WY[gk[ bWbbWcWZWYWdj_ZWZZ[ ikijWdY_WWZeb[pYWZ[b c_ice Z[\[Yje gk[ [b \9 obWYe)dijWdj[ gk~c_YW'feh be gk[ Z[X[ Z[i[Y^Whi[)

@Zir Z[`Wb_Xh[bWkd_ZWZZ[ cWiW' bWYWdj_ZWZZ[ ikijWdY_WYe_dY_Z[Yedbe gk[ i_[cfh[ i[ ^WbbWcWZed•c[he Z[ ceb[i) >i' fk[i' ^ece]}d[W Yed bWcWiW'o de) ^Wo hrp€d fWhWWcfb_WhbWXWi[ Yed kdW cW]d_jkZ c|i)

)L_ i[ gk_[h[ ZWhWbceb kd i~cXebe gk[ [nfh[i[ Y€ce [ij| h[bWY_edWZeYed bWkd_ZWZZ[ cWiW' i[ fk[Z[ fheY[Z[h Yece i_]k[5

, ]*Fh 33 , ceb(]6 , a]*Fh 33 , ceb(a]'

ZedZ[ Z [i [b d•c[he Z[ ceb[i o C bWYedijWdj[Z[ bei ]Wi[i f[h\[Yjei)<kWdZei[ gk_[h[ cWoeh Wfhen_cWY_€d'i[ ikij_jko[ bW[YkWY_€dS0',Ufeh ejhWi c|i Yecfb_YWZWi'f[he i_[cfh[ bWj[cf[hWjkhW j[hceZ_d|(

c_YWWWfWh[Y[ckbj_fb_YWZWfeh bWYedijWdj[ @' 'L_ S0',U\k[i[ bW[nfh[i_€d Z[ kdWb[o kd_l[hiWbYWXh~W'[d OBhjkZZ[

dk[ijhe i[]kdZe feijkbWZe' fh[iY_dZ_hZ[ bWYedijWdj[ @%Yed be gkri[]k_h~Wi_[dZe ik\_Y_[dj[bWXWi[jh_Z_c[di_edWbZ[ bWF[Y|d_YW):kd Wi_'de i[ Z[X[h~WWjh_Xk_hWWbWc_icW Z_c[di_€d gk[ WbfheZkYje \ G #[d[h(]~W$'fk[i [b d•c[he Z[ ceb[i' Wf[iWhZ[ ik Z[dec_dWY_€d'de [i kd d•(c[he fkhe' i_de kdWcW]d_jkZ ^ece]}d[W Yed bWcWiW)>d jeZe YWie

i[ Z[X[h~Wfed[h5 S0'-UZedZ[ ;a [i kd d•c[he gk[ i[ [dYk[djhW [d bWiXWXbWiZ[ cWiWi ceb[YkbWh[ih[bWj_l5Wi'Z_ij_dje fWhWYWZW[if[Y_[ Z[ fWhj~YkbWio gk[ de Z[f[dZ[ Z[b i_ij[cWZ[ kd_ZWZ[i gk[ i[ WZefj[)

Page 84: Análisis dimensional

,13 :GyEBLBL =,bTcGLBHG:E QBO) M>KFH=BGyb"jbb<: ,14

Yece ^_Y_cei [gk_leYWZWc[dj[[d kd jhWXW`eWdj[h_eh#1-$) =[Y_cei[gk_leYWZWc[dj[fehgk[ [ijW \€hckbWZ_c[di_edWbi€be [i kj_b_pWXb[[dWgk[bbei\[d€c[dei gk[ [ij}d h[]_Zei feh bW[YkWY_€dS0',U'feh [`[cfbe'[d bei i_ij[cWi ]Wi[eiei o [d bWiZ_iebkY_ed[iZ_bk_ZWi)Ieh de ^WX[hj[d_Ze [d Yk[djW[ijW Y_hYkdijWdY_W'eXjkl_cei kd cedec_e f_ }ifkh_eWbh[iebl[h [b fheXb[cWZ[ ;ekii_d[ig [d [b Y_jWZejhWXW`e#1-$)

o' i_ i[ jecW [d Yedi_Z[hWY_€dbWb[o Z[ :le]WZhe' [d YkoWl_hjkZ Y(>^ ^WZ[i[h \kdY_€dkd_l[hiWbZ[ X%D%[' h[ikbjW5

XD0^@N%<Q

gk[ [i bWiebkY_€dYehh[YjW)-)v <ed bWXWi[h[ZkY_ZW53" 3 K[)<ece S3"U3 =+E&+%h[ikbjW5

XD 3 Y/!R">^#%(! 3= @DFAGLDXG@AE=MAFIAK=MNK=!

A[cei ZWZeoW bWihWped[i feh bWigk[ bWj[cf[hWjkhW Z[X[ Yedi_Z[hWhi[Z_c[di_edWbc[dj[ _dZ[f[dZ_[dj[ Z[ bWicW]d_jkZ[i c[Y|d_YWi' f[he Yece [ij[Wikdje [i eX`[je Z[ Yedjhel[hi_W' Yedl_[d[ _di_ij_hieXh[ [b c_ice) EWZ_iYki_€d\k[ _d_Y_WZWfeh ;kYa_d]^Wc o MebcWd #,2$) >ij[ •bj_ce Wkjeh' gk[ Yh[~Wgk[bWiZ_c[di_ed[i [nfh[iWXWdbW[i[dY_WZ[ bWicW]d_jkZ[i' Z[iWhhebb€kd hWpedW(c_[dje XWiWZe[d Wjh_Xk_hWbWj[cf[hWjkhW bWc_icW Z_c[di_€d gk[ WbW[d[h(]~W);kYa_d]^Wc eX`[j€ gk[ [bbede [hWWZc_i_Xb['o MebcWdh[YedeY_€ik [hheh)I[he ;h_Z]cWd #--$ ieij_[d[ gk[ MebcWd[ijWXW[d ik f[h\[Yje Z[h[Y^e Wbikfe(d[h gk[ bWj[cf[hWjkhW [hW^ece]}d[W Yed bW[d[h]~Wi_ [bbe Yedl[d~WWik fhe(f€i_je' be gk[ [gk_lWb[ WYedi_Z[hWhbWiYedijWdj[i kd_l[hiWb[i Yece YeceZ_d[igk[ f[hc_j[d Wjh_Xk_hbWZ_c[di_€d gk[ i[ gk_[hWWbWicW]d_jkZ[i gk[ cej_lWdbW_djheZkYY_€dZ[ Z_Y^WiYedijWdj[i)

EWYk[ij_€d i_]k[ i_d h[iebl[h) EWdZWko E_\i^_jp #1.$' feh [`[cfbe' ZWdfehi[]khe gk[ bWj[cf[hWjkhW [i ^ece]}d[W Yed bW[d[h]~W' o de \WbjWgk_[d' YeceK[_Y^[dXWY #-+$' ef_dW gk[ j_[d[ Z_c[di_€d dkbW)

>l_Z[dj[c[dj[' [b fb[_je de fk[Z[ \WbbWhi[feh Yedi_Z[hWY_ed[ij[€h_YWi'i_deh[Ykhh_[dZe WbWYecfheXWY_€d[nf[h_c[djWb o' fWhW[bbe' XWijWh|Wfb_YWh[b:d|b_i_i Z_c[di_edWbWkd fheXb[cW YkoWiebkY_€di[W YedeY_ZW)>ije [i be gk[^Wh[cei WYedj_dkWY_€d)

gk[ Ye_dY_Z[Yed bWiebkY_€dWdj[h_eh).)v O[Wcei be gk[ ikY[Z[ i_ i[ ^WY[bWj[cf[hWjkhW ^ece]}d[W Yed bW

[d[h]~Wo i[ _djheZkY[ [d bWb_ijWZ[ cW]d_jkZ[i bWYedijWdj[ C Yed bW\€hckbW)Z_c[di_edWb G@I3 <(M)

:Z[c|i Z[ ;a o Z[ ,7& h[ikbjW [b cedec_e ,7' 3 U@%gk[ [i [ifkh_e o [iYWkiWZ[ gk[ bWiebkY_€d

\G 3 ,O";^#%

\ D 3 U@,O";^% U@#

i[W c[dei fh[Y_iWgk[ bW WbbWZWfeh bei Zei c}jeZei Wdj[h_eh[i)/)v MeZWl~Wi[ fk[Z[ l[h be gk[ ikY[Z[ i_ i[ Wjh_Xko[WbWj[cf[hWjkhW bW)

c_icW \€hckbW Z_c[di_edWb gk[ WbW[d[h]~W o i[ _]dehWbW[n_ij[dY_WZ[ bW)

YedijWdj[ C' L[ bb[]WWbWiebkY_€d

gk[ [i dejeh_Wc[dj[ \WbiWfehgk[ de \_]khWbWcWiWZ[b ]Wi)0)+ IWhWj[hc_dWh' lWcei W[nWc_dWhbWYk[ij_€d [d jeZW ik ][d[hWb_ZWZ)

Lkfed]Wcei gk[' Z[ WYk[hZeYed ?h) Kkiie #-/$ o Yed jeZei bei \~i_Yei Z[ bW)[iYk[bWZ[ ;h_Z]cWd' jWd i€be [ij| Z[\_d_ZWbWZ_c[di_€d Z[b fheZkYje @,%fehbe gk[ 1 feZh~Wj[d[h kdWZ_c[di_€d YkWbgk_[hWYed jWbZ[ Wjh_Xk_hWC bWZ_c[d(

i_€d Yedl[d_[dj[)L[W

)! 0?N=?DXG@AEHLC=LALIAKBA?MHL!

MhWj[cei Z[ Wl[h_]kWh'Yed Wkn_b_eZ[b :d|b_i_i Z_c[di_edWb' bWh[bWY_€dgk[b_]WbWfh[i_€d Z[ kd ]Wi' X%Yed [b lebkc[d' D%bWcWiW' Y%o bWcWiWceb[YkbWhh[bWj_lW'Fh)

,) X <ed bWXWi[Yecfb[jW5

>b fheXb[cW gk[ dei eYkfW' fh[iY_dZ_[dZe Z[b YediWX_Ze;^% i[ fbWdj[Wh~WWi~5

\ D U 1 @

: ( , . > > '; , > , > >E "' > > > "'1 > > > , ,

,7& , , (, ( , (,

<ece ;a [i Z[ Z_c[di_€d dkbW'bWiebkY_€d [i5

\ D 3 U@NO";Z#%

\ D Y 4 C

: ( , . > eY -(eY; , > , W "8B (- > > D (#- & o$

,7, , , ( , , ,,7' > , 16 14 3@

8N 8 .reY&o

14 8.#- & o$

-#eY& o$

.o3@ 8 (

-#eY& o$

Page 85: Análisis dimensional

,2+ :GyEBLBL =BF>GLBHG:E QBO) M>KFH=BGyFB<: ,2,

<ed [b cedec_e !, i[ eXj_[d[ bWiebkY_€dYehh[YjW)>b cedend_e !- [i [ifk(h_e) EW•d_YWcWd[hWZ[ gk[ de WfWh[pYW[i ^WY[h#C 8 -' ,. 8 +' o 8 ( -' Z[WYk[hZeYed dk[ijhW j[i_i)

!4) <Wiei [d gk[ [i l_WXb[bWXWi[ckj_bWZW)

Eei [`[cfbei [ijkZ_WZei[d bei tt 2 R 3 fhk[XWdgk[ XMQY\Q^M`a^MQ_PUYQZ_U[ZMXYQZ`QUZPQ\QZPUQZ`QPQ XM_YMSZU`aPQ_YQOjZUOM_'>d jeZebbheXb[cW[d gk[ _dj[hl[d]W bWj[cf[hWjkhW Z[X[h| kj_b_pWhi[kdWXWi[YkWZh_Z_c[di_edWb'jWbYece bW=%>%E%1)>nY[fY_edWbc[dj['[d Wgk[bbeiYWiei[d gk[ i[ j[d]W bWY[hj_ZkcXh[Z[ gk[ bWj[cf[hWjkhW de fk[Z[\_]khWhi_de [d [b cedec_e C.% i[ fk[Z[ [cfb[Wh bWXWi[h[ZkY_ZW=%;% B%f[he WYedZ_Y_€dZ[ [cfb[Wh' fh[Y_iWc[dj[' bWi\€hckbWi Z_c[d(i_edWb[i S1U3 =+E&+R G@I3 F(bV <ed [bbe de i[ j_[d[ ejhWl[djW`Wi_de i_cfb_\_YWhWb]ebei Y|bYkbei)

A[ Wgk~ejhW[di[•WdpWbe]hWZWYedbei [`[cfbei gk[ ^[cei WdWb_pWZe)EW\€hckbWZ_c[di_edWbS1U3 =+E&+%Z[ZkY_ZWZ[ bW[YkWY_€dZ[ [ijW((ZeXG 3 ZC. Wbfh[iY_dZ_hZ[ C%de ^Wh[ikbjWZel_WXb[i_de [d YWiei([if[Y_Wb[W'>bbe i[ Z[X[' [l_Z[dj[c[dj[' Wgk[ Z_Y^W[YkWY_€di€be [iWfb_YWXb[Wkd ]hkfe fWhj_YkbWhZ[ \[d€c[dei #beigk[ eYkhh[d[d i_ij[cWi]Wi[eiei o Z_iebkY_ed[iZ_bk_ZWi$'o de Z[ kd ceZe ][d[hWb)=[ Wgk~i[_d\_[h[gk[' \M^MTMXXMXMPUYQZ_UmZPQaZM YMSZU`aP\^UYM^UMQ_\^QOU_[^QOa^^UMaZM XQeaZUbQ^_MX'EWib[o[i fWhj_YkbWh[i'jWb[iYece bW[nfh[(iWZWfeh bW[YkWY_€dZ[ bei ]Wi[i f[h\[Yjei' de i_hl[d fWhW[ij[ fhef€i_je)=[ ^WX[h[ijWXb[Y_Zefh[l_Wc[dj[ [ij[ h[gk_i_jede i[ ^kX_[hWfbWdj[WZei_gk_[hW[bfheXb[cWZ[ Wl[h_]kWhK_C [i e de ikf[h\bkW)

3) >d\h_Wc_[djeZ[ kdW[i\[hW)

:b kj_b_pWhbWXWi[h[ZkY_ZWYed 1" 3 @,%^[cei j[d_Ze bWiebkY_€dYehh[YjW'o feZh~WYh[[hi[ gk[ [d jeZe fheXb[cW [d gk[ \_]kh[ bWj[cf[hWjkhW i[ bWfk[Z[Yedi_Z[hWhYece ^ece]}d[W Yed [b YkWZhWZeZ[ bWl[beY_ZWZ'o ^WY[h\_]khWhede bWYedijWdj[ C i[]•d bW~dZeb[Z[bfheXb[cW) I[he [b i_]k_[dj[ [`[cfbe Z[ck[i(jhWgk[ de [i Wi~)

NdW [i\[hW f[h\[YjWc[dj[ YedZkYjehWj_[d[ [d [b _dijWdj[ ` 3 H' kd [nY[ieZ[ j[cf[hWjkhW r1e ieXh[ bWj[cf[hWjkhW WcX_[dj[) L[ WZc_j[ gk[ [b [d\h_W(c_[dje Z[f[dZ[ jWd i€be Z[b Ye[\_Y_[dj[ Z[ YedZkYj_l_ZWZikf[h\_Y_Wb'6%Z[bYWbeh[if[Y~\_Yeh[\[h_Ze WbWkd_ZWZZ[ lebkc[d' ["' o Z[b hWZ_e' %L[ jhWjWZ[YWbYkbWh[b [nY[ie Z[ j[cf[hWjkhW' r 1' [d \kdY_€d Z[b j_[cfe)

:fb_YWdZebWb[o Z[ G[mjed i[ eXj_[d[ \|Y_bc[dj[5

< ,9bd(( 3 ( &&`'

r1e O!^

Nj_b_Y[cei W^ehW[b :d|b_i_i Z_c[di_edWb),) e <ed bWXWi[Yecfb[jW)=[iZ[ bk[]e' kd cedec_e f_ [i5

<,S",3(("

r1e

o [b ejhe i[ eXj_[d[ Yece i[ _dZ_YWWYedj_dkWY_€d5W

< 9 [" ^

: H H (, , H> H , , H HE H "( "' H ,1 , ( , (, H H

' H , (, ( , ,

%( ;aTa\MOU[ PQ(! XM_YM]ZU`aPQ_

YQOQZUOQ_'

L[ l[ gk[ [b i_ij[cW" [i _dYecfWj_Xb[Wde i[h dkbe [b [nfed[dj[ Z[ r1) <ed[ijW YedZ_Y_€d[i !- 3 9`VO!^%o bWiebkY_€d

9

99

99

L*O\

?B@) -) ( K[fh[i[djWY_€d l[Yjeh_WbZ[ bWicW]d_jkZ[i >%7%1' C

[i Yehh[YjW)-)+ <ed bWXWi[h[ZkY_ZW'=%;% E R S1U3 =+E&+':Z[c|i Z[ bei Zei cedec_ei f_ ^WbbWZeiWdj[i' WfWh[Y[[b cedec_e [ifk(

h_e!. 3 h.`+(^+%gk[ h[l[bW gk[ [b [cfb[e Z[ bWXWi[ckj_bWZWde [i l_WXb[[d [bYWiegk[ dei eYkfW)

>b WZ`kdje[igk[cW #\_])-$ fk[Z[ i[hl_h fWhWWYbWhWhdk[ijhe f[diW(c_[dje) EWh[fh[i[djWY_€dZ[ bWiZ_c[di_ed[i Z[ bWicW]d_jkZ[i c[Y|d_(#bWih[gk_[h[ kd ikX[ifWY_el[Yjeh_Wbjh_Z_c[di_edWb'f[he i_ dei Wj[d[ceiWYWieiZ[ [gk_b_Xh_e'XWijWdZei cW]d_jkZ[i X|i_YWi'gk[ fk[Z[d i[h bW

Page 86: Análisis dimensional

&,' :GyEBLBL =BF> LBHG:EQBO) M>KFH=BGyFB<: &,(

#"! 9HEN?DXG@AEIKH>EAF=@A-HNLLDGALJ!

XekY^_diao [i Yehh[YjW'o Z[`WbW_cfh[i_€d Z[ gk[ [ij[ [`[cfbe [i kdWhWp€dc|i fWhW kij_\_YWhik [iY[fj_Y_ice [d jeZe be gk[ i[ h[\_[h[ Wb:d|b_i_i Z_(c[di_edWb)

=[iZ[ dk[ijhe fkdje Z[ l_ijW' bWYk[ij_€d i[ h[ik[bl[ \|Y_bc[dj[) IbWdj[WZe[b fheXb[cW' [ije [i' \_`WZWbWb_ijWZ[ bWicW]d_jkZ[i gk[ _dj[hl_[d[d [d [b \[d€(c[de' i[ eXj[dZh| bWiebkY_€dYehh[YjWkj_b_pWdZebWXWi[Yecfb[jW :%;% B%,'I[he [d [b fbWdj[Wc_[dje ^Wogk[ Z[Y_Z_hi_ _dj[hl[dZh| e de bWYedijWdj[ Z[ bei]Wi[i) >ijW Z[Y_i_€dYW['[l_Z[dj[c[dj[' \k[hWZ[b WbYWdY[Z[b:d|b_i_i Z_c[di_e(dWb)MWbYece [b fheXb[cW \k[ fbWdj[WZefeh behZ KWob[_]^'de \_]khWC [d bWb_ijW'^_f€j[i_i fbWki_Xb['fk[ije gk[' jhWj|dZei[ Z[ kd \bk_Ze fh|Yj_YWc[dj[_dYecfh[i_Xb[' bWfh[i_€d de _d\bk_h|Z[ kd ceZe Wfh[Y_WXb['o ^k[b]W jecWh [d(Yedi_Z[hWY_€dbW[YkWY_€dZ[ [ijWZe) L[h|' fk[i5

[d[h]~W'7%R bWcWiW'>' EWj[cf[hWjkhW' feh i[h _dZ[f[dZ_[dj[ Z[ bWicW]d_jkZ[i c[Y|d_YWi'^WZ[ h[fh[i[djWhi[ feh kd l[Yjeh gk[ [ij} \k[hWZ[ Z_Y^eikX[ifWY_e'o ejhe jWdje ikY[Z[ Yed bWYedijWdj[ C' I[he [bcedec_e CQ%feh i[h ^ece]}d[e Yed [b YkWZhWZeZ[ bWl[beY_ZWZ'YW[[d [b ikX[ifWY_eZ[ bWicW]d_jkZ[i c[Y|d_YWi)

<ed be gk[ fh[Y[Z[ [ijWcei oW[d YedZ_Y_ed[iZ[ _dj[hl[d_h [d bWfeb}c_YW[djWXbWZW[d jehde Z[b fheXb[cW Z[ ;ekii_d[ig' Z[b gk[ jhWjWcei oWWb WXbWhZ[ bWj[eh~WZ[ bWYedZkYj_X_b_ZWZj}hc_YW)EWiebkY_€dZWZWfeh behZ KWob[_]^\k[ Yh_j_YWZWfeh K_WXekY^_diao#1/$' gk_[d ^_pe dejWh gk[' i_ [d l[p Z[ Yedi_(Z[hWhbWj[cf[hWjkhW Yece cW]d_jkZ _dZ[f[dZ_[dj[' i[ Z[\_d[ Yece bW[d[h]~W'c[Z_W Z[ bWiceb}YkbWi'i[ bb[]WWkd h[ikbjWZeZ_\[h[dj[)

>d [\[Yje5 kj_b_pWdZebWXWi[ckj_bWZW=%E%?%o Wjh_Xko[dZeWbWj[cf[(hWjkhWj[hceZ_d|c_YW bWc_icW Z_c[di_€d gk[ W?% [b fheXb[cW i[ fbWdj[Wh~WYece _dZ_YW[b i_]k_[dj[ YkWZhe5

] M b 1 Q! 9

: H , , H "( ( ,E , H , H H (,B , H H , H H

85 , (, H (, H (,8' H , , H , (,8( H ( H H , H

] M b 1 Q! <

: ' , , H ( , ,; , H H H , ,E "( H ( , H "' "(1 H H H , ( , (,

rb , (, H (, H ( ,8' H , , H , ( ,

rb 3 MU.1MQ!b

h+2&I1

0e [ijW iebkY_€d' gk[ h[fkjWcei Yehh[YjW'Ye_dY_Z[Yed bWZWZWfeh behZ

KWob[_]^)=[`Wcei WbYk_ZWZeZ[b b[Yjeh[b YecfheXWhgk[' i_ i[ kj_b_pWbWXWi[ckj_bW(

(ZW:%;% B%o bWi\€hckbWi Z_c[di_edWb[i5

<ece bWYWhWYj[h~ij_YW[i T 3 .' h[ikbjWdjh[i cedec_ei f_ _dZ[f[dZ_[dj[i5S1U8 =+>E&+1 JQX8 =&,1 G9I 8 7Z$/ G@I8 F(b'

h & ] ', ( M<.! "i[ eXj_[d[ [b cedec_e [ifkh_e Q!M,L

Yed be gk[ bWiebkY_€d[i c[dei fh[Y_iWgk[ bWZWZWfeh behZKWob[_]^): bWeXi[hlWY_€dZ[ K_WXekY^_diaoh[fb_Y€behZ KWob[_]^[d bei i_]k_[dj[i5

j}hc_dei5

uEWYk[ij_€d fhecel_ZW feh K_WXekY^_diaof[hj[d[Y[ c|i X_[d Wbr E€]_YW)gk[ Wbkie Z[b fh_dY_f_eZ[ i_c_b_jkZ' gk[ [i be gk[ c[ YedY_[hd[)F[h[Y[' i_d[cXWh]e' i[h Z_iYkj_ZWW\edZe) EWiebkY_€dWgk[ bb[]k} i[ XWiW[d bWi[YkWY~ed[i'Z[ ?ekh_[h fWhWbWYedZkYY_€dZ[b YWbeh'[d bWigk[ bWj[cf[hWjkhW o [b YWbehi[Yedi_Z[hWdYece _aUSQZQ^U_'<_[hjWc[dj[ i[h~WfWhWZ€`_Ye[b gk[ kd c[`eh Yede(Y_c_[dje Z[ bWdWjkhWb[pWZ[b YWbeh'be]hWZefeh bWj[eh~Wceb[YkbWh'dei fki_[hW[d f[eh[i YedZ_Y_ed[iWbjhWjWhZ[ h[iebl[h kd fheXb[cW fWhj_YkbWh)EWiebkY_€dfWh[Y[Yedi_ij_h[d gk[ bWi[YkWY_ed[iZ[ ?ekh_[h bb[lWd[dlk[bje Wb]eWY[hYWZ[bWdWjkhWb[pWZ[b YWbeho Z[ bWj[cf[hWjkhW' gk[ [i _]dehWZe[d bWWh]kc[djWY_€dZ[ K_WXekY^_diao)x

;h_Z]cWd' WbYec[djWh bWYedjhel[hi_W fh[Y[Z[dj[' Z_Y[ gk[ bWh[ifk[ijWZ[ behZ KWob[_]^b[ Z[`W\h~e) Hf_dW' i_d `kij_\_YWhbe'gk[ bWiebkY_€d Z[ K~W(

##! 8AE=?DXGAGMKAE=ODL?HLD@=@R E=?HG@N?MDOD@=@MVKFD?=@ANG C=LIAKBA?MH!

EWh[bWY_€dl*D [djh[ bWl_iYei_ZWZY_d[c|j_YWV bWYedZkYj_l_ZWZ"j}hc_YW'fWhWlWbeh[iZ[j[hc_dWZei Z[ bWfh[i_€d V Z[ bWj[cf[hWjkhW'i€be feZh| Z[f[dZ[h Z[ bWdWjkhWb[pWZ[bYk[hfe gk[ i[ Yedi_Z[h['[ije [i'(Z[ bei Ye[\_Y_[dj[iQ!%#b#) V n' gk[ Z[j[hc_dWd"[bYecfehjWc_[dje j[hceZ_(d|c_Ye Z[ kd Yk[hfe YkWbgk_[hW'i[]•d i[ Z[ZkY[ Z[ bei fh_dY_f_eiZ[ bW"M[hceZ_d|c_YW)Eei Ye[\_Y_[dj[i#b#) o n Z[h_lWdZ[ bW[YkWY_€dZ[ [ijWZeo')i_i[ jhWjWZ[ kd ]Wif[h\[Yje' i€be feZh| Z[f[dZ[h Z[ bWilWh_WXb[iX o [C"Z[ bWYedijWdj[C'

Page 87: Análisis dimensional

&,) :GyEBLBL =BF>GLBHG:E

b(< Q! @ \ H

: , (, ' (, >; (, , > , >B ' "' "' "' >[ , ( , (, > ,

,j!, , , > > >,j!- > , > ( , ,

T ' Q!Q,", 8 (( Q1 ,"- 8 ((e

`Q A

QBO) M>KFH=BGyFB<: &,*

o bW[YkWY_€dZWZWfeZh| jecWh bW\ehcW5

IWhWYecfb[jWhbW_d\ehcWY_€dikc_d_ijhWZWfeh [b :d|b_i_i Z_c[d(i_edWb'eXi[hlWh[cei gk[ [djh[ [b YWbeh[if[Y~\_Yeh[\[h_ZeWbWkd_ZWZZ[lebkc[d' Q!%o [b YWbehcebWh@b [n_ij[ bWh[bWY_€d5

LWble\WYjeh[idkc}h_Yei' bWicW]d_jkZ[i >T! D7R [b Ye_dY_Z[dYedbWiYedijWdj[i Yh~j_YWiZ[b ]Wi [d Yk[ij_€d' o [d bW[YkWY_€dfh[Y[Z[dj[ [ij|Yedj[d_ZWbWb[o Z[ bei [ijWZei Yehh[ifedZ_[dj[i)

L[ l[ \|Y_bc[dj[ gk[ YkWbgk_[h[YkWY_€dZ[ [ijWZe gk[ Yedj[d]WjWdi€be jh[i fWh|c[jhei o f[hc_jW YWbYkbWh[d \kdY_€d Z[ bei c_icei beilWbeh[iZ[ bWiYedijWdj[iYh~j_YWi'bb[lWYedi_]ebWlWb_Z[pZ[ bWh[\[h_ZWb[o)

#%! /DLMKD>N?DXG@AIKALDHGALAGE==MFXLBAK=!

% @bQ 3((G!

L[ WZc_j[ gk[ bWfh[i_€d Wbd_l[b Z[b cWh [i YedijWdj[ o lWb[A[% Rgk[ bWj[cf[hWjkhW [ij| b_]WZWYedbWWbjkhW'f%feh bW[YkWY_€d5

A

[ 8 Q[&Mf'\ f ++ M S C

: ( , , > (, , '; , > > > > >E "' > > > "' "'H > > , , > (,

,j!- > , ( , , > >,j!. > > > (, , (,

ZedZ[ G [i [b lebkc[d cebWh)K[ikbjW Wi~5

Q!Q

o [i iWX_Zegk[ @b(C [i kd d•c[he \_`e' fhefehY_edWbWbd•c[he' X%Z[|jecei Yedj[d_Zei [d bWceb}YkbW)L[h|' fk[i5

l["(( 3 YedijeKgX A

,", 3((Ib

#$! 3AR @AEHLALM=@HL?HKKALIHG@DAGMAL

EW[YkWY_€dZ[ OWdZ[ PWWbi'h[\[h_ZWWbcWb' [i5 "Mf S#

A 8 A[`#i 1+" MC '

!"\ & 6-$ "D & K#3 @NEW\€hckbWYecfb[jW [i5

o Yed bWicW]d_jkZ[i gk[ [d [bbW\_]khWdfk[Z[d \ehcWhi[ bei i_]k_[dj[i)cedec_ei f_5

" Q[&Mf#A 3 A[ [e

SMC

\N+ A,", 8 (( 8 ((6

M A*

N@K [,"-8((8((6

M [bD D

,".8( 8((N G*

Page 88: Análisis dimensional

<:I~MNEH QO

40.T52., 09:,/W9:2.,

#! 3= ?HGLM=GMA@A-HEMSF=GG!

>d F[Y|d_YW[ijWZ~ij_YWi[ _djheZkY[kdWdk[lW cW]d_jkZ' bWfheXW(X_b_ZWZH%gk[ j_[d[ Z_c[di_€d dkbWV gk[' feh jWdje' de Wbj[hW[b i_ij[cWZ_c[di_edWb)EWWbj[hWY_€di[ fheZkY[ YkWdZei[ [ijWXb[Y[bWYed[n_€dYed bWM[hceZ_d|c_YW feijkbWdZe gk[' [d jeZe i_ij[cW j}hc_YWc[dj[W_ibWZe'bW[djhef~WZ[ YWZW[ijWZe[i \kdY_€dkd_l[hiWbZ[ ik fheXWX_b_ZWZ)>ij[ feijkbWZe XWijWfWhWgk[ [b :d|b_i_i Z_c[di_edWbfh[l[W bW[n_ij[dY_WZ[ kdWdk[lW YedijWdj[ kd_l[hiWb'S%gk[ h[Y_X[[b decXh[ Z[ YedijWdj[Z[ ;ebjpcWdd #%$V gk[ [i d[Y[iWh_WfWhWgk[ bWh[bWY_€d

_ 3 S(" E# 3 S Bd E &AW S,',U

YkcfbWbWYedZ_Y_€dZ[ ^ece][d[_ZWZ)>d jeZe fheXb[cW Z[ F[Y|d_YW[ijWZ~ij_YWWXh|gk[ YedjWhYed bW

YedijWdj[ Z[ ;ebjpcWdd) :Z[c|i' Yece

GSI3 GAI3 :+;B&+,&* S,'-U

i[h|d fh[Y_iWiYkWjhecW]d_jkZ[i X|i_YWi)

#%$ MeZei bei Wkjeh[i bbWcWdWW YedijWdj[ Z[ ;ebjpcWdd' f[he IbWdYa[d ik WkjeX_e]hW\~W#-1$h[_l_dZ_YWfWhWi~[b^WX[heXj[d_Ze bWh[bWY_€dD 3 WXZH%V ^WX[hZ[ceijhWZe gk[ W [i bWYedijWdj[ Z[ bei ]Wi[i h[\[h_ZWWkdWceb}YkbW)L[]•d IbWdYa' ;ebjpcWdd' dkdYW_djheZk`e jWbYedijWdj[' d_ ckY^e c[deijhWj€Z[ Wl[h_]kWhik lWbeh)Ik[i' Z[ ^WX[hbe [Y^e' ^WXh~Wj[d_Ze gk[ YWbYkbWh[b d•c[he Z[ |jecei gk[ [n_ij[d [d kd fehY_€d Z[j[hc_dWZWZ[ cWj[h_W'jWh[Wgk[ Z[`€ Wik Yeb[]WEeiY^c_Zj' c_[djhWi }b' [d iki fhef_ei Y|bYkbei'i[ Wjklei_[cfh[ WbWfei_X_b_ZWZZ[ gk[ bWj[eh~WY_d}j_YWZ[ bei ]Wi[i de fWiWhWZ[ i[hkdW_cW][d c[Y|d_YWZ[ bWh[Wb_ZWZ)

,5T32929 /;2059K65,3! #$

Page 89: Análisis dimensional

&,- :GyEBLBL =BF>GLBHG:E

=[ WYk[hZeYeddk[ijhe i[]kdZe feijkbWZe' XMO[Z_`MZ`QPQ4[X`fYMZZQ_UZQXaPUNXQ%fk[ije gk[ bW[djhef~W o bWfheXWX_b_ZWZied _di[fWhWXb[i)

EWc[Z_ZWZ[ bWfheXWX_b_ZWZZ[f[dZ[ Z[ bWZ[\_d_Y_€dgk[ i[ WZefj[' o bW[nf[h_[dY_W W^[Y^e l[h gk[ [i fh[Y_ie fheY[Z[h Z[ Z_ij_dje ceZe i[]•d beiYWiei'o Z[ Wgk~gk[' WZ[c|i Z[ bW[ijWZ~ij_YWYb|i_YWZ[ ;ebjpcWdd' ^WoWd[djhWZe[d l_]eh bWidk[lWi [ijWZ~ij_YWiYk|dj_YWiZ[ ;ei[(>_dij[_d o Z[ ?[hc_(=_hWY)>d jeZe YWie'bWfheXWX_b_ZWZ[i kdWcW]d_jkZ Z[ Z_c[di_€d dkbW'feh begk[ [d YkWbgk_[hfheXb[cW Z[ F[Y|d_YW[ijWZ~ij_YW[d gk[ \_]kh[d cW]d_jkZ[ij[hceZ_d|c_YWi ^WXh|gk[ YedjWhYed bWYedijWdj[ Z[ ;ebjpcWdd o Wjh_Xk_hb[bW\€hckbWZ_c[di_edWbS,'-U) :Z[c|i' ik lWbehdkc}h_Ye ikXi_ij[ [d bWidk[lWi[ijWZ~ij_YWi'fk[ije gk[' feh \_]khWh[d S,',U [b be]Wh_jce Z[ bWfheXWX_b_ZWZ'kd YWcX_e[d bWc[Z_ZWZ[ H W\[YjWh|jWdi€be WbWYedijWdj[ WZ_j_lWD['

$! Ih~dY~f~e@AAJNDI=KMD?DXG!.HGLM=GMA@A, OHC=@KH!

EW Yed[n_€d [djh[ bWj[cf[hWjkhW V bWicW]d_jkZ[i c[YWcYWii[be]hW]hWY_WiWbfh_dY_f_eZ[ [gk_fWhj_Y_€dZ[ bW[d[h]~W' gk[ [ijWXb[Y[gk[' [d jeZe i_ij[cW [d [gk_b_Xh_e[ijWZ~ij_Ye'bW[d[h]~WYehh[ifedZ_[dj[WYWZW]hWZeZ[ b_X[hjWZlWb[' feh j}hc_de c[Z_e5

N 3 ) ))) SN'-

>i _dj[h[iWdj[ ^WY[hl[h gk[' i_ [n_ij[ kdWh[bWY_€d[djh[ bW[d[h]~WY_d}j_YWc[Z_WZ[ bWiceb}YkbWiV bWj[cf[hWjkhW' [b :d|b_i_i Z_c[di_edWbf[hc_j[ fh[l[h bWh[bWY_€dS-',U)

<ed bWicW]d_jkZ[i [' Y%[' S o b%i€be fk[Z[ \ehcWhi[ kd cedec_ef_' [d [b gk[ de \_]khWbWcWiWd_bWl[beY_ZWZc[Z_W)AWZ[ i[h' feh jWdje5

[5 3 2SN

o gk[ZWWi~Z[ceijhWZWbWfhefehY_edWb_ZWZ[djh[ bWj[cf[hWjkhW o bW[d[h]~WY_d}j_YWc[Z_W Z[ jhWibWY_€d)

IWhWbei cel_c_[djei Z[ hejWY_€d Wo gk[ h[[cfbWpWhbWcWiWfeh [b ce(c[dje Z[ _d[hY_W':%Yed be gk[ WfWh[Y[kd dk[le cedec_e f_ gk[ Yecfb_YWbWiebkY_€d5

o oWde i[ fk[Z[ W\_hcWhgk[ [n_ijWbWfhefehY_edWb_ZWZ[djh[ 1 o >)

S-', U

nl) F><yGB<: >LM:={LMB<: &,.

>b gk[ ckY^ei Wkjeh[i' Z[ WYk[hZeYed MebcWdo ;h_Z]cWd' ef_d[d gk[ bWj[cf[hWjkhW fk[Z[ j[d[h bWc_icW Z_c[di_€d gk[ bW[d[h]~WfheY[Z[ Z[ ikfed[hgk[ bWYedijWdj[ Z[ ;ebjpcWdd [i ikf[h\bkW' Yed be gk[ i[ fk[Z[ ^WY[hW 3 ,' RZ[ S-',U h[ kbjWS1U3 S>U)I[he ^[cei l_ije [d [b YWf~jkbefh[Y[Z[dj[ gk[ WbfheY[Z[h Wi~WfWh[Y[dcedec_ei f_ [ifkh_ei YkWdZei[ Wfb_YW[b :d|b_i_i Z_c[d(i_edWbWY_[hjeifheXb[cWi' o [bbeXWijWfWhWW\_hcWhgk[ bWYedijWdj[ Z[ ;ebjp(cWdd [i _d[bkZ_Xb[)

L\b]•d bWF[Y|d_YW[ijWZ~ij_YW'bei YedY[fjei Z[ [djhef~Wo Z[ fheXWX_b_ZWZi€be j_[d[d i[dj_Ze [d i_ij[cWi \ehcWZei feh ]hWdd•c[he Z[ [b[c[djei iec[j_ZeiWiki WYY_ed[ickjkWi' Z[ jWbceZe gk[ i[Wfei_Xb[ Wjh_Xk_hkdWfheXWX_b_ZWZ'H%WYWZW[ijWZe Z[b i_ij[cW YecfWj_Xb[Yed bWiYedZ_Y_ed[i[nj[h_eh[i' o bei fh_d(Y_f_ei \kdZWc[djWb[i feijkbWd gk[ ^W Z[ ^WX[hfhefehY_edWb_ZWZ[djh[ bW[d(jhef~Wo [b be]Wh_jce Z[ bWfheXWX_b_ZWZ'feh kdWfWhj[' o [djh[ bWj[cf[hWjkhWo bW[d[h]~Wc[Z_W Yehh[ifedZ_[dj[ WYWZW]hWZeZ[ b_X[hjWZ'feh ejhW)L[ jhWjWZ[ fWh[`Wi\ehcWZWifeh cW]d_jkZ[i' _di[fWhWXb[i'feh be gk[' [d l_hjkZ Z[dk[ijhe i[]kdZe feijkbWZe' [b \WYjehZ[ fhefehY_edWb_ZWZ^WZ[ i[h kdWYedi(jWdj[ kd_l[hiWb_d[bkZ_Xb[)

EWYedijWdj[ Z[ ;e,jpcWdd o bWYedijWdj[ Z[ bW]hWl_jWY_€dZ[i[cf[•Wd

fWf[b[i Wd|be]ei) <ed bW\€hckbW YS 3 G8YU i[ fk[Z[ [b_c_dWhZ[ jeZWi bWi\€hckbWi bWcWiW_d[hY_Wbe bW]hWl_jWjeh_W)=[b c_ice ceZe' bW[YkWY_€dS-',Ufk[Z[ i[hl_h fWhWfh[iY_dZ_hZ[ bWj[cf[hWjkhW j[hceZ_d|c_YW' 1' ikij_jko}d(ZebWfeh bWcW]d_jkZ ,O 3 S,' Ge ^Wo gk[ ebl_ZWh'Wb WY[h[ijW ikij_jkY_€d'

[

34

?

?B@) .) ( =_W]hWcWl[Yjeh_Wbgk[ ck[ijhW bWih[bWY_e(d[i [djh[ bWicW]d_jkZ[i Z[ bWF[Y|d_YW[ijWZ~ij_YWYed bWiZ[ bWF[Y|d_YWYb|i_YWo Yed bWj[cf[hWjkhW

gk[ bWdk[lW cW]d_jkZ' gk[ feZ[cei bbWcWhQY\Q^M`a^MOUZk`UOM%feh bbWcWh(bWZ[ Wb]•d ceZe' [i YeiWjejWbc[dj[ Z_ij_djWZ[ bWj[cf[hWjkhW i[di_Xb[) EWfh_c[hW' feh Z[\_d_Y_€d'WZ[ c[Z_hi[ ^WbbWdZebW[d[h]~Wc[Z_WZ[ YWZWfWhj~Yk(bW'Z_l_Z_[dZefeh [b d•c[he Z[ ]hWZeiZ[ b_X[hjWZ'o ckbj_fb_YWdZefeh -6 [i' fehjWdje' ^ece]}d[W Yed bW[d[h]~W)>d YWcX_e'bWcW]d_jkZ 1 [i bWj[cf[hWjkhWi[di_Xb[' bWgk[ i[ c_Z[ Yed bei j[hc€c[jhei o' i[]•d ^[cei ^[Y^e l[h Wdj[h_eh(c[dj[' ik \€hckbWZ_c[di_edWbde fk[Z[ i[h [ijWXb[Y_ZWWXWi[Z[ cW]d_jkZ[ic[Y|d_YWi)

Page 90: Análisis dimensional

,3+ :GyEBLBL =BF>GLBHG:E nl) F><yGB<: >LM:={LMB<: ,3,

EW\_]khW.' Yecfb[c[dje Z[ bW-' ck[ijhW bWih[bWY_ed[i[djh[ bWicW]d_jk(Z[i W o b[' gk[ ied bWifhef_Wi Z[ bWF[Y|d_YW[ijWZ~ij_YW'Yed bWicW]d_jkZ[iZ[ bWF[Y|d_YWYb|i_YWo Yed bWj[cf[hWjkhW' Yedi_Z[hWdZeYece l[Yjeh[i ikih[if[Yj_lWi Z_c[di_ed[i Z[ WYk[hZeYed bWj[eh~WZ[ K) LWdCkWd)L[ ^W_dYbk_ZeejhW YedijWdj[ kd_l[hiWb' [b d•c[he Z[ :le]WZhe' <1% gk[' Yece [i iWX_Ze'[ij| b_]WZeYed bWiejhWiZei YedijWdj[i' S o @%feh bW[YkWY_€d5

:Z[c|i Z[ 1' Z%D o bWYedijWdj[kd_l[hiWbS%_dj[hl[dZh| bWYecfh[(i_X_b_ZWZ'n) <ece Yed[ijWi cW]d_jkZ[i i€be fk[Z[ \ehcWhi[ [b cedec_eZ[ Z_c[di_€d dkbW

d.WMB, 3 (('

D

@0<''7'S h[ikbjW5

o YkoW\€hckbW Z_c[di_edWb #%$[i5

G<''7'I3 <(M)

, D" ($- V "IW.#BQ Z&Z &Yf ((((l( )

%! 3AR @A@DLMKD>N?DXG@A-HEMSF=GG!>d bW\€hckbWYecfb[jW [i5

r # nr[ $ r G nr[ )=WZe kd i_ij[cW Yedij_jk_Zefeh kd ]hWdd•c[he' <%Z[ i_ij[cWi[b[c[djWb[i [d [gk_b_Xh_e[ijWZ~ij_Yeo cWdj[d_Ze Wj[cf[hWjkhW Yedi(jWdj[' 1' Wl[h_]kWh[b d•c[he Z[ bei gk[ fei[[d [d[h]~WiYecfh[dZ_ZWi[djh[ [5 o [5& r[5) L[ ikfed[ gk[ [5 fk[Z[ lWh_WhZ[ ceZe Yedj_dke)

<ed bWicW]d_jkZ[i ZWZWii[ fk[Z[ Yedijhk_hkd cedec_e f_' MB3 [5*a1'o Zei \WYjeh[iZ[ \ehcW' #6$, 3 *O\(< o #6$-3 r[5*[5) >b i[]kdZe fk[Z[h[[cfbWpWhi[feh #6$. 8 r[5*a1) L[h|' fk[i5

'! 3AR @A@DLMKD>N?DXG@A4=QPAE2!

?[ &? #V[5 r$O20 Yf S,! S, '

=WZWkdW cWiW]Wi[eiW\ehcWZWfeh kd d•c[he cko ]hWdZ[' <%Z[ ceb}YkbWi_]kWb[i'Z[ cWiWY%Wl[h_]kWh[b d•c[he' P?%Z[ bWigk[ j_[(d[d l[beY_ZWZ[iYecfh[dZ_ZWi[djh[ Q o Q& PQ%YkWdZebWj[cf[hWjkhW[i 1) L[ ikfed[ gk[ bWiWYY_ed[i[djh[ bWiceb}YkbWiYedi_ij[d [nYbki_lW(c[dj[ [d Y^egk[i [b|ij_Yei)

<ed bWicW]d_jkZ[i c[dY_edWZWio bWYedijWdj[ Z[ ;ebjpcWdd i[fk[Z[d \ehcWhjh[i cedec_ei f_5EWiebkY_€dYecfb[jW' [d [b YWieZ[ kd ]Wif[h\[Yje' [i5

r[5

W.P?

MB ( VV e

*& < !PQ

MB- 3 ((1N

YO+

MBi 3((S,

>d kd i_ij[cW [d [gk_b_Xh_e[ijWZ~ij_Ye'cWdj[d_Ze Wj[cf[hWjkhWYedijWdj[' [b d•c[he Z[ fWhj~YkbWiYedj[d_ZWi[d Y_[hjelebkc[d' D%[i'feh j}hc_de c[Z_e V' yl[h_]kWh [b lWbehc[Z_e Z[ bW\bkYjkWY_€dYkWZh|(j_YWZ[\_d_ZWfeh5

o bWiebkY_€d[i Z[ [iYWiWkj_b_ZWZ'fk[i [d [bbW\_]khWkdW\kdY_€dZ[i(YedeY_ZWYedZei fWh|c[jhei)

&! 1EN?MN=?DHGALALM=@WLMD?=L!

L[ fk[Z[ fh[Y_iWhWb]ec|i bW_d\ehcWY_€dikc_d_ijhWZWfeh [b :d|b_i_i Z_(c[di_edWb j[d_[dZe fh[i[dj[ gk[' feh bW_iejhef~WZ[b [ifWY_eo bWWki[dY_WZ[\k[hpWi [nj[h_eh[i' i_ i[ h[fh[i[djWd bWil[beY_ZWZ[iZ[ bWiceb}YkbWifeh i[dZeil[Yjeh[i jhWpWZeiZ[iZ[ kd fkdje YkWbgk_[hW'[b lWbehZ[ ZG i[h| _]kWbWbd•c[(he Z[ l[Yjeh[i Ykoei [njh[cei gk[ZWd [djh[ Zei [i\[hWi Z[ hWZ_ei[ o [ & Z[' ei[W [d kd lebkc[d /,j[-Z[) >ije fed[ Z[ cWd_\_[ije gk[ [b [b[c[dje Z[ Z[X[\_]khWhckbj_fb_YWZefeh Q+%YeiWgk[ i[ be]hWikij_jko[dZe ,j- feh

#%$ FkY^ei \~i_YeiYh[[d [hh€d[Wc[dj[ gk[ [b d•c[he Z[ :le]WZhe j_[d[Z_c[di_€d dkbW'fehgk[ i[ eXj_[d[ YedjWdZe[b d•c[he Z[ ceb}YkbW(igk[ ^Wo[d kd ceb) I[he ebl_ZWdgk[ [b ceb Z[f[dZ[ Z[ bWkd_ZWZZ[ cWiW'feh be gk[kd ceb(a]' feh [`[cfbe' lWb[ ,+++ ceb(])

Page 91: Análisis dimensional

,3- :GyEBLBL =BF>GLBHG:E nl) F><yGB<: >LM:={LMB<: ,3.

o fk[Z[ W\_hcWhi[gk[

P? 3 ? " 0 \- N+^ " r- $Z[)

EW\€hckbWYecfb[jW [i5

)! <DL?HLD@=@@AEHL]Wi[i)

# $

.*- #-? U UL+

P? 8 'J) (( [- [nf ( (($ Z[)G QQ +W/ +W/

EWj[eh~WY_d}j_YW[nfb_YWbWl_iYei_ZWZZ[ bei ]Wi[i Yece kd jhWdi(fehj[ Z[ ~cf[jk [djh[ Y^egk[ o Y^egk[) >i kd \[d€c[de fkhWc[dj[c[Y|d_Ye' gk[ i[ fheZkY[ Wkdgk[de ^WoWZ_\[h[dY_WiZ[ j[cf[hWjkhW o'[d Yedi[Yk[dY_W'fWhWWfb_YWh[b :d|b_i_i Z_c[di_edWbXWijWh|kdWXWi[Z[ jh[i' gk[ fk[Z[d i[h =%>% E' EWicW]d_jkZ[i WYedi_Z[hWhied5 bWcWiW'Y%Z[ bWiceb}YkbWi6[b d•c[he' GB9 Z[ bWiYedj[d_ZWi[d bWkd_ZWZZ[ lebkc[d6 ik l[beY_ZWZc[Z_W' Q%o [b h[Yehh_Zeb_Xh[c[Z_e) A[ Wgk~[b fbWdj[Wc_[djeo bWiebkY_€d5

AWbbWhbWh[bWY_€dgk[ b_]WbWfh[i_€d' X%Z[ kd ]Wi f[h\[Yje Yed [bd•c[he' <7! Z[ ceb}YkbWiYedj[d_ZWi[d bWkd_ZWZZ[ lebkc[d' Yed bWcWiW'Y%Z[ YWZWkdW'o Yed bW[d[h]~WY_d}j_YWc[Z_W' >' feh ]hWZeZ[b_X[hjWZ)L[ WZc_j[ gk[ bWiZ_c[di_ed[i b_d[Wb[iZ[ bWiceb}YkbWiiedcko f[gk[•Wi [d YecfWhWY_€dYed [b h[Yehh_Zeb_Xh[c[Z_e)

>d [ij[ fheXb[cW_dj[hl_[d[d cW]d_jkZ[i c[Y|d_YWi[nYbki_lWc[dj['feh be gk[ XWijWdjh[i cW]d_jkZ[i X|i_YWi':%;% B%R bWiebkY_€d[i5

#C) Y GB [ 5

: " & e "( & &> , & e e eE (, e e "& e

2jB , (, "& "& (,

2j- e e &$( e &

"8' 3 Y?XQ3h53?X(,#'

(! 7KALDXG@ANG=F=L= ]Wi[eiW)

L_de i[ jhWjWZ[ ]Wi[i kbjhW[dhWh[Y_Zei'eYkhh[gk[ 5 2 2 *(?X*(,%

feh begk[' Yed]hWdWfhen_cWY_€d'fk[Z[ Wjh_Xk_hi[Wr [blWbehH 3 ^"W#.

"8' 3 @Y?XO3'L[ fk[Z[ ^WY[h_dj[hl[d_h bWj[cf[hWjkhW h[Ykhh_[dZeWbfh_dY_f_eZ[[gk_fWhj_Y_€d5

<ece Y?X 8 f' h[ikbjW5

o2hW/' !

"8' 3 >O75) S2',U

EWj[eh~WYecfb[jW ZW+8 ,*.)Yed be gk[ h[ikbjW5

?=M3((Y

D!

*! .HG@N?MDOD@=@MVKFD?=@AEHL]Wi[i

EWYedZkYY_€dZ[b YWbeh[d bei ]Wi[i i[ Z[X[ WbjhWdifehj[ Z[ [d[h]~WY_d}j_YW[\[YjkWZefeh bWiceb}YkbWi'feh be gk[ Yedij_jk_h~Wkd fheXb[cWc[Y|d_Ye Wde i[h fehgk[ bWcW]d_jkZ WYWbYkbWh[i kdWcW]d_jkZ j}h(c_YW)AWXh|'fk[i' gk[ W]h[]WhbWYedijWdj[Z[ ;ebjpcWdd WbWb_ijWZ[bWicW]d_jkZ[i gk[ \_]khWd[d [bfheXb[cWWdj[h_eh'V i[h|d fh[Y_iWiYkWjhecW]d_jkZ[i X|i_YWi'feh [`[cfbe' =%>%E%3) >d [ijW XWi['bW\€hckbWZ_c[di_edWbZ[ bWYedZkYj_l_ZWZj}hc_YW[i5

V Yece' i_ ? [i [b d•c[he jejWbZ[ ceb}YkbWi'G [b lebkc[d' ?3 bWYedi(jWdj[ Z[ : le]WZheV V [bd•c[he Z[ ceb[i' i[ Ykcfb[ gk[5

gk[ZW[d Z[\_d_j_lW5

e X_[d5 J<K 3 =>E&,R;&X

XD 8 =!V@-' o [b :d|b_i_i Z_c[di_edWbYedZkY[WbW[nfh[i_€d

< 3 ?1k13'Wh"3?X(,#%

Page 92: Análisis dimensional

,3/ :GyEBLBL =BF>GLBHG:E

gk[' fWhWlWbeh[i de [nY[i_lWc[dj[ f[gk[•ei Z[ bWZ[di_ZWZ'i[ Yed(l_[hj[ [d5

S3',U

=[ bWYecfWhWY_€dZ[ S2',U o S3',U h[ikbjW5

":<* 3 Yedij'fD

lGe i[W VV ,G 8 Yedij'9

gk[ [ij| Z[ WYk[hZeYed [b h[ikbjWZe WbbWZe[d [b t ,,' YWf~jkbeQBO'fk[i Q! [i fhefehY_edWbW< TT'

+! /AGLD@=@@AFH@AK=?DXG@AEHLGANMKHGAL!

>d bWj[eh~W[b[c[djWb Z[ bei h[WYjeh[ii[ fh[i[djW [b fheXb[cW Z[Wl[h_]kWh[b d•c[he Z[ d[kjhed[i' Z"7#P7% gk[ [d YWZWkd_ZWZZ[lebkc[d fei[[d [d[h]~WiYecfh[dZ_ZWi[djh[ 7 o 7 &P7' >ijW cW](d_jkZ Z[f[dZ[h| Z[ bWii_]k_[dj[i lWh_WXb[i5

,)v EWbbWcWZWPQZ_UPMPPQY[PQ^MOUmZ%]"7# "_X[cUZSP[cZ PQZ_U`e#%gk[ [i [b d•c[he Z[ d[kjhed[i gk[' [d YWZWkd_ZWZZ[ lebkc[d' WjhWl_[(iWdYWZWkd_ZWZZ[ j_[cfe [b d_l[b Z[ [d[h]~W3'

-)v =[ bW[d[h]~WYedi_Z[hWZW'3'.)v =[ bWcWiW'Y%Z[b d[kjh€d) >ijW cW]d_jkZ fk[Z[ ikij_jk_hi[

feh bWl[beY_ZWZ] 3 G+7GU%fk[i 7 \_]khWoW[d bWb_ijW)/)v =[ bWdWjkhWb[pWZ[b ceZ[hWZeh'Z[b YkWbi€be _dj[h[iW[b \[PQ^

Y[PQ^MP[^ P0'gk[ h[fh[i[djW bWf}hZ_ZWbe]Wh~jc_YWc[Z_W Z[ [d[h]~Wfeh kd_ZWZZ[ YWc_de)

<ece fk[Z[ l[hi[ [d YkWbgk_[hWZ[ bei ckY^ei b_Xheigk[ jhWjWdZ[[ijW Yk[ij_€d' bWiebkY_€di[ be]hWjhWiZ[ hWpedWc_[djeiWbWcX_YWZeioY|bYkbeidWZWi[dY_bbei)?[hc_ _dZ_Y€kd c[Z_e \|Y_b'f[he i[ b[ ^WY[bWeX`[Y_€dZ[ i[h feYe h_]kheie) OWcei Wl[h gk[ [b :d|b_i_i Z_c[di_edWb`kij_\_YW[b c}jeZe Zr ?[hc_)

<ece ck[ijhW [b i_]k_[dj[ YkWZhe5

& #! b ' #! # 8/1'= "* , "( - ( ,> ( , H H , HB - ( , (, (- H

&!05 , , (, , ,&!0p H , (, H .

QO) F><y B<: >LM:={LMb<: ,30

[b :d|b_i_i Z_c[di_edWbYedZkY[W

"G*1-=/- #'V"3# 3 Y"3#

b7*1= hf Y"3#3

>i [l_Z[dj[ gk[' W_]kWbZWZZ[ ejhWiY_hYkdijWdY_Wi'V"3# ^WZ[ i[hfhefehY_edWbWY"3# o Yece [ijW lWh_WXb[_dj[hl_[d[ [d [b Wh]kc[djeZ[ hf' [i fh[Y_ie gk[ [ijW \kdY_€dZ[][d[h[ [d kd d•c[he \_`e' 5' Ieh

jWdje5

V"3# 8 5Y"3# 'b7*1=

3

IWhWWbbWh[b d•c[he < XWijWh|Yedi_Z[hWhkd YWiei[dY_bbe'be gk[ `ki(j_\_YW[b ikfed[h' Yece ^WY[?[hc_' gk[ bWf}hZ_ZWbe]Wh~jc_YWZ[ [d[h]~W[d YWZWY^egk[' ,63 ( *$)Bd3%[i _d\_d_jWc[dj[f[gk[•W' Yedbe gk[ i[

eXj_[d[ \|Y_bc[dj[ [b lWbeh8 3 ,)

Page 93: Análisis dimensional

I_J . <&9=D&+%

=;J€NOFI RPC

9+.3+-3S6 ;R953-+ = 5/-Q63-+ -<+6;3:;+

$" 6A?ALC@>@@ANG> GNAO>?HGLM>GMANGCOAKL>E"

>]em]kljY dY]ph]ja]f[aY im] ]f lg\Y [Yna\Y\ eYfl]fa\Y Y l]e)h]jYlmjY[gfklYfl]' [gf lYd\] im] [gfl]f_Y mfYhYjl€[mdY\] mf [m]jhgf]_jg' ]klg ]k' \] mf [m]jhg [YhYr \] YZkgjZ]jq ]ealaj jY\aY[agf]k \]lg\Yk dYk j][m]f[aYk' k] ]klYZd][] mf ]klY\g \] ]imadaZjag]f ]d im] dY\]fka\Y\ \] ]f]j_€Y q dY[gehgka[a‚f ]kh][ljYd \] dYjY\aY[a‚f kgf af\])h]f\a]fl]k \]d lYeY•g q ^gjeY \] dY[Yna\Y\ q \] dYfYlmjYd]rY\] kmkhYj]\]k* =geg dYhYjl€[mdYYZkgjZ]fl] gZjYk‚dgYeYf]jY \] [YlYdarY\gjim] hjgng[Y ]d hYkgYd]klY\g \] ]imadaZjage~k ]klYZd]'j]kmdlYim] fg`Yq e~k nYjaYZd]af\]h]f\a]fl] im] dYl]eh]jYlmjY' hgj dg im] [mYd)ima]j gljY eY_falm\' q ]f hYjla[mdYjdY\]fka\Y\ \] ]f]j_€Y' `YZj~ \]k]j ^mf[a‚f \] \a[`Y nYjaYZd]#%$*

Ma_ ]k dY\]fka\Y\ \] ]f]j_€Y' [geg

k] n] afe]\aYlYe]fl] im] ]k aehgkaZd]gZl]f]j mf egfgeag \] \ae]f[a‚ffmdY]f im] fg afl]jn]f_Yf e~k im] ` q ]' hgj dgim] ]d ;f~dakak\ae]fkag)

#%$ L]^a]j] JdYf[c ]f kmYmlgZag_jY^€Y#.3$ im]' hYjY dg_jYj im] dYeY_fa)lm\ F% im] ^a_mjY]f dY^‚jemdY C . V Cf F% hm\a]k] k]j afl]jhj]lY\Y [gegmfYhjgZYZada\Y\' lmng f][]ka\Y\ \] afljg\m[aj mfYfm]nY [gfklYfl] mfan]jkYdS%im]' hgj l]f]j dYeakeY \ae]fka‚f im] dYY[[a‚f #]f]j_€Y > la]ehg$' \]fgeaf‚&N`LY_ZPWPXPY_LWOPLNNTnY'

Hg ]k ^~[ad`Y[]j [gfb]lmjYk Y[]j[Y \]d jYrgfYea]flg e]\aYfl] ]d [mYd'hgj[gfka\]jY[agf]k \ae]fkagfYd]k' dd]_‚ JdYf[c Y kmeYjYnaddgkg\]k[mZjaea]flg' q\]Z] j]hmlYjk] [geg gZjY \] mf _]fag* =gf fm]kljg k]_mf\g hgklmdY\gP [gf dY`ah‚l]kak \] dgk^glgf]k dY[gkY j]kmdlYgZnaY*

Page 94: Análisis dimensional

&** ;HzFCMCM >CG? !MCIH;F RPC* L;>C;=C} N{tdC=; P G?=z C=; =O;HNCMN; &*+

fYd]pa_] im] ]f \a[`Y ^mf[a‚f ]kl• hj]k]fl] mfY[gfklYfl] mfan]jkYd*Ha dY*n]dg[a\Y\ \] dYdmrfa dY[gfklYfl] \] dgk_Yk]kkajn]f hYjY]d [Ykg'hm]k*]f km^‚jemdY\ae]fkagfYd fg ^a_mjYdYeYkY*;_glY\gk [gf ]klg dgkj][mj)kgk\] dYN]jeg\af~ea[Y' [YZ] dY]kh]jYfrY \] im] k] j]km]dnYdY\a^a[md)lY\ [gf Yqm\Y\] dYG][~fa[Y ]klY\€kla[Y*

JYjY Yhda[Yjdgke•lg\gk ]klY\€kla[gkYdYjY\aY[a‚f l•jea[Y' aeY_af‚:JdYf[c mf kakl]eY \] j]kgfY\gj]k daf]Yd]k]f ]imadaZjag[gf dYeakeY*>] ]kl] eg\g' k] gh]jYZY[gf _jYf fƒe]jg \] ]d]e]flgk ]flj] dgk[mYd]k*]jYf hgkaZd]kdYkljYfk^]j]f[aYk \] ]f]j_€Y' [gf\a[a‚f af\akh]fkYZd] hYjY*hg\]j Yhda[Yj\a[`gk e•lg\gk* =gf ]kl] Yjla^a[agdg_j‚ JdYf[c kmhjgh‚)kalg' h]jg Y`gjYqYfg ]k f][]kYjaYdYafljg\m[[a‚f \] ]d]e]flgk ]pljY•gk'*hgjim] k] kYZ]im] dYjY\aY[a‚f ]kl~ [gfklalma\Y hgj hYjl€[mdYk\] dmrg)^glgf]k' im] ^gjeYj~f mfY [gd][lana\Y\ ]klY\€kla[Yka k] `Y[] hgkaZd]d] ljYfk^]j]f[aY \] ]f]j_€Y ]flj] dgk eakegk* {kl] ]k' hj][akYe]fl]' ]ddhYh]d\] dYhYjl€[mdY\] [m]jhg f]_jg im] `Yq im] [gdg[Yj ]f dY[Yna\Y\'[mYf\g kmkhYj]\]k kgf h]j^][lYe]fl] j]^d][lgjYk' hYjYYk]_mjYj]d ]ima)daZjag]klY\€kla[g*

?f G][~fa[Y ]klY\€kla[Y\akhgf]egk \] dY[gfklYfl] \] <gdlreYff'*q hjg[]\] ]fkYqYj ka[gf dYkeY_falm\]k `%]' ] q V k] hm]\] ^gjeYj mfegfgeag ha* J]jg g[mjj] im] dYk][mY[agf]k im] k] gZla]f]f YdhdYf)l]Yj ]d hjgZd]eY kgf af[gehYlaZd]k' hm]k dY[YjY[l]j€kla[Y\] dYeYljar7^gjeY\Y [gf dgk ]phgf]fl]k \ae]fkagfYd]k6

?f dYhjae]jY ]\a[a‚f \] ]kl] daZjg\~ZYegk hgj kmhm]klgim] ]klYk"=gfka\]jY[agf]k ZYklYZYfhYjY ]k[jaZaj' ]f najlm\ \] fm]kljg k]_mf\g)hgklmdY\g6

]6 . cn'

)h]jg ]d hjg^]kgj N]‚^adgCkfYj\a fgk `Y `][`g fglYj' emq YlafY\Ye]fl]')im] hgj a_mYdjYr‚f k] hg\€Y `Y[]j6

)\gf\] c ]k mf fƒe]jg jY[agfYd[mYdima]jY'hgkalangg f]_Ylang*Jgj lYflg'*k‚dgk] hm]\] Y^ajeYjim] dY ‚jemdY \ae]fkagfYd \] V \]Z] k]j6

IVJ . <+=D&+$c%

)]f dYim] b ]k mf fƒe]jg jY[agfYdaf\]l]jeafY\g*

?k ]na\]fl] im] ]d ;f~dakak \ae]fkagfYd' hgj k€kgdg' fY\Y hm]\] \][ajfgk j]k)h][lg \]d nYdgj \] c' J]jg' ]f em[`Yk g[Ykagf]k' ZYklYmf [gfg[aea]flg ]d])e]flYd \] dYhYjl] ^€ka[Y\]d hjgZd]eY im] k] YZgj\Y hYjYdd]_YjYj]kmdlY\gk im]hj][akYf e~k dYkgdm[a‚f*PYegk Y \]egkljYj im]' ]f fm]kljg [Ykg' ZYklYl]f]j

)]f [m]flY dYd]q \] Qa]f6

` V ] ]

< %( ' I (= ( ( I ID "' "' I %(] I %( ( I

]% . [gfkl'-1

nYd]0' im] ]k bmklYe]fl] ]d fƒe]jg \] eY_falm\]k* Jgj lYflg' PW2Yk&WT^TOTXPY^TZYLW[P]XT_PLQT]XL]\`P PY WL_PZ]mLOPWL]LOTLNTnYSL OPTY&_P]aPYT]YL Y`PaL NZY^_LY_PYTaP]^LW'

hYjY hg\]j Y^ajeYj im] `Y \] k]j' hj][akYe]fl]' c . -*L]hj]k]flYf\g hgj mn\n dY]f]j_€Y [gjj]khgf\a]fl] Ydafl]jnYdg ]kh][ljYd \n'

\]Z]j~ `YZ]j mfY j]dY[a‚f ]flj] mN$ a%] q dYk[gfklYfl]k mfan]jkYd]k V%] q S'JYjY ^Y[adalYjdgk[~d[mdgkl]f\j]egk hj]k]fl] im]' hgj ljYlYjk] \] mf hjgZd]eY)\] G][~fa[Y ]klY\€kla[Y' dYkeY_falm\]k V q ] `Yf \] ^a_mjYj^gjeYf\g ]d eg)fgeag c]* ?f ]d ka_ma]fl] [mY\jg k] af\a[Y ]d eg\g \] hdYfl]Yj q j]kgdn]j ]d

hjgZd]eY \ae]fkagfYd6

%" 4> ?HGLM>GMA@A8E>G?D"

` N c] ] S

< ) - I ' - '= - I - I -D ) - ) - "' % ( #$"+

&20 - #$#+' / % (&2' I G ) - I -

M]_ƒf fm]kljg k]_mf\g hgklmdY\g'hYjYim] mfY [gfklYfl] mfan]jkYdk]Yaf\akh]fkYZd]]k hj][akg im] ^a_mj]]f dYj]dY[a‚f im] da_YdYke]\a\Yk*\] \gk eY_falm\]k afk]hYjYZd]k*?f dgk^glgf]k' k‚dg [YZ] [gfka\]jYj \gkeY_falm\]k nYjaYZd]k'dY]f]j_€Y' ]' q dY^j][m]f[aY' a%hm]k dYn]dg[a\Y\[gf im] k] em]n]f ]f ]d nY[€g]k [geƒf Y lg\gk ]ddgk'[Yj][]f \] eYkY*]f j]hgkg' q km[Yj_Y]k fmdY*

q j]kmdlYf \gk egfgeagk ha6

/3! &2' . VA"

Page 95: Análisis dimensional

-5, ;HzFCMCM >CG?HMCIH;F RPC* L;>C;=C}H N{LGC=; S G?=zHC=; =O;HNCMN; -5-

hgj dg im] `YZj~*\] k]j6 ?d ^dmbghgj mfa\Y\ \] kmh]j^a[a]q hgj mfa\Y\ \] la]ehg nYd]6

\gf\] 9]k mfY ^mf[a‚f af\]l]jeafY\Y* P]Yegk Y`gjY kadYhj][]\]fl] ][mY[a‚f]kl~ \] Y[m]j\g [gf dYd]q \] Qa]f* ; ]kl] ^af' `Ydd]egk ]d nYdgjne hYjY]d [mYdY\ima]j] <N kmnYdgje~paeg* >]Z]j~ k]j6

!) & p$n6!&r9# S00 # & nt&r ^" # Sg/X # S @%R I&&ca_Y. $V/

\gf\] [j . 4V-:-N+V, ]k dY[gfklYfl] \] Ml]^Yf*FY l]gj€Y [gehd]lY \Y#n•Yk]'hgj ]b]ehdg' D*JYdY[agk'02' h~_* //.$'

[j 9 .3l dQ]p$ e,Oeef PH & -g

. 1'23.*-,)1 _ M)/ ,=)0*

g k]Y6

!) # b$* # Sa X # # \ # SFIX# SaeX b . 9

V/ V/ c4 " 0* ?[mY[a‚f \] dgj\ LYqd]a_`*

\] dYim]' \]kh]bYf\g `GX:/ k] \]\m[]6

=@H)2) . [gfkl'

FY G][~fa[Y ]klY\€kla[Y\] <gdlreYff' im] `YZ€Ydg_jY\g _jYf\]k•palgk Ydk]j Yhda[Y\YY dgk_Yk]k' ^jY[Yk‚lglYde]fl] [mYf\g k] ljYl‚\] gZl]f]j [gf kmYmpadagdY\akljaZm[a‚f \] dY]f]j_€Y ]f ]d ]kh][ljg \]dYjY\aY[a‚f f]_jY* L]hj]k]flYf\g hgj mn\n dY\]fka\Y\ \] ]f]j_€Y [g)jj]khgf\a]fl] Ydafl]jnYdg ]kh][ljYd \n' \]Z]j~ `YZ]j mfYj]dY[a‚f ]flj]_a! !*%2' V S [* ?d ;f~dakak \ae]fkagfYd #%$[gf\m[] afe]\aYlYe]fl] Y

q ZYklY[gehYjYj [gf dYd]q \] Qa]f hYjY \]\m[aj im] `Y \] k]j c . -*

?f j]kme]f6 kak] Y\eal] im] dYjY\aY[a‚f ]kl~ ^gjeY\Y hgj ^glgf]k' im] km:]klY\g \] ]imadaZjag\]h]f\] lYf k‚dg \] dYl]eh]jYlmjY q im] km]klm\ag hm]\])]^][lmYjk] hgj e•lg\gk ]klY\€kla[gk' ]d ;f~dakak \ae]fkagfYd h]jeal] Y^ajeYjim]' Y\]e~k \] dYk[gfklYfl]k mfan]jkYd]k] q V% Y \] afl]jn]faj gljY' S%qfm]kljg k]_mf\g hgklmdY\g [gf\m[] Y dY^‚jemdY \ae]fkagfYd

im]' [gf 4 . 43l' [gaf[a\] [gf dY^‚jemdY`YddY\Yhgj dgj\ LYqd]a_` qD]Yfk'dY[mYd'[geg ]k kYZa\g']k lglYde]fl] afY[]hlYZd]*FY \a^a[mdlY\k‚dghm\g k]j j]km]dlY[gf Ympadag\]d [mYflg \] Y[[a‚f \] JdYf[c' [gegn]j]egk ]f ]d YhYjlY\g im] ka_m]*

;\]e~k' hYjY im] k] [mehdY dYd]q \] Qa]f `Y \] k]j c . -*

?d _jYf e•jalg \] JdYf[c [gfkakl] ]f `YZ]j dg_jY\g' hgj [gfka\]jY[agfYk\ae]fkagfYd]k' dd]_YjY dY[gf[dmka‚f \] im] \]Z€Y ]paklaj lYd[gfklYfl]' q `YddYjkm ^‚jemdY \ae]fkagfYd kaf `Y[]j mkg' fa \] dY`ah‚l]kak \] dgk ^glgf]k fa \]$j]^]ja\g hgklmdY\g*

1* F]q \] Qa]f q ][mY[a‚f \] JdYf[c*

;Zgj\]egk ]d hjgZd]eY \]d YhYjlY\gYfl]jagj lgeYf\g ]f [gfka\]jY)[a‚f dY[gfklYfl] \] JdYf[c' V' L]kmdlYfYk€\gk egfgeagk ha6

/* F]q \] Ml]^Yf*

AjY[aYkY dYfm]nY [gfklYfl]' V%j]kmdlYqY naYZd]]d hjgZd]eY \]`YddYjdY^mf[a‚f im] |a_YdY\]fka\Y\ \] ]f]j_€Y [gf dYl]eh]jYlmjY*YZkgdmlY'hm]k[gf dYkeY_falm\]k `%[* V%V q 2 hm]\] ^gjeYjk] mf egfg)eag ha6

3la .cn

3l )+&DP!

#%$ SY Bgh^ !+*" ljYl‚ \] `YddYjdY ‚jemdY \] LYqd]a_` hgj [gfka\]jY[agf]k\ae]fk€gfYd]k' h]jg af[mjja‚ ]f ]d ]jjgj \] `Y[]j dYl]eh]jYlmjY `geg_•f]Y [gfdY]f]j_€Y' [gf dg im] gZlmng6

N.2* On . [gfkl ))'

[.

q `YZj~ \] k]j6

U/'-W]f dYim] dY[gfklYfl] fg ]k mf fƒe]jg ^abg'kafg mfY [gfklYfl] \ae]fkagfY\Y*

Page 96: Análisis dimensional

-5. ;HzFCMCM >CG?HMCIH;F

g Za]f6`n

3l ))). ) VC!

P dYkgdm[a‚f ]k6

% & g _ #`P$<N% %% S]/ cM

U1'-W

>] ]klY ^‚jemdY k] \]\m[] afe]\aYlYe]fl] dYd]q \] Qa]f #%$'k]_ƒfdY[mYd'ka 2X ]k dYdgf_alm\ \] gf\Y Y dYim] [gjj]khgf\] dYe~paeY]f]j_€Y' `Y \] k]j6

2X? 9 [gfkl 9 M'

=geg ]d egfgeag

! .! - . !-!. )

la]f] lYeZa•f \ae]fka‚f fmdY'dY]phj]ka‚f U1'-Whm]\] lgeYj dY^gjeY6

dg im] j]n]dY im] On+M/ ]k ^mf[a‚f mfan]jkYd\] M+n* Jgj lYflg' ]d nYdgj\] M+n . ;M+]' im] `Y[] e~paeY dY\]fka\Y\ \] ]f]j_€Y On hYjY [Y\YnYdgj \] M YZj~ \] k]j mfY[gfklYfl] mfan]jkYd'im] ]k dYd]q \] Qa]f #%$*

;eM 9 [gfkl 9 M% U1'.W

FY kgdm[a‚f [gehd]lY \]d hjgZd]eY ^m]dg_jY\Yhgj JdYf[c _jY[aYkYkm `ah‚l]kak \] dgk [mYflgk' q ]k6

43l` n/

<N.%%]/ ]ph #`n+cM$) -

im] ]kl~ \] Y[m]j\g [gf U1'-Wq \Y hYjY dY[gfklYfl] \] dYd]q \] Qa]f)]dnYdgj

M9 C( SPr V"

* #%$*JYjY dY\]\m[[a‚f \] dYkd]q]k \] Ml]^Yf q \] Qa]f hgj [gfka\]jY[agf]k)\ajf]fkagfYd]k [gf Ympadag\]d [mYflg \] Y[[a‚f' n•Yk] ]d Yjla[mdg\] Lmf_] #22$*

RPC* L;>C;=C}H N{LGC=; S G?=zHC=; =O;HNCMN; -5/

\gf\] e ]kl~ \Y\g hgj dY][mY[a‚f #%$6

1#- ) P&e#9 e'

AjY[aYkY fm]kljg k]_mf\g hgklmdY\g' q ZYk~f\gfgk ]f dY]pakl]f[aY\] dgk^glgf]k' `]egk dg_jY\g hj]\][aj dY]pakl]f[aY \] dY[gfklYfl] \]JdYf[c q' [gf kmYmpadag'`]egk \]\m[a\g dYkd]q]k \] Ml]^Yfq \] Qa]f[gf kmkj]kh][lanYk [gfklYfl]k' kYdngk]f\gk ^Y[lgj]k fme•ja[gk*

FY jY\aY[a‚f l•jea[Y kajna‚ Y MljYf]g #23$ \] ]b]ehdg hYjY hgf]j Y hjm]ZYmf e•lg\g ZYkY\g ]f mf kmhm]klg naf[mdg im] `Y \] ]paklaj ]flj] dYk\an]jkYk[gfklYfl]k mfan]jkYd]k \] mfY l]gj€Y* >Y hgj kmhm]klg im] ]f dYjY\aY[a‚f k]j]ima]j]f [mYljg eY_falm\]k Z~ka[YklYd]k[geg <%=%D%2' q im] `Yf \] afl]j)n]faj dYk[gfklYfl]k mfan]jkYd]k]' S q V%lg\g dg [mYd]k [gjj][lg' q ZYklY'k]_ƒf`]egk naklg' hYjY dg_jYj ]d j]kmdlY\g Yh]l][a\g* J]jg Y\eal] dm]_g' kaf bmkla^a)

[Y[a‚f' im] `Y \] ]paklaj mfY j]dY[a‚f'

_ . *#/%?$%

\gf\] I ]k mfY [gfklYfl] mfan]jkYdnaf[mdY\Y =ICd ]' S q V' =gf ]klYk daealY[ag)f]k hj]naYk [gfka_m] \]\m[aj lYf k‚dg dYd]q \] Ml]^Yf' h]jg fg dYeYf]jY \]gZl]f]j I YhYjlaj \] ]' S q V' ?klg em]kljY im] ]d e•lg\g \] MljYf]g fg Y_j]_YfY\Y fm]ng Yd;f~dakak \ae]fkagfYd* ;fl]k Za]f7 k‚dg ]k Yhda[YZd]]f [Ykgkemq]kh][aYd]k q' Ymf ]flgf[]k' kmeafakljY e]fgk af^gjeY[a‚f im] dYim] k] dg_jY

Yhda[Yf\g ]d l]gj]eY \] ha*?f mf Yjl€[mdg YhYj][a\g j][a]fl]e]fl]' ljYlY \] hjgZYj ]d hjg^]kgj ?h)

kl]af #24$im]' mfY n]r ]klYZd][a\Y dYd]q \] Qa]f' ]d ;f~dakak \ae]fkagfYd h]jeal]hj]n]j dY]pakl]f[aY \] dY[gfklYfl] \] JdYf[c* ?f j]Yda\Y\' dg im] \]em]kljY]k im] la]f] im] `YZ]j mfY [gfklYfl] mfan]jkYdim] fg hm]\] gZl]f]jk] e]\aYf)l] mfY ]phj]ka‚f egfgeaY ^gjeY\Y [gf dYk[gfklYfl]k ] q V' J]jg \] ]ddgfg k]\]\m[] im] lYd [gfklYfl] l]f_Y f][]kYjaYe]fl] dY eakeY \ae]fka‚f im] dY

[gfklYfl] \] JdYf[c*

(" 8KALCVG@AK>@C>?CVG"

=geg ]f dYjY\aY[a‚f l•jea[Y fg `Yq e~k nYjaYZd]af\]h]f\a]fl] im]dYl]eh]jYlmjY' dYhj]ka‚f \]Z]j~ k]j ^mf[a‚f \] M' q hg\j~f ^a_mjYjdYk[gfklYfl]k ]' S q V' =gf dYkeY_falm\]k [alY\Ykk‚dg hm]\] ^gjeYjk]mf egfgeag ha' q dYkgdm[a‚f ]k6

#%$ P•Yk]' hgj ]b]ehdg' ]d daZjg\]d Ymlgj #02$'h~_* //-*

;HzFCMCM >Oj?HMCIH;F* ) -4

Page 97: Análisis dimensional

JYjY dgk ^af]k \] dYG][~fa[Y ]klY\€kla[Y[d~ka[Y'mf _Yk h]j^][lgim]\Y \]^afa\g hgj dYeYkY' X%\] [Y\Y mfY \] kmkegd•[mdYk*Jgj gljYhYjl]' dY]pakl]f[aY \] dY[gfklYfl] im€ea[Yk] hj]\a[] e]\aYfl] ]d l]j[]jhjaf[ahag \] N]jeg\af~ea[Y' g l]gj]eY \] H]jfkl' im] ]imanYd]Yhgklm)dYjdY]pakl]f[aY \] mf \geafag ^afalg\] a_mYdhjgZYZada\Y\]f ]d ]khY[ag^~ka[g' \geafag [mqYk\ae]fkagf]k ]kl~f j]dY[agfY\Yk[gf ]d [mYflg \]Y[[a‚f \] JdYf[c* >] Yim€j]kmdlYim] dY[gfklYfl] im€ea[Y' ;% `Y \]\]h]f\]j \] X%Vq S' L][gj\Yf\g dY ‚jemdY\ae]fkagfYd \] dY[gfklYfl]im€ea[Y \Y\Y ]f ]d v 0 \]d [Yh€lmdgPC' j]kmdlY6

=;J€NOFI RPCC

-50 ;HzFCMCM >CG?HMCIH;F

g Za]f' l]fa]f\g hj]k]fl] U/'-W6

[ . iWE'

FY l]gj€Y [gehd]lY \Y ,- . -+/*

)" -HGLM>GMAJNUFC?>"

/4/-;975+16/;3:57

$" 5>BGCMN@ALIKCF>KC>L"

; X S V

< %( I . .= ( ( ( (D ). I %( ).] ) 1+. I I %(

,M ( ( ) /+. / ) 1+.

&%'X,Q+V.Q+

S,

>] lg\Yk dYkeY_falm\]k [gf im] k] gh]jY ]f ?d][ljgeY_f]lakeg' dYkƒfa[Yk im] aehgjlYf hYjY]klYZd][]j ]d kakl]eY \ae]fkagfYd kgf dYkim]`]egk ddYeY\ghjaeYjaYk']klg ]k' Yim]ddYkhYjYdYk[mYd]k]k hgkaZd]\])^afajdYMmeYhgj n€Ygh]jY[agfYdq mfan]jkYdkaf f][]ka\Y\ \] j][mjjaj YdYe]\a\Y \] gljYk eY_falm\]k* ; [gflafmY[a‚f ]fme]jYegk dYkeY_fa)lm\]k hjaeYjaYk[gf ]d hgklmdY\gim] kajn] hYjY]klYZd][]j ]d [jal]jag \]kmeY ]f [Y\Y mfY*

?L]RL PWlN_]TNL'FY [Yj_Y]d•[lja[Y' A%k] eYfa^a]klYhgj dY[j]Y[a‚f]f lgjfg kmqg\] mf [Yehg ]f ]d im] k] gZk]jnYf [a]jlgk ^]f‚e]fgk h][m)daYj]kim] \Yj]egk hgj [gfg[a\gk* Mm[Yj~[l]j \] eY_falm\ hjaeYjaYj]kmdlY\] Y\ealaj im] WL^NL]RL^ PWlN_]TNL^^P ^`XLY [Z] LN`X`WLNTkY#[Yh€lmdgCC'v 1$*

4Z]]TPY_PPWlN_]TNL'FYk [gjja]fl]k ]d•[lja[Yk k] eYfa^a]klYf hgj \])l]jeafY\gk ]^][lgk gZk]jnYZd]k#l•jea[gk' eY_f•la[gk q ]d][ljgd€la[gk$im] h]jeal]f \]^afaj mfY eY_falm\ hjaeYjaY' ddYeY\Yafl]fka\Y\* Mm[jal]jag \] a_mYd\Y\]k gZnag' q]f [mYflg Yd\] kmeY' ZYklYhgklmdYjim]dYkafl]fka\Y\]k kgf Y\alanYkhgj Y[memdY[a‚f*M]\aj~' hgj ]b]ehdg' im]mfY[gjja]fl] ]k a_mYdYdYkmeY\] gljYk\gk [mYf\g dYhjae]jY hjg\mr[Ydgkeakegk ]^][lgk ]d][ljgd€la[gk im] dYkgljYk \gk hm]klYk]f hYjYd]dg*

FPN_Z]PPWlN_]TNZ^'?f lg\g hmflg \] mf [Yehg ]d][ljgkl~la[g hm])\]f gZk]jnYjk] \gk eY_falm\]k \aja_a\Yk im] k] eYfa^a]klYf hgj k]f\gk]^][lgk [YjY[l]j€kla[gk*OfY ]k dYTY_PY^TOLO%6%j]khgfkYZd]\] dYk m]jrYkim] k] ]b]j[]f kgZj] dgk[m]jhgk ]d][ljarY\gk* FY gljY ]k dYTYO`NNTnY%5%

FY ^‚jemdY \]\m[a\Y l]‚ja[Ye]fl] hgj MY[cmjq N]ljg\] ]k6

$\gf\] R j]hj]k]flY dYemdlahda[a\Y\' g h]kg ]klY\€kla[g +W# - \] dgk]klY\gk [m~fla[gkeY_f•la[gk \]d fan]d ^mf\Ye]flYd*

Page 98: Análisis dimensional

RPCC* ?F?=NLICd-;*AH?NCMGI -53-52 ;HzFCMCM >CG?HMCIH;F

im] ]k dY[YmkY\] dgk^]f‚e]fgk \] ]d][ljarY[a‚f hgj af^dm]f[aY']klg ]k'\] dYYhYja[a‚f \] [Yj_Yk\] ka_fg [gfljYjag ]f dYk[YjYk\] mfYd~eafYe]l~da[Y' [Yj_Ykim] Y\ima]j]f kmnYdgj e~paeg [mYf\g dYd~eafY k][gdg[Y ]f \]l]jeafY\Y hgka[a‚f*

NYflg 6 [geg 5 kgf eY_falm\]k hjaeYjaYk]f najlm\ \] mf []TYNT[TZOP ^`([P][Z^TNTZY%im] hm]\] ]fmf[aYjk] YM|6WL^XLRYT_`OP^ 6 d 5 ^PNZX[Z]_LYNZXZ `PNTZ]P^%]klg ]k' dYk[Yfla\Y\]k \] [Y\Y ]kh][a] k] kmeYfhgj dYj]_dY \]d hYjYd]dg_jYeg*

M]_ƒf ]d j]^]ja\g hjaf[ahag' kax? ]k dY^m]jrY im] k] ]b]j[] kgZj] dYmfa\Y\ \] [Yj_Y' dYim] Y[lƒY kgZj] mfY [Yj_YA nYd\j~6

Jgj k]j < q < n][lgj]k [g]pakl]fl]k ]f mf hmflg' `YZj~ \] [me)hdajk] im]6

1 . F81$ U-'/W

\gf\] F8]k mf l]fkgj' [YjY[l]j€kla[g\]d e]\ag' im] k] \]fgeafY [P]XPL&MTWTOLOXLRYl_TNL%]d [mYd]f dgke]\agk ak‚ljghgk k] [gfna]jl] ]f mf ]k)[YdYj*

.* F]q]k ^mf\Ye]flYd]k*

F. 6A' U-'-W >] em[`Yk eYf]jYk k] hm]\]f [dYka^a[YjdYkd]q]k \]d ?d][ljgeY_f])lakeg ]f ^mf\Ye]flYd]k q \]janY\Yk' q [Y\Y Ymlgj]da_][geg ^mf\Ye]flY)d]kdYkim] [gfka\]jY e~k Y\][mY\Yk\]k\] ]d hmflg \] naklYh]\Y_‚_a[g*JYjY ]d ;f~dakak \ae]fkagfYd kajn] [mYdima]jkakl]eY \] ][mY[agf]k ^mf)\Ye]flYd]k' hm]k lg\gk [gf\m[]f Ydeakeg kakl]eY \] ^‚jemdYk\€e]f)kagfYd]k'h]jg [gf gZb]lg \] hgf]j \] eYfa^a]klg im] k] [mehd] fm]kljghjae]j hgklmdY\g' Y\ghlYj]egk dYk][mY[agf]k im] hm]\]f ]fmf[aYjk][geg j]dY[a‚f \] hjghgj[agfYda\Y\ ]flj] [Yfla\Y\]k*

<Pd OP 7LXOLd&8L`^^' Ng\Y [Yj_Y ]d•[lja[Y ]f_]f\jY mf [Yehg]d•[lja[g ]f ]d im] dYaf\m[[a‚f ]k hjghgj[agfYd Y \a[`Y [Yj_Yq ]kl~ ]fjYr‚f afn]jkY \]d [mY\jY\g \] dY\aklYf[aY6

;\]e~k' hgj k]j ? q > n][lgj]k [g]pakl]fl]k ]f mf hmflg' \]Z]j~ k]j6

> . ]?' U-'.W

\gf\] ] ]k mf l]fkgj' [YjY[l]j€kla[g\]d e]\ag' im] k] \]fgeafY [P]XPL&MTWTOLOPWlN_]TNL%[P]XT_TaTOLOg NZY^_LY_POTPWlN_]TNL%]d [mYdk] [gfna]jl]]f mf ]k[YdYj]f dgke]\agk ak‚ljghgk*

4LX[Z XLRYl_TNZ' FYk [Yj_Yk]d•[lja[Yk*]f egnaea]flg q dgkaeY)f]k [j]Yf ]f lgjfg kmqgmf [Yehg eY_f•la[g' im] k] eYfa^a]klYhgj^]f‚e]fgk h][mdaYj]kim] \Yj]egk hgj [gfg[a\gk*

?f lg\g hmflg \] mf [Yehg eY_f•la[g hm]\]f gZk]jnYjk] \gk eY_)falm\]k \aja_a\Yk im] k] eYfa^a]klYf hgj k]f\gk ]^][lgk [YjY[l]j€kla[gk*OfY ]k dYTYO`NNTnYXLRYl_TNL%<' j]khgfkYZd] \] dgk]^][lgk hgf\]jYd]k*FY gljY ]k ]d [ZOP] TXLYLOZ]%B' im] ]k dY[YmkY\] dgk^]f‚e]fgk \]aeYfY[a‚f hgj af^dm]f[aY#%$*;eZYk kgf eY_falm\]k hjaeYjaYk]f naj)lm\ \] mf hjaf[ahag \] kmh]jhgka[a‚f im] hm]\] ]fmf[aYjk] Yk€6WL XLR&YT_`OP <q B ^P NZX[Z]_LY NZXZ aPN_Z]P^'

#5$ d #A$ *!$

#]flj] [Yfla\Y\]k$* U.'-W

;d hYkYjY dY][mY[a‚f ]flj] e]\a\Yk' `Yq im] hgf]j mf ^Y[lgj \]hjghgj[agfYda\Y\ im] j]kmdlYk]j af\]h]f\a]fl] \]d e]\ag7 ]k mfY [gfk)lYfl] mfan]jkYd*J]jg [geg dYj]dY[a‚f U.'-Wfg da_Y\gk eY_falm\]kafk]hYjYZd]k'fm]kljg k]_mf\g hgklmdY\gY^ajeY im] lYd [gfklYfl] ]kkmh]j^dmY'q hm]\] j][aZaj mf nYdgjfme•ja[g [mYdima]jY*

=gf 4 . - j]kmdlY]d kakl]eY fg jY[agfYdarY\g6#%$ =mYf\g GYpo]dd ^gjemd‚ dYk ][mY[agf]k \]d [Yehg ]d][ljgeY_f•la[gfg k] hj]g[mh‚ tf \Yj dYk\]^afa[agf]k ]hakl•ea[Yk \] dgk [mYljg n][lgj]k 4 ><' *B'S fg ]k ^~tdd]f[gfljYj lYd]k\]^afa[agf]k ]f dgkdaZjgk\] ?d][ljgeY_f]lu_"eg6imar~ hgjimt ha]fkYf dgk Ymlgj]k im] ZYklYf dgk fgeZj]k g im] kmk\]^afa[agf]k]kltf [gfl]dddtYk ]f dYkj]^]ja\Yk ][mY[agf]k* J]jg' kafgk Yl]f]egk Y dYk\]fgjfa)fY[CIftk [d~Ya[Yk#B . afl]fka\Y\' < . af\m[[a‚f$' `YZj€Yegk \] YljaZmajY BdYkY[[agf]k hgf\]jYd]k q Y < dgt ^]f‚e]fgk \] aeYfY[a‚f hgj af^dm]f[aY*qtm[]\] i*mt' ]f PCjlm\ 87d]dYk][mY[agf]k \]d [Yehg ]d][ljgeY_f•la[g P ]f [gfljY

t dYghafa‚f \]d hjghCI GYpo]dd' dYk[gkYk g[mjj]f bmklYe]fl] Ydj]n•k' k]_ƒf`CTI*fglYj Mgjfe]j^]d\ #25$' hgj dg im] B \]Za]jY ddYeYjk] af\m[[a‚f q < af)q']fkC\t\* NYd [geg ]kl~f dYk[gkYk' dg e~k naYZd] hYj][] k]j k]_maj ddYeYf\ge\m[[t‚f Ydn][lgj <' hgj k]j ]d [YmkYfl] \] dYk[gjja]fl]k af\m[a\Yk' q ddYeYjhg\]j CeYfY\gj Ydn][lgj B' k]_ƒf `]egk hjghm]klg ]f mf ljYZYbgYfl]jagj*

A5Y1&

]+#]flj] e]\a\Yk$'

YdhYkgim]' [gf = . -+0-l k] gZla]f] ]d kakl]eY jY[agfYdarY\g6

5 . X-X F*0-l '*.

U.'.W

Page 99: Análisis dimensional

&+* ;HzFCMCM >CG?HMCIH;F RPCC* ?F?=NLIdd^;AH?NCMdV-, &++

?d ^Y[lgj \] hjghgj[agfYda\Y\ ]k af\]h]f\a]fl] \]d e]\ag' q kmh]j)^dmgk]_ƒf fm]kljYk fgjeYk* FY ][mY[a‚f ]flj] e]\a\Yk ]f ]d kakl]eY

jY[agfYdarY\g]k6

;\]e~k \] dYkd]q]k im] `]egk ]fmf[aY\g' `Yq gljYk im] k] j]^a]j]f Y^]f‚e]fgk hYjla[mdYj]k'lYd]k[geg dgk]d][ljgd€la[gk g dgkgja_afY\gk hgjdYk[Yj_Yk]f egnaea]flg' h]jg ]f lYd]kd]q]k fg k] afljg\m[]f fm]nYkeY_falm\]k hjaeYjaYkfa [gfklYfl]k mfan]jkYd]kaf]dm\aZd]k'hgj dg im] fg]k hj][akg lgeYjdYk ]f [m]flY ]f ;f~dakak \ae]fkagfYd*

/* Makl]eY\ae]fkagfYd*

?flj] dYkfm]n] eY_falm\]k hjaeYjaYk'^%<%D%A%*%6%5%3%9%S dYk[gfklYfl]k ] q UF' ]pakl]f dYkka]l] ][mY[agf]k af\]h]f\a]fl]k im] `]egk^gjemdY\g ]f dgk \gk YhYjlY\gk Yfl]jagj]k* ?f najlm\ \] dg \a[`g ]f]d v 1 \]d [Yh€lmdgCP' hg\j~f ]d]_ajk] [mYljg eY_falm\]k hYjY^gjeYj dYZYk]' q [gf ]ddg im]\Yj~f \]l]jeafY\Yk dYk ‚jemdYk\ae]fkagfYd]k t]lg\Yk dYk\]e~k* =mYdima]jY\] -,1 _jmhgk ^gjeY\gk hgj dYklj]k eY_e)lm\]k e][~fa[Yk q mfY]d][ljgeY_f•la[Y kajn] hYjY]d [Ykg'hm]k ]k k]_m)jg im] kgf \ae]fkagfYde]fl] af\]h]f\a]fl]k* ;\]e~k' dY^m]jtY tm]\]kmklalmajk]hgj dYeYkYY^af \] im] lg\g k] j]\mr[Y YmfYYeh`Y[tgf *\]dYZYk] im] `]egk mladarY\g]f G][~fa[Y* ;\ghlYf\g dY[Yj_Y]t][ljd=Y[geg [mYjlYeY_falm\ Z~ka[Y'k] la]f] ]d ka_ma]fl] kakl]eY \] ^gjemdYk

\ae]fkagfYd]k6

?d ]ehd]g \] mfg m gljg kakl]eY la]f] aehgjlYf[aY [mYf\g k] ljYlY\] gZl]f]j kakl]eYk \] mfa\Y\]k [g`]j]fl]k' q ]k Y[lmYde]fl] [m]kla‚f\]ZYla\Y ]f dgk gj_Yfakegk afl]jfY[agfYd]k #3,$*JYjY fm]kljgk ^af]k' \Ydg eakeg mf kakl]eY im] gljg' hm]k ]d [YeZag \] ^Y[lgj]k fme•ja[gk fgYdl]jYdY]kljm[lmjY \ae]fkagfYd* ?f dg im] ka_m]fgk Yl]f\j]egk Ydkak)l]eY jY[agfYdarY\g*

=geZafYf\g U-'.W'U-'/WS U.'.W'k] gZla]f] dYd]q \] =gmdgeZ*<Pd OPBZbWLYO' FY afl]fka\Y\ \] mfY [gjja]fl] ]k hjghgj[agfYd Y

dY[Yj_Y im] YljYna]kY[Y\Y k][[a‚f ljYfkn]jkYd ]f dYmfa\Y\ \] la]ehg6

Q. 3WW'

#*$ "! T+<'#^$

FY [gfklYfl] mfan]jkYdim] hm\a]jY ^a_mjYj]f dY][mY[a‚f ]flj] e]\a\Yk]k kmh]j^dmY]f najlm\ \] fm]kljg k]_mf\g hgklmdY\g'hgj dg im]' [gf mfa)\Y\]k [g`]j]fl]k `YZj~ \] k]j6

W1d'_

U.'/W

$<Pd OP 2Ya[l]P' Ng\Y [gjja]fl] j][lad€f]Y af\]^afa\Y ]f_]f\jY ]f

lgjfg kmqg mf [Yehg eY_f•la[g ljYfkn]jkYd [mqg hg\]j aeYfY\gj ]khjghgj[agfYd Y dYafl]fka\Y\ \] dY[gjja]fl] q ]kl~ ]f jYr‚f afn]jkY \]dY\aklYf[aY6

I*J . AD&WI6J 9 <=D&+A&W

I5J . <&+AU]W. <&,=&*D+A+

?f dY][mY[a‚f ]flj] e]\a\Yk ^a_mjYmfY [gfklYfl] mfan]jkYdim]'k]_ƒf fm]kljYk fgjeYk' ]k kmh]j^dmY*?f ]d kakl]eY jY[agfYdarY\g]k6

j]kmdlY]d eakeg kakl]eY \ae]fkagfYd*

81KWK+._] !

U.'0W

M][gehjm]ZY ^~[ade]fl] im] [gf dYk][mY[agf]k \] GYpo]dd6q ]f ]d fg jY[agfYdarY\g

81d'\ U.'0"W

>9]?

<Pd OP<L([WLNP' Ng\Y [gjja]fl] ]d•[lja[Y' [gdg[Y\YljYfkn]jkYde]fl]]f mf [Yehg eY_f•la[g' ]ph]jae]flY mfY^m]jrY'h]jh]f\a[mdYj Yd[Yehgq YdYhjghaY [gjja]fl]' im] ]k hjghgj[agfYd YdYaf\m[[a‚f eY_f•la[Y \]d[Yehg' YdYafl]fka\Y\ \] dY[gjja]fl] q Ykmdgf_alm\6

\an > 9 \

' L5jglB9 _#%%L_

"Q# ! #3$ #*$ #W$'

U.'1W

I8J . <&*D&*A

I3J . =D&*A&W

AA8B9 <=A&+'

1 . A85

\an < 9 I

Y<jgl? 9 )))'

L_

Page 100: Análisis dimensional

.,, ;HzFCMCM >CG?HMCIH;F

'" 4> K>?CHG>ECP>?C(G@A2A>OCLC@A"

>] Y[m]j\g [gf fm]kljg [jal]jag' dYkmfa\Y\]k \]janY\Yk `Yf \] [me)hdajdY[gf\a[a‚f \] k]j [g`]j]fl]k [gf ]d kakl]eY \] ][mY[agf]k ^mf\Y)e]flYd]k* >] Yim€im] k]Yf][]kYjag hj][akYj lYd]k][mY[agf]k' q km[]\]im] dgk\a^]j]fl]k Ymlgj]kdYk]k[jaZ]f \] \aklaflY eYf]jY' hgj dgim] Ymf)im] k] ^ab]fdYkmfa\Y\]k Z~ka[Yk'fg im]\Yf mf€ng[Ye]fl] \]l]jeafY\YkdYkmfa\Y\]k \]janY\Yk*Jgj gljY hYjl]' fg `Yq mfYfaea\Y\ Y[]j[Y \] ka'YhYjl] dYl]eh]jYlmjY' k] f][]kalYf lj]k g [mYljgmfa\Y\]k hYjY^gjeYjdYZYk]*Ng\g ]klg `Y gja_afY\g mfYkalmY[a‚f[Y‚la[Y]f dYim] `Yq _jYffƒe]jg \] mfa\Y\]k hYjY[Y\Y eY_falm\' q j]kmdlYmf n]j\Y\]jg jge)h][YZ]rYk ]d kYZ]j [m~f\g \]Z] mladarYjk][Y\Y mfY q ]d Yn]ja_mYjqj]l]f]j dgk^Y[lgj]k \] [gfn]jka‚f* <m]fY hjm]ZY\] ]ddg]k im] dY=g)eaka‚f M*O* H* fg `Y ka\g [YhYrlg\Yn€Y\] \]^afaj dYmfa\Y\ \] hg\]jaeYfY\gj ]f ]d kakl]eY \] Aagj_a*

OfY \] dYk[YmkYk\]d ]eZjgddg ]k ]d ]ehd]g \] \gk kakl]eYk\] ][mY)[agf]k' dYkhjaealanYk q dYkjY[agfYdarY\Yk'im] \a^a]j]f ]f dYhj]k]f[aY\]d ^Y[lgj 0-l ]f Yd_mfYk\] ]ddYk*?d [YmkYfl]\] ]klY [gehda[Y[a‚f ^m]B]Ynaka\]' ima]f' ]f -44,' ddYe‚ dYYl]f[a‚f kgZj] dYw]jmh[a‚f \]d 03ly'

im] [gfkakl] ]f dYYhYja[a‚f\] ]kl] fƒe]jg ]f [Ykgk]f im] kmhj]k]f[aYfg d] hYj][a‚ bmkla^a[Y\Y*?kl] ^€ka[g]eaf]fl] l]f€Y dYghafa‚f )hgj dgnaklg [gehYjla\Y hgj dgk _]‚e]ljYk q dgk \]e~k ^€ka[gk) \] im] lYdfƒe]jg ]kl~ naf[mdY\g\] Yd_ƒfeg\g ]f dY[mjnYlmjY'q' hgj ]kg' [gf)ka\]jYZYYZkmj\g]d im]' hgj ]b]ehdg' YhYj]r[Y]f dY^‚jemdY im] \Y dY[YhY[a\Y\ \] mf [gf\]fkY\gj hdYfg' ka]f\g Yk€im] fg `Yq ]f •d fY\Y[mjng*

?d fƒe]jg DP hjg[]\] \] dYA]ge]lj€Y q k] afljg\m[] ]f @€ka[Y[mYf\g k]gh]jY [gf dgf_alm\]k' ~j]Yk' ngdƒe]f]k' ~f_mdgk hdYfgk q ~f_mdgk k‚da\gk*

?d hjae]j ]f[m]fljg [gf ]d fƒe]jg ,M g[mjj] ]f dY][mY[a‚f im] \Y dYdgf_alm\\] dY[aj[mf^]j]f[aY6

W. YO0 U0'-W

?k •klY mfY d]q _]ge•lja[Y im] la]f] dYh][mdaYja\Y\ \] im] [gfla]f] lYf k‚dg\gk [Yfla\Y\]k OT]PN_LXPY_PNZX[L]LMWP^%hm]k YeZYk kgf dgf_alm\]k* ?klgima]j] \][aj im]' YdhYkYj \] dYj]dY[a‚f \] hjghgj[agfYda\Y\6

#W$%''''%#O$ #]flj] [Yfla\Y\]k$ U0'.W

Y dY][mY[a‚f ]flj] e]\a\Yk U0'-W'im]\Y \]l]jeafY\g ]d ^Y[lgj \] hjghgj[ag)fYda\Y\' im] j]kmdlY k]j ]d fƒe]jg DP . /'-0-15. *** ?f ]kl] [Ykg hYjla[mdYj'dY][mY[a‚f fg \]^af] faf_mfY mfa\Y\7 [mYdima]jmfa\Y\ \] dgf_alm\ ]k [g`]j]fl][gf ]ddY*

RPCC* ?F?=NLIG;AH?NCMGI .,-

P]egk im] ]d fƒe]jg DP fg ]k ]d j]kmdlY\g \] faf_ƒf [gfn]fag* L]kmdlY\][gehYjYj dYdgf_alm\ \] mfY [aj[mf^]j]f[aY [mYdima]jY[gf dYdgf_alm\ \] km\a~e]ljg* ?klY [gehYjY[a‚f hm]\g `Y[]jk] ]eh€ja[Ye]fl] [gf lg\Y dYhj][a)ka‚f im] k] \]k]]' q Yk€k] hg\j~ [gehjgZYj dYd]q _]ge•lja[g* im] kajn] \] ^mf)\Ye]flg hYjY ]d [~d[mdgl]‚ja[g \]d fƒe]jg ]f [m]kla‚f*

?k \] fglYj im] dYd]q U0'-Wk‚dg ]k n~da\Y [mYf\g dY [aj[mf^]j]f[aY ]kl~ljYrY\Y kgZj] mf hdYfg* MaYhgqYf\g ]f mfY kmh]j^a[a] [mYdima]jYdYhmflY \]mf [geh~k' k] ljYrY dY[mjnY im] \]k[jaZ] dYgljY hmflY' dYjYr‚f WTO]flj] dYdgf_alm\ \] dY[mjnY q ]d \gZd] \] dY\aklYf[aY ]flj] YeZYk hmflYk hg\j~ lgeYjmf nYdgj [mYdima]jY'im] \]h]f\]j~ \] dY^gjeY \] dYkmh]j^a[a]q \]d nYdgj \] O'Jgj [gfka_ma]fl]' PWYoXP]Z DP P^ NL]LN_P]m^_TNZOPW[WLYZg' OTNSZOPZ_]ZXZOZ%OPQTYPWL`[P]QTNTPOPN`]aL_`]LY`WL'?klY [gfka\]jY[a‚f ][`Y hgj la]jjY dYjYr‚fY\m[a\Y hgj B]Ynaka\] ]f hjg \] dYjY[agfYdarY[a‚f im] e~k Za]f \]Za]jY ddYeYj)k] \]kjY[agfYdarY[a‚f*

M] ljgha]rY fm]nYe]fl] [gf ]d fƒe]jg DP ]f dY]phj]ka‚f \]d ~j]Y \]d [€j[mdg6

U0'/D

;`gjY k] ljYlY qY \] \gk [Yfla\Y\]k' ~j]Y q dgf_alm\' im] fg kgf [gehYjYZd]k'hm]k fg `Yq [jal]jag im] h]jealY Yn]ja_mYj[m~flYk n][]k ]kl~ dYmfY [gfl]fa\Y*]f dYgljY* ?f gljgk l•jeafgk7 dY ][mY[a‚f U0'/Wk‚dg ]k n~da\Y Y [gf\a[a‚f \]im]' \Y\Y dYmfa\Y\ \] dgf_alm\' k] Y\ghl] mfY mfa\Y\ \] ~j]Y im] k]Y [g`]j]fl]

[gf dYj]^]ja\Y ][mY[a‚f*?d hjg^]kgj J]jm[[Y kgkla]f] im] dYmfa\Y\ \] ~j]Y la]f] im] k]j' f][]kYjaY)

e]fl]' ]d ~j]Y \]d [mY\jY\g im] la]f] hgj dY\g dYmfa\Y\ \] dgf_alm\' q \Y[geg jYr‚f ]d im] [gf [mY\jY\gk k] hm]\] j][mZjaj [mYdima]j~j]Y hdYfYkaf \]bYjafl]jkla[agk* ?klY jYr‚f [Yj][] \] nYdgj' hm]k ]f dYmfa\Y\ \] ~j]Y dg im] aehgjlY*]k ]d lYeY•g q fg dY gjeY* FY qmflY' dY Yf]_Y\Y' ]d ha] [mY\jY\g g dY ][l~j]Yhm]\]f l]f]j ^gjeYk [mYd]kima]jY*Jgj gljY hYjl]' ka k] Y\eal] dY \]^afa[a‚f\] [g`]j]f[aY hjghm]klY hgj ]d =geal• M*O* >'%`YZj€Yim] hj]k[af\aj \]d ^Y[lgjfƒe•ja[g ]f U0'/Wq ]k[jaZaj6

q' [gf ]d []fl€e]ljg [geg mfa\Y\ \] dgf_alm\' dYmfa\Y\ \] ~j]Y k]j€Y ]d NPY&_mXP_]Z]POZYOZ%g k]Y ]d ~j]Y \]d [€j[mdg[mqg jY\ag ]k mf []fl€e]ljg' [gkY afY\)eakaZd] hgjim] ]k Za]f kYZa\g im] dYmfa\Y\ \] ~j]Y [g`]j]fl] [gf U0'/W]k ]d

[]fl€e]ljg [mY\jY\g*FY d]q e~k _]f]jYd ]flj] dYkim] j]dY[agfYf ~j]Yk [gf dgf_alm\]k' ]k dYim]

Y^ajeYim] dYk~j]Yk \] \gk ^a_mjYkk]e]bYfl]k kgf hjghgj[agfYd]k Y kmk\ae]f)kagf]k daf]Yd]k*?klY d]q' Yhda[Y\YYd[€j[mdg \] jY\ag ]%k] ]phj]kYj~ Yk€6

#2$ %''''%#\$+ #]flj] [Yfla\Y\]k$*

;d hYkYj Y dY][mY[a‚f ]flj] e]\a\Yk k] hm]\] hjg[]\]j \] \gk eYf]jYk6 g k]kmhjae] ]d ^Y[lgj \] hjghgj[agfYda\Y\ q k] ]k[jaZ]6

#]flj] e]\a\Yk$'

Page 101: Análisis dimensional

'%' ; zFCMCM>ddVC?MCIH;F

[gf dg im] dYmfa\Y\ [g`]j]fl] ]k ]d im] `]egk ddYeY\g []fl€e]ljg j]\gf\g' gZa]f k] aehgf] NZYaPYNTZYLWXPY_PgljY mfa\Y\ [mYdima]jY*Mak] [gfna]f] ]f im]dYmfa\Y\ k]Y hj][akYe]fl] ]d []fl€e]ljg [mY\jY\g' dYkd]q]k \] dYA]ge]lj€YhdYfY]pa_]f im] ]d ^Y[lgj \] hjghgj[agfYda\Y\ k]Y hj][akYe]fl] ]d fƒe]jg _P%]d eakeg im] k] gZla]f] Yd YddYjdYjYr‚f ]flj] dY[aj[mf^]j]f[aY q ]d \a~e]ljg*

?d jYrgfYea]flg hj][]\]fl] ]k Yhda[YZd]Yd~j]Y \] dYkmh]j^a[a]]k^•ja[Y qYdngdme]f im] daealY' [gf dg im] dd]_YegkY dYkka_ma]fl]k [gf[dmkagf]k6

6W YoXP]Z KKQTR`]LPY WZPN`LNTnY\`P OL WLWZYRT_`OOP N`LW\`TP]NT]N`YQP]PY&NTLPY Q`YNTnYOP^` ]LOTZNZXZ NZY^PN`PYNTLOP`YL WPdYL_`]LW' > Z SLd PY PWWZYLOL NZYaPYNTZYLW'6Y NLXMTZ% L[L]TNTnY PY WL^Qn]X`WL^ \`P OLY WL^k]PL^Z WZ aZWoXPYP^OP NTP]_L QTR`]L^ PY Q`YNTnY OP ^`^ OTXPY^TZYP^WTYPLWP^%P^ PW]P^`W_LOZOP`Y NZYaPYTZPY WLPWPNNTnYOP^`^ ]P^[PN_TaL^YTOLOP^'

>]k\] fm]kljg hmflg \] naklY'YdhYkYj\] dYj]dY[a‚f \] hjghgj[agfY)da\Y\ ]flj] [Yfla\Y\]k Y dY][mY[a‚f ]flj] e]\a\Yk' ka]ehj] hm]\] hg)f]jk] [geg ^Y[lgj \] hjghgj[agfYda\Y\ #Y\]e~k \] dY[gfklYfl] mfan]jkYdg [YjY[l]j€kla[Y'ka^m]j] f][]kYjaY$mf fƒe]jg ^abg'im] hm]\] k]j ]d 03l mgljg [mYdima]jY*>] Yim€im]' kaZa]f fg kgf n~da\gk dgkjYrgfYea]flgkY\m[a\gk ]f hjg \] dYjY[agfYdarY[a‚f' fg `YqY af[gfn]fa]fl] ]f Y\e€)lajdY*@m][gkY \]k\a[`Y\Y hgjim] Yme]fl‚ ]d ]eZjgddg' h]jg mfY n]rY\eala\Y hgj Y[m]j\g afl]jfY[agfYd' dge]bgj ]k Y[]hlYjdY*

B] Yim€dYk\gk eYf]jYk \] ]k[jaZaj dYk][mY[agf]k \] GYpo]dd' im]lgeYj]egk [geg ^mf\Ye]flYd]k6

Hg jY[agfYdarY\Yk6

5Y . ]f? #Y$7 < 9 Q:'Y8Y #Z$ U0'0W

\an 5Y 9 03li #[$7 \an < 9 I #\$

l 5 & 35Y #]$7<<

#^$*jg Y 9 03ll # %% jgl? 9)))3^ 3^

LY[agfYdarY\Yk6

1 . ^D*B !D"

\an<9I #\$

<<jgl? 9 )) #^$'

3^

3 . ]? #Y$7

\an 3 9 \ #]$7

jgl 5 9 T# 35 #]$73^

U0'0"W

\gf\] Tj]hj]k]flY dY\]fka\Y\ \] [gjja]fl] q \ dY\]fka\Y\ \] [Yj_Y*>]d ]pYe]f \] dYk][mY[agf]k U0'0Wq U0'0"Wj]kmdlY'afe]\aYlYe]fl]'

im] dYke]\a\Yk \] a' 6 S 3 fg k] Ydl]jYf hgj ]^][lg \] dYjY[agfYdarY)[a‚f* Fg eakeg km[]\]j~' ]na\]fl]e]fl]' [gf dY[Yj_YA q [gf dYafl]f)

ONKK&?F?=NLIG;A ?NCMGI '%(

ka\Y\' *%\] dY[gjja]fl]* ?f [YeZag' dYke]\a\Yk \] ]' ^D*'5 S 8 [YeZaYf\]d ka_ma]fl] eg\g6

]f . -YP0

5Y . 03l>7

Q:'Y. ^D*+03l

8Y . 03lB*

U0'1W

JYjY dgk ]^][lgk \] dY\]^afa[a‚f \] mfa\Y\]k' `Yq im] \]k[YjlYj dY][mY[a‚f #O$ hgjim] ]k n~da\Y[gf mfa\Y\]k [mYd]kima]jY*Km]\Yf' hm]k'[af[g ][mY[agf]k ^mf\Ye]flYd]k YdYkim] `Yq im] Y_j]_Yj dYkka_ma]fl]k\]^afa[agf]k6

6 K Q(A0 \ & A(F0 * K A(_0 G%<UC%

im] \]l]jeafYf dYkmfa\Y\]k \] 6%\%*%a' kak] aehgf]f dYkmfa\Y\]k \]dgf_alm\' \] ^m]jrY#g\] eYkY$'\] la]ehg q \] [Yj_Y]d•[lja[Y* =gf ]klg'dYk][mY[agf]k #]$' #L$%"Q#% #P$q #M$ \]l]jeafYf' j]kh][lanYe]fl]' dYkmfa)\Y\]k \] 5%]' 3%8 ? ^D**

?f j]kme]f6 hYjY^gjeYj mf kakl]eY \] mfa\Y\]k [g`]j]fl] [gf dYk][mY[agf]k \] GYpo]dd' kgf f][]kYjaYk q km^a[a]fl]k [mYljg mfa\Y\]kZ~ka[Yk'mfY \] dYk[mYd]k Y \] k]j' f][]kYjaYe]fl]' \] fYlmjYd]rY]d•[)lja[Y g eY_f•la[Y*

1* Makl]eY\] Aagj_a*

Jm]\] \]^afajk] ]d kakl]eY \] Aagj_a [geg mf kakl]eY \] mfa\Y\]k8[g`]j]fl]k [gf dYk][mY[agf]k jY[agfYdarY\YkU0'0"W']f ]d im] k] lgeYf#DgeYZ~ka[Yk]d e]ljg' ]d cadg_jYeg q ]d k]_mf\g' q dY[mYjlYmfa\Y\ k]^abY[gf dY[gf\a[a‚f \] im] dYh]je]YZada\Y\ \]d nY[€gl]f_Y hgj e]\a\Y

]d fƒe]jg^D*g. 03lx -,)3 #mfa\Y\]k \] Aagj_a$*

JYjY n]j [‚eg ]klY [gf\a[a‚f \]l]jeafY dYmfa\Y\ \] [Yj_Y' im] ]f]kl] kakl]eY k] \]fgeafY [mdgeZag #?$%ZYklYl]f]j hj]k]fl] im] \] dYl]gj€Y \] GYpo]dd k] \]khj]f\] dYj]dY[a‚f6

\gf\] ] ]k dYe]\a\Y \] dYn]dg[a\Y\ \] dYdmr]f ]d nY[€g*?f ]d [YkgY[lmYdk]j~6

( (]6g.%%.

^D*I=-. 03lx -,)3=-.

Page 102: Análisis dimensional

.,0 *;HzFCMCM>CG?HMCIH;F RPCC* ?F?=NLIG;AH?NCMdVdI .,1

\gf\] ]d . .'5535x -,4 t /x -,4 ]k dY e]\a\Y \] dYn]dg[a\Y\ \] dY*dmr ]f e]ljgk hgj k]_mf\g*

;hd€im]k] Y`gjY ]d l]gj]eY \] AYmkkhYjY' e]\aYfl] dY ][mY[a‚fU0'0" #[$WYddYj]d ^dmbgim]' hjg[]\]fl] \] mfY [Yj_Y A%YljYna]kYmfY*kmh]j^a[a]]k^•ja[Y \] jY\ag ] im] la]f] km[]fljg ]f dY[Yj_Y*M]j~6

=geg j]kmdlY\g \] dY[gfljgn]jkaY' dgk \]^]fkgj]k \] dYjY[agfYdarY[€‚f \]"=Yfla\Y\]k Y^ajeYf im] ]d k€eZgdg (M im] ^a_mjY]f dYk][mY[agf]k \]d ]d][ljgeY_)f]lakeg fg ]k mf fƒe]jg whmjgy'kafg im] j]hj]k]flY dYe]\a\Y \] dY[mYjlYhYjl] \]d ~f_mdg k‚da\g [gehd]lg [mYf\g k] lgeY [geg mfa\Y\ ]d ]kl]jjY\a~f*;k€' \] U1'0W\]\m[]f6

AD&WI8J . %% . <D&9A' kj)-

< ' ]\U1'1W

U1'-D

03l-66j.U1'.s

8\gf\] kj ]k ]d k€eZgdg \]d ]kl]jjY\a~f*?k ^~[ad\]egkljYj im] lYd afl]jhj]lY[a‚f \]d k€eZgdg KK]k afY[]hlYZd]*?f

]^][lg7 ]f ]d [Yehg eY_f•la[g ]f_]f\jY\g ]f dg afl]jagj \] mf kgd]fga\] adaea)

lY\g g[mjj] im]6

q' Y Z]f]^a[ag \] #Y$j]kmdlY6

6 . &&'/A%&&&

8 . YWUW U1'2W

q dY^m]jrY im] Y[lƒY kgZj] mfY [Yj_Y A" [gdg[Y\Y Y dY\aklYf[aY \ \] AnYd\j~6

8\gf\] Y ]k ]d fƒe]jg \] ]khajYkhgj mfa\Y\ \] dgf_alm\* >] ]klY ]phj]ka‚f' ]f

dY im] fg ^a_mjY3-!' k] \]\m[]6

U1'/s I8J . <D&9A U1'3W

im] ]k dYd]q \] =gmdgeZ jY[agfYdarY\Yq \]l]jeafY' hgj [g`]j]f[aY']d [mdgeZag*=gf ]klg' dYk][mY[agf]k U1'.Wq U1'/W\Yf dYkmfa\Y\]k \])5 q 6%j]kh][lanYe]fl]' q dYmfa\Y\ \] [gjja]fl]' im] k] \]fgeafY*Yeh]jag #2$%j]kmdlY\] dY\]^afa[a‚f6

im] ]k af[gehYlaZd] [gf U1'1W*?klg hjm]ZY im] ]d k€eZgdg (M `Y \] l]f]j \a)

e]fka‚f fmdY*

!(" :CLMAF>L?ABALCF>EAL"

8 9 :(+._]% U1'0s

Mm]d]Y^ajeYjk] im] dgk kakl]eYk []_]kaeYd]k mladarYflYf k‚dg lj]kmfa\Y\]k ^mf\Ye]flYd]k6 ]d []fl€e]ljg' ]d _jYeg q ]d k]_mf\g' BYj]egkn]j im] fg ]k Yk€'kafg im]' [geg km[]\] ]f ]d kakl]eY \] Aagj_a' ka]ehj]6k]aehgf] mfY [gf\a[a‚f im] \]l]jeafY dY[mYjlYmfa\Y\*

Fgk kakl]eYk []_]kaeYd]k' im] k] mkYf lg\Yn€Y ]f em[`gk daZjgk\]@€ka[Yl]‚ja[Y' kgf lj]k6 ]d PWPN_]Z^_k_TNZ%im] j]hj]k]flYj]egk hgj =AM?']d XLRYl_TNZ #=AMG$'q ]d PWPN_]ZXLRYl_TNZg eaplg im] lYeZa•f k] ddYeY"Makl]eY\] AYmkk*Fgk \gk hjae]jgk kgf [g`]j]fl]k [gf dYk][mY[agf]k \]GYpo]dd fg jY[agfYdarY\Yk'ea]fljYk im] ]dkakl]eY \] AYmkk]k af[g`]j]f)l]' hgj dg im] ljYlYj]egk \] •d e~k Y\]dYfl]*

?f ]d kakl]eY =AM? k] aehgf] dY[gf\a[a‚f \] im] dYh]jealana\Y\\]d nY[€gl]f_Y hgj e]\a\Y ]d fƒe]jg6

* 9 A(_'

;hda[Yf\g ]d l]gj]eY \] Mlgc]k YdY][mY[a‚f U0'0"#]$W'k] gZla]f] hYjY*]d hg\]j aeYfY\gj ]f_]f\jY\g hgj mfY [gjja]fl] j][lad€f]Y ] af\]^afa\Y*dY][mY[a‚f6

im] \]l]jeafY dYmfa\Y\ \] hg\]j aeYfY\gj' hYjYdYim] k] `Y hjghm]klg]d fgeZj] \] WPYe#F$*

FY mfa\Y\ \] afl]fka\Y\ g af\m[[a‚f eY_f•la[Y k] \]fgeafY _P^WL!;"q ]tl~ \]^afa\Y hgj dY][mY[a‚f U0'0"#Z$W'k]_ƒf dY[mYd]f lg\g hmflg \]dnY=dI]f im] `YqYmf hg\]j aeYfY\gj 8 `YZj~ mfYaf\m[[a‚f eY_f•la[Y6

6Y . - #m*=AM?$' U2'-W

1 . 03lx -,)3B #m*Aagj_a$*#Dgfdg im] dY][mY[a‚f \] =gmdgeZ fg jY[agfYdarY\Y6

tYk \]e~k mfa\Y\]k \] ]kl] kakl]eY' lYd]k[geg ]d ZSXTZ%]d QL]LOTZ%]dSPY]TZq ]d `TPMP]k] gZla]f]f hgj [g`]j]f[aY [gf dYk][mY[agf]k \] \]^a)fa[a‚f \] dYkj]kh][lanYk eY_falm\]k*

U2'.W

Page 103: Análisis dimensional

.,2 ;HzFCMCM >CG?HMCIH;F ONKK&?F?=NLIG;AH?NCMGI .,3

^df 9 - #m*=AMdV-$' U2'/D

im] fgk \a[] im] ]d g]jkl]\ ]klYj~ j]YdarY\g]f [mYdima]jhmflg \]d nY[€gim] \akl] mf []fl€e]ljg \]* mfY [gjja]fl] j][lad€f]Y ] adaealY\Y[mqYafl]fka\Y\ nYd_Ye]\ag Zagl*

=geg' ]f _]f]jYd' 3 . `'90 S ]f ]d kakl]eY im] ]klYegk [gfka\])jYf\g dYh]je]YZada\Y\ \]d nY[€g`Y \] nYd]j -' dYmfa\Y\ \] af\m[[a‚fg afl]fka\Y\ eY_f•la[Y' im] k] \]fgeafY RL`^^ #Ak$']klYj~ j]YdarY\Y*]f [mYdima]jhmflg \]d nY[€g\gf\] ]d hg\]j aeYfY\gj nYd_Y- I]*

FY mfa\Y\ \] ^dmbg\] af\m[[a‚f k] ddYeYXLcbPWW#Gp$ q ]klYj~*j]YdarY\Y]f lg\g hmflg \] mf e]\ag [mYdima]jY\gf\] dYaf\m[[a‚fnYd_Y( Ak*

\]l]jeafY' hgj [g`]j]f[aY' dYmfa\Y\ \] [Yj_Y'im] `Y j][aZa\g ]d fgeZj]\] Q\LYVWTY#@j$*

?f ]d kakl]eY =AMG' dY[mYjlYmfa\Y\ ]kl~ ^abY\Yhgj dY[gf\a[a‚f\] im] dYh]je]YZada\Y\ \]d nY[€gl]f_Y hgj e]\a\Y ]d fƒe]jg

[gf dg im] im]\Y \]l]jeafY\Y dY [mYjlY mfa\Y\ Z~ka[Yq' [gf ]ddY'lg\Yk dYkmfa\Y\]k \]janY\Yk*

=geg' ]f _]f]jYd6]^d 9 W(Pf

q ]f dgkkakl]eYk []_]kaeYd]k ] . .'55352" -,-, 66666/x -,-,' dYh]jealana)\Y\ \]d nY[€gl]f\j~ hgj e]\a\Y6

)" 0>?MHKAL@A?HGOAKLCVG"

(#m*=AMG$* U2'0$

Jm]klg im] ]d kakl]eY ]d][ljgkl~la[g P ]d eY_f•la[g kgf YeZgk [g`])j]fl]k [gf mf eakeg kakl]eY \] ][mY[agf]k ^mf\Ye]flYd]k' q `]egknaklg im] k] j]ima]j]f [mYljg mfa\Y\]k Z~ka[Yk'dYj]dY[a‚f ]flj] dYkmfa)\Y\]k \] mfYeY_falm\ [mYdima]jYk] gZl]f\j~ YhYjlaj \] dY[gjj]khgf)\a]fl] ^‚jemdY \ae]fkagfYd [gehd]lY' ]klg ]k' ]f mfYZYk]^gjeY\Y [gf[mYljg eY_falm\]k \ae]fkagfYde]fl] af\]h]f\a]fl]k' im] hg\j~f k]jdYdgf_alm\' dYeYkY' ]d la]ehg q dY[Yj_Y ]d•[lja[Y* ;\]e~k' [geg dYkmfa\Y\]k \] dYklj]k hjae]jYk fg [YeZaYf' ZYklYj~lgeYj ]f [gfka\]jY)[a‚f ]d ]phgf]fl] \] A ]f dY^‚jemdY \ae]fkagfYd* ;k€' \]

?f ]kl] ƒdlaeg kakl]eY k] `Y \Y\g ]d fgeZj] \] MTZ_#<a$YdYmfa\Y\\] afl]fka\Y\ \] [gjja]fl]* FY mfa\Y\ \] [Yj_Y fg la]f] fgeZj]7 ]fYl]f[a‚f Y km^‚jemdY \ae]fkagfYd k] j]hj]k]flY hgj ]d k€eZgdg ,C R k*

JYjY `YddYjdYj]dY[a‚f ]flj] ]d ^jYfcdaf q ]d ,C R k' ZYklYj][mjjajY dY^‚jemdY \ae]fkagfYd6

U2'1s I8J 9 <&*D&*A

\] dYim] k] \]\m[]6

$ ,C > k $.9

( @j

PY #m*=AM?$

PY #m*=AMG$

k] \]\m[] im] dYem\Y\ \] hg\]j aeYfY\gj ]f ]d kakl]eY ]d][ljgkl~la[g'im] j]hj]k]flYj]egk hgj ]d k€eZgdg @jb[ex k' ]kl~ \Y\Y hgj6

q' ]f najlm\ \] U2'-Wq U2'0W'( @jb[e" k

( I]

- @j

- <ax k

- (

/x -,-,U3'-W.%Q%%%%

]

( <a > k . ] @j '****'/x ('-, @j*;f~dg_Ye]fl]' [geg ]d hgl]f[aYd ]d•[lja[g la]f] hgj ^‚jemdY \a)

e]fkagfYd6*' JYjY gtl]f]j dYkmjaatY\]k\]janY\Yk `Yq im] j][mjjaj YYd_mfY][mY)[agf im] da_m]dYeY_falm\ im] k] [gfka\]j] [gf gljY [mqYkmfa\Y\]k`YqYf ka\g qY \]^afa\Yk*NjYl]egk' hgj ]b]ehdg' \] `YddYjdYmfa\Y\ \])hg\]j aeYfY\gj' im] ]f ]d kakl]eY =AMG k] \]fgeafY ZP]^_PO #I]$*?f td kakl]eY fg jY[agfYdarY\g']d hg\]j aeYfY\gj ]f_]f\jY\g hgj mfY'[gjja]fl] j][lad€f]Y adaealY\Y]kl~ \Y\g hgj6

9j . +*(]%

dYmfa\Y\ eY_f•la[Y k]j~ ] n][]k e]fgj im] dY]d][ljgkl~la[Y*=gf ]klg im]\Y ]f [dYjgmfYhYjY\gbYim] `Y dd]nY\g\] [YZ]rYYdgk

^€ka[gk*Hg k] [gehj]f\] ]d im] dYjYr‚f ]flj] \gk mfa\Y\]k \] mfYeakeYeY_falm\' im] kgf [Yfla\Y\]k `geg_•f]Yk' n]f_Y ]phj]kY\Y ]f ^mf[a‚f\] dYn]dg[a\Y\ \] dYdmr]f ]d nY[€g*L]kmdlYhYjY\‚ba[g' hgj ]b]ehdg'

Page 104: Análisis dimensional

'%* ;HzFCMCM >CG?HMCIH;F

]d im] dYj]dY[a‚f ]flj] dYk\gk mfa\Y\]k \] [Yj_Y' ]d @j q ]d <a *k' im]\]Za]jY k]j mf fƒe]jg' j]kmdl] k]j a_mYdYmfYn]dg[a\Y\* Ng\g [gfkakl]]f im] dYk[gf\a[agf]k YjZaljYjaYkim] ^abYfdY[mYjlYmfa\Y\ k] `Yf]d]_a\g \] lYd eg\g im] dYj]^]ja\Y j]dY[a‚f k]Y a_mYdYdfƒe]jg im]ea\] \a[`Y n]dg[a\Y\ ]f ]d kakl]eY =AM*

?d hjgZd]eY \] `YddYjdgk^Y[lgj]k \] [gfn]jka‚f k] [gehda[Y [mYf\gk] ljYlY \] hYkYj\] dgkkakl]eYk []_]kaeYd]k Ydkakl]eY \] Aagj_a' hm]k[geg ]kl] ƒdlaeg ]k af[g`]j]fl] [gf dYk][mY[agf]k fg jY[agfYdarY\Ykfg k] hm]\]f Yhda[YjdYk ‚jemdYk\ae]fkagfYd]k* Jgj ]klYjYr‚f' [gfna]f]]^][lmYj ]d hYkg]f \gk ]lYhYk*Jjae]jg' \] mf kakl]eY =AM' ]d =AMG'hgj ]b]ehdg' YdGEM= fg jY[agfYdarY\g' q ^afYde]fl]' Ydkakl]eY \]Aagj_a' l]fa]f\g hj]k]fl] im] ]d [mdgeZagfg k] Ydl]jYYdjY[agfYdarYj*

?d hjae]j hYkgk] j]\m[] Y `YddYjdYjYr‚f ]flj] ]d <ax k q ]d [mdge)Zag*L][mjjaj]egk fm]nYe]fl] Y dY^‚jemdY \ae]fkagfYd6

dY[mYd'j][gj\Yf\g im]6

]6f 9 *(N+

]6"Y . -+-,)3[-.

#m*=AMG$

#m*GEM=$'

[gf\m[] Y6

# $)/ # $)- # $.]6f - H - c_ - 2]6"Y . - [e C_ - <a *k "

\] \gf\]6

- = 9 -,)- <a *M* U3'.W

OfY*n]r `YddY\YdYjYr‚f ]flj] ]d [mdgeZag q ]d <ax k' k] hm]\]f`YddYjdgk^Y[lgj]k \] [gfn]jka‚f hYjYlg\Yk dYkmfa\Y\]k im] fg k] Ydl])jYf hgj dYjY[agfYdarY[a‚fkaf e~k im] Yhda[YjdYkj]kh][lanYk ^‚jemdYk\ae]fkagfYd]k* ;k€' \]6

A(B9 D&*Ak] \]\m[]6

- ; . -,)- <a'

hgj dg im] ]d Zagl k] hm]\] ddYeYjOPNLYa[P]TZ%

FY mfa\Y\ \] hgl]f[aYd ]f ]d kakl]eY \] Aagj_a ]k ]d ngdlag*?f ]dkakl]eY =AMG [Yj][] \] fgeZj]' h]jg [geg dY^‚jemdY \ae]fkagfYd \]dhgl]f[aYd ]k6

'%+RPCC* ?F?=NLI G;AH?NCMGI

kmk€eZgdghm]\] k]j ]j_+<a *k' q j]kmdlY6

- F . -,4 ]j_+<a 6M*

FY ^‚jemdY \ae]fkagfYd \] dYafl]fka\Y\ ]d•[lja[Y ]k6

I6J . <=D&+A&*

q kmkk€eZgdgkhm]\]f k]j6 H+= ]f ]d kakl]eY \] Aagj_a q \af+<a" k]f ]d =AMG*=gf ]klg6

- H+= . -,2

\€f+<a 6k t - \af+<ax M*[ /* -,0

FYmfa\Y\ \] af\m[[a‚f eY_f•la[Y ]f ]dkakl]eY =AMG]k ]d_Ymkk#Ak$*?f ]d kakl]eY \] Aagj_a]k ]d l]kdY#N$*=geg dY ‚jemdY\ae]fkagfYd ]k6

I3J . =D&*A&*%

j]kmdlY6

- N 9 -,0 Ak'

\] eg\g im] mf l]kdY]k dg eakeg im] mf eajaY_Ymkk*FYk mfa\Y\]k \]d ^dmbg\] af\m[[a‚f' -(/$ kgf ]d o]Z]j #QZ$ ]f ]d

kakl]eY \] Aagj_aq ]d eYpo]dd #Gp$]f ]d =AMG*=geg6

k]j~6- QZ . -,4Gp*

Fgk hj][]\]fl]k ^Y[lgj]k \] [gfn]jka‚f nYd]f lYflg hYjY ]d kakl]eYGEMG fg jY[agfYdarY\g[geg hYjY]d kakl]eY \] Aagj_a*?f ]d [Ykg\]dgkn][lgj]k > q B `Yq im] j][mjjaj YdYk][mY[agf]k U0'1W*

=geg6I5J . <&+A%

dgkk€eZgdgk\] kmkmfa\Y\]k ]f dgkkakl]eYk fg jY[agfYdarY\gkhg\j€Yfk]j6 #4(X+$Y q <a *k+[e)$ [gf dg [mYd6

+6Q43:3: .35/6:376+4" !! $'

Page 105: Análisis dimensional

.-, ;HzFCMCM >CG?HMCIH;F RPDC* ?F?=NLIG;AH?NCMGI .--

q' ]f najlm\ \] U0'1W'l]fa]f\g hj]k]fl] im] dYke]\a\Yk ]kl~f ]f jYr‚fafn]jkY \] dYkmfa\Y\]k' dY*mfa\Y\ \] Aagj_a' nYd\j~6

>]k\] dm]_g'Yim]ddYk][mY[agf]k]f im] k‚dg]fljYf eY_falm\]k \] mfY[dYk]']d•[lja[Ykg eY_f•la[Yk' im]\Yj~f afYdl]jY\Yk*?f [YeZag' lg\Y ][mY)[a‚f im]' [geg dY\] FYhdY[]6

- 4(X+ . 03l „ -,)1 <a *^(NX+g

I8J 9 <&9D&9A

_. 3:W%

- "2(X#Y . -,)/ I]'

[gfl]f_Y YeZYk ]kh][a]k \] eY_falm\]k' l]f\j~ im] k]j eg\a^a[Y\Y*?klY ][mY[a‚f ]k n~da\Y[gf [mYdima]jkakl]eY [g`]j]fl]' hgj ]b]ehdg' [gf]d =AMG' ]f ]d im] * k] ea\] ]f Zaglkq 3 ]f _Ymkk*Mak] ima]j] e]\aj *[gf gljY mfa\Y\' `YZj~ im] afljg\m[aj mf NZPQTNTPY_P[L]k^T_Z im] k]\]fgeafY NZY^_LY_PPWPN_]ZXLRYl_TNL%q6

>]d eakeg eg\g' hYjY]d hg\]j aeYfY\gj6

k] gZla]f]6

P- 2WX . 03lx -,)/ I]' Q. Q 3WW'

q

g Za]f' kak] Y\ghlY ]d fgeZj] WPYe#F$hYjYdYmfa\Y\ \] hg\]j aeYfY\gj]f ]d kakl]eY \] Aagj_a6 ?f ]d kakl]eY \] AYmkkYq im] e]\aj * ]f 7]W^%q [geg6

- F 9 03l „ -,)/ I]*- <a . ] 7]W^%

4* Makl]eY\] AYmkk* k]j~ q . ]' q dYd]q \] FYhdY[]k] ]k[jaZaj~ Yk€6

>] dYk][mY[agf]k \]d [Yehg ]d][ljgeY_f•la[g ]k[jalYk ]f dY^gj)eY U0'-Whm]\] \][ajk] im] kgf [gjj][lYk hgjim] ]f ]ddYkfg k] `Y km)hjaea\g faf_mfY [gfklYfl] af\akh]fkYZd] fa Y•Y\a\g faf_mfY kmh]j^dmY*NYeZa•f dgk\gk kakl]eYk =AM' ]d ]d•[lja[g q ]d eY_f•la[g' e]j][]f k]j[Yda^a[Y\gk\] h]j^][lgk hgjim] YeZgk kgf [g`]j]fl]k [gf dYkj]^]ja\Yk][mY[agf]k*Fg eakeg hm]\] \][ajk] \]d kakl]eY \] Aagj_a'hm]k dYjYg€g)fYdarY[a‚f [gfkakl] ]f afljg\m[aj ]d ^Y[lgj 03l ]f Yd_mfYk][mY[agf]k' dg[mYd'kaZa]f [gehda[Y afƒlade]fl] ]d hjgZd]eY \] `YddYjdgk^Y[lgj]k \][gfn]jka‚f' fg Ydl]jYdY]kljm[lmjY \ae]fkagfYd*

Hg hm]\] \][ajk] dg eakeg \]d kakl]eY \] AYmkkim]' hgj \]k_jY[aY']k ]d im] k] mladarY]f [Ykalg\gk dgkdaZjgk\] @€ka[Yl]‚ja[Y* ?kl] kakl]eY]k mf `€Zja\g ]f ]d im] dYkeY_falm\]k A%h' *%a' 6%5%]' k] ea\]f [gfdYkmfa\Y\]k \]d kakl]eY ]d][ljgkl~la[g' ea]fljYk im] dYk3%8%8C:q uD*'

k] ea\]f [gf dYk\]d kakl]eY eY_f•la[g* Jgj ]kg k] ddYeYkakl]eY!eaplg*?k' hm]k' mf kakl]eY af[g`]j]fl] [gf dYk][mY[agf]k im] `]egk ddYeY\g[gjj][lYk q' hYjYhg\]j mladarY\g']k hj][akg afljg\m[aj ]f dYk][mY[agf]k[g]^a[a]fl]k hYj~kalgkim] dYk\]knajlƒYf lglYde]fl]* ?k \] ]kh]jYj im]'[gf dYY\gh[a‚f \]d kakl]eY \] Aagj_a' \]kYhYj]r[Yf ]klgk af[gfn]fa]fl]k'h]jg ]flj] lYflg fg `Yq e~k j]e]\ag im] kYZ]j [‚eg `Yf \] ]k[jaZajk]dYk][mY[agf]k \]d ]d][ljgeY_f]lakeg hYjY im] k]Y naYZd]]d kakl]eY \]AYmkk*

Q. Q 3WW']

Jgj ]kl] eakeg hjg[]\aea]flg k] \]em]kljY im]' hYjYhg\]j mladarYjdYmfa\Y\]k \] AYmkk'Yq im] ]k[jaZaj dYk][mY[agf]k \] GYpo]dd ]f dY^gjeY6

3I.4 < 19Y

\an 5Y . 03lh \an B . I

T L6 ( Y<jgl 9Y . 03l ) &)) jgl 4 .%% L_ $

[ L_ ]

g k]Y6\an 4 . 03lh \an < . I U4'-W

T L6 ( Y<jgl < . 03l ) &)) jgl 4 .%% ))

[ L_ ] L_

;hYj]fl]e]fl]' k] `Y dg_jY\g mfY kaehda^a[Y[a‚f ]f dYk^‚jemdYk'[gkYemq \]d Y_jY\g \] dgkeYl]e~la[gk' im] ]phda[Y]d •palg \]d kakl]eY\] AYmkk*>]k\] ]d hmflg \] naklY^€ka[g'dYkaehda^a[Y[a‚fla]f] ]d af[gf)n]fa]fl] \] im] [gf^mf\] > [gf ? q < [gf B* J]jg dg e~k _jYn] ]k im]'

Page 106: Análisis dimensional

?I 9 -7 U4'.W

.-. ;HzFCMCM >CG?HMCIH;F RPCC* ?F?=NLIG;AH?NCMGI .-/

]f dm_Yj\] dYk\gk [gfklYfl]k [YjY[l]j€kla[Yk\]d nY[€g' mfY \] [Yj~[l]j]d•[lja[g' ?Y' q gljY \] fYlmjYd]rYeY_f•la[Y' #*Fg' YhYj][] mfY lYf k‚dg'dY]' im] ]k \] €f\gd] e][~fa[Y* ?kl] ]k[Yegl]g ]k [YmkY\] im] em[`gk^€ka[gkk] gZklaf]f lg\Yn€Y ]f im] ZYklYflj]k mfa\Y\]k Z~ka[Yk'dYklj]ke][~fa[Yk*

?f ]d kakl]eY \] AYmkkk] aehgf]f Y dYkmfa\Y\]k Z~ka[Ykfg mfY'kafg \gk [gf\a[agf]k' YkYZ]j6

#m*AYmkk$'

;\eala‚ im] dgk e]ljgk q dgk j]dgb]k k] [gehgjlYf L`_ZXk_TNLXPY_P\]Y[m]j\g [gf ]ddYkP \ag hgj kmhm]klgim] dYafnYjaYf[aY\] dYn]dg[a\Y\\] dYdmr]jY mf ^]f‚e]fg fYlmjYd'q fg [gfk][m]f[aY \]d ]ehd]g \] j]dgb]k[gfljY€\gk q \] j]dgb]k YeY•Y\gk*

Hg ]k Yn]flmjY\g Y^ajeYj im] ka Fgj]flr fg `mZa]k] Y\ghlY\g ]feYdY`gjY ]d kakl]eY \] AYmkk'l]f\j€Yegk mfYl]gj€Y \] j]dYlana\Y\ daZj]\] dYkhYjY\gbYkim] YhYj][]f ]f dYl]gj€Y \] ?afkl]af q im]' emq hjg)ZYZd]e]fl]' `YZj€Y [gfljaZma\g em[`g e~k ]^a[Yre]fl] Yd hjg_j]kg[a]fl€^a[g*

J]jg ka]ehj] ]k la]ehg hYjYYZYf\gfYj ]d eYd [Yeafg' q [mYflg Yfl]ke]bgj* =geg \a[] MljYllgf #3.$' j]^aja•f\gk] Ydkakl]eY \] AYmkk6w[mYflgYfl]k k] \]hgf_Y Ydna]bg ^Yngjalg' lYflg e]bgj hYjYhgf]j ^af Y mfY^m]fl] aff][]kYjaY \] [gf^mkagf]ky*

q [geg' k]_ƒf dYl]gj€Y \] GYpo]dd)B]jlr' dYn]dg[a\Y\ \] hjghY_Y[a‚f\] dYkgf\Yk ]d][ljgeY_f•la[Yk ]f ]d nY[€g ]kl~ \Y\Y hgj6

] 9 d+P?g^-*g' U4'/W

faf_ƒf kakl]eY []_]kaeYd hg\j~ k]j [g`]j]fl] [gf ]klY ][mY[a‚f q kYlak)^Y[]j dYk[gf\a[agf]k U4'.Wkafg im]' \Y\g ]d []fl€e]ljg' `YZj~ im] ]d]_ajdYmfa\Y\ \] la]ehg \] eg\g im] dYe]\a\Y \] dYn]dg[a\Y\ \] dYdmr]kl• \Y\Y hgj ]d fƒe]jg d* JYjY im] k]Y naYZd]]d kakl]eY \] AYmkk'`Yq im] afljg\m[aj ]f U4'/Wmf [g]^a[a]fl] hYj~kalg' ]' [gf dg im] im]\Yj]\m[a\Y YdYa\]fla\Y\ ] . [*=geg k] n]' ]d kakl]eY \] AYmkk]k[Yegl]Y'hgj Yjl] \] ZajdaZajdgim]'mfY \] dYke~k aehgjlYfl]k d]q]k fYlmjYd]k*

FY \]k\a[`Y\Y Y\gh[a‚f \]d kakl]eY \] AYmkkY l]fa\g ^YlYd]k[gf)k][m]f[aYkhYjYdY@€ka[Yl]‚ja[Y* ?f dgk^]f‚e]fgk \]Za\gk YdYkY[[agf]kemlmYk]flj] [gjja]fl]k ] aeYf]k afl]jna]f] lYf k‚dg ]d egnaea]flg j])dYlang'dg im] ]pa_] im] dYk][mY[agf]k fg k] Ydl]j]f Yd[YeZaYj ]d kakl]eYaf]j[aYd*Jgj lYflg' ka dYk][mY[agf]k k] ]k[jaZ]f Y dYeYf]jY \] AYmkk'k]j~ hj][akg' [Y\Yn]r im] k] [YeZaY\] kakl]eY af]j[aYd' Ydl]jYjdYkmfa\Y)\]k \] dgf_alm\ q \] la]ehg \] eYf]jY im] dYe]\a\Y \] dYn]dg[a\Y\ \]dYdmr k]Y a_mYdYdfƒe]jg hYj~kalg ] im] ^a_mjY]f ]ddYk*{klY ]k' kaf\m\Y' dYjYr‚f hgj dYim] Fgj]flr k] nag gZda_Y\gY afljg\m[aj ]d _TPX[ZWZNLW]f kmk][mY[agf]k \] ljYfk^gjeY[a‚f q' [gf _jYf Y[a]jlg' dg[gfka\]j‚*[geg mf Yjla^a[ageYl]e~la[g im] fg l]f€Y e~k gZb]lg im] dg_jYj dYafnYjaYf[aY\] [*

>]k\] fm]kljg hmflg \] naklY']d Yjla^a[ag\] Fgj]flr \]Z] YljaZmajk]Ydhjgh‚kalg \] [YeZaYj dY mfa\Y\ \] dgf_alm\ q \] kaf[jgfarYj dgkj]dgb]k \] eg\g im] dYe]\a\Y \] ] j]kmdl] afYdl]jY\Y' q `]egk \]egk)ljY\g #3-$im] ]klg k] dg_jY_jY[aYkYdY[gfljY[[a‚f \] dgke]ljgk' im] ]kmf ^]f‚e]fg fYlmjYd'q Y XLYTZM]L^`][`Yk [gf dgk j]dgb]k*=geg ]kkYZa\g' ?afkl]af lge‚ dYk][mY[agf]k \] Fgj]flr [geg ZYk]\] kml]gj€Y*

5* >ak[jaeafY[a‚f \] dYk\ae]fkagf]k \]d ]khY[ag*

FYk eY_falm\]k ?' >' < S B kgf n][lgj]k' hgj dg im] hm]\] `YZ]j n]flYbY]f \aklaf_maj dYklj]k \ae]fkagf]k \]d ]khY[ag Yd^gjeYj dYZYk]*

>] dY][mY[a‚f n][lgjaYd U-'-Wk] \]\m[] hYjY [Y\Y mfY \] dYk[gehgf]f)l]k \] 6/

+7*6T 9 ) G9 -' .' /'

A

q k]j~6

JYjY `YddYjdYk\ae]fkagf]k \] dYk[gehgf]fl]k \] 5%hYjlaj]egk \] dY*

][mY[a‚f6\an > 9 \%

\gf\] \ ]k dY\]fka\Y\ \] [Yj_Y]f ]d hmflg [gfka\]jY\g* ;k€ j]kmdlY6

FY ^‚jemdY \ae]fkagfYd \] dYh]je]YZada\Y\ ]d•[lja[Y j]kmdlYk]j6

FY d]q \] FYhdY[]6^9dddV<

\Y' hYjY dgk [gehgf]fl]k \] dY^m]jrY6

\] \gf\]6

Page 107: Análisis dimensional

JgdYjarY[a‚f ]d•[lja[Y6@j . 5 & PL6

Gge]flg ]d•[lja[g6 XP & AW

I@J . <&+A

IXPJ . <A

RPCC* ?F?=NLIG;AH?NCMGI .-1.-0 ;HzFCMCM >CG?HMCIH;F

jgl 5 . -'

\] [gfn]fagk' h]jg kafgk Yl]f]egk Ydka_fa^a[Y\g\] dgkn][lgj]k 3c 8%hjg[]\]j€Y Yl]f]jk] Y dYkka_ma]fl]k\]^afa[agf]k6

>] dY][mY[a‚f \] GYpo]dd6

]f im] G]k dY\]fka\Y\ \] [gjja]fl] ]f ]d hmflg [gfka\]jY\g' j]kmdlY6

L9m L9m ')) ) )) 9tD*6"

LHT LHm

CeYfY[a‚f6 G ) C(C < ) B^Fg

]f n]r \]6 G" < ) ^FgB

I=J . <&9D&9A

I="J 9 =D&9A&W'q [geg6

?d ege]flg \] mf \ahgdg eY_f•la[g j€_a\g k] \]^afaj~ [geg ]d n][lgjim]' emdlahda[Y\gn][lgjaYde]fl] hgj <' ]k a_mYdYdhYj \] ^m]jrYk'I' im]Y[lƒY kgZj] ]d \ahgdg Ydk]j [gdg[Y\g ]f mf [Yehg eY_f•la[g mfa^gje]6

k] la]f]6

FYk h]je]YZada\Y\]k ]6 q ^F kgf l]fkgj]k im]' ]f e]\agk ak‚ljghgk' \]_]f]jYf]f ]k[YdYj]k*J]jg ]f ]d [Ykg \] ^F' [Y\Y ]d]e]flg \]d l]fkgj [gfk]jnY km\ae]f)

ka‚f* =geg 3_ . Q<^8^%k]j~6

Gge]flg eY_f•la[g6 I ) Uee<W

]f n]r \]6 I AH X9J

IXXJ 9 <+D&9A

IX" XJ 9 <,=D&9A&W'

$#" 5>BGCMN@ALLA?NG@>KC>L"

Fgk ^Y[lgj]k \] [gfn]jka‚f \] dYkeY_falm\]k k][mf\YjaYkk] gZla]f]f^~[ade]fl] YhYjlaj \] kmk ‚jemdYk\] \]^afa[a‚f*

M] ]ehd]Yf ]f ?d][ljgeY_f]lakeg _jYf fƒe]jg \] eY_falm\]kk][mf\YjaYk'\]^afa\Yk [gfn]f[agfYde]fl] e]\aYfl] ][mY[agf]k ]flj] e])\a\Yk* 0 [gflafmY[a‚f \Yegk mfY daklY\] dYke~k aehgjlYfl]k' [gf km][mY[a‚f \] \]^afa[a‚f q km^‚jemdY \ae]fkagfYd6

$$" 7MKHLLCLMAF>L@CFAGLCHG>EAL"

0 l *E &$ < 7m gjg O==dIf6 . %%%%

& O:UO_

Hm]kljYk fgjeYk fgk `Yf [gf\m[a\g Y mf kakl]eY \] ^‚jemdYk \ae]fkagfYd]kim] hm]\] ddYeYjk][d~ka[g' hgjim] [gaf[a\] [gf ]d mkY\g hgj dgk^mf\Y\gj]k \]d;f~dakak \ae]fkagfYd' ]flj] dgk im] [alYj]egk hgj n€Y \] ]b]ehdg Y D]Yfk q Y<m[caf_`Ye* J]jg' \]k\] dgk gj€_]f]k \] dYkl]gj€Yk ]d•[lja[Yk' k] km[]\]f dgkafl]flgk \] j]^]jaj dYkeY_falm\]k ]d][ljgeY_f•la[Yk Y mfY ZYk] [gfklalma\Y hgjeY_falm\]k e][~fa[Yk ]p[dmkanYe]fl]* FY [gkY ]eh]r‚ [gf AYmkk#-40,$' im]ljYl‚ \] ^mf\aj ]f mfg kgdgdgkkakl]eYk ]d][ljgkl~la[g q ]d][ljgeY_f•la[g' ka_ma‚[gf B]jlr #-45,$' q [gflafƒYf YhYj][a]f\g fm]ngk kakl]eYk [gf mfY ZYk]\] lj]keY_falm\]k e][~fa[Yk Y dgk im] [Y\Y Ymlgj YljaZmq] \]l]jeafY\Yk n]flYbYk*?flj] dgk e~k eg\]jfgk [alYj]egk dgk \] ;hjYar #3/$' >af_d] #/0$' ?kfYmdl)

J]dl]ja] #30$q <]j_]j #31$*?f dg \] emladYj dYZYk] `Yq eYfg daZj]' hm]k k] hm]\] YljaZmajY [mYdima]j

eY_falm\ ]d][ljgeY_f•la[Y' Y dY[Yj_Y ]d•[lja[Y' hgj ]b]ehdg' dY^‚jemdY \ae]f)kagfYd im] [Y\Y mfg l]f_Y hgj [gfn]fa]fl]' kaf im] ]ddg [gf\mr[Y Y faf_ƒfYZkmj\g* J]jg dgk kakl]eYk Yk€gZl]fa\gk kgf af]^a[Y[]k' hgjim] YdemladYj dYZYk] ]k hgkaZd]^gjeYj egfgeagk im] ]f YhYja]f[aYla]f]f \ae]fka‚f fmdYq ]fj]Yda\Y\ fg' dg im] Y[Yjj]Y mfY aehj][aka‚f ]f ]d j]kmdlY\g' k]_ƒf `]egk hm]klg

\] eYfa^a]klg [gf fme]jgkgk ]b]ehdgk*?f ]d kakl]eY ]d][ljgkl~la[g k] \]khgbY \] km\ae]fka‚f Y dYh]je]YZada\Y\

]d•[lja[Y' 3 q ? j]kmdl]f `geg_•f]gk* L]kmdlY Yk€hYjY dY [Yj_Y dY^‚jemdY6

Jgl]f[aYd ]d•[lja[g6 _jY\ F K & 6

=YhY[a\Y\69 C <E

: &l] * B OE]kak f[aY6 .%%".,

@m]jrY]d][ljgegljar6 7 & (#'F & :B I7J . <+=D&+A&W

BYq \ak[mkagf]kY[]j[Y \] [‚eg \]Z] \]^afajk] ]d ege]flg \] mf ae~fq dYkeY_falm\]k [gf •dj]dY[agfY\Yk*FYhgd•ea[Y ]k ZYd\€Yhgjim] k] ljYlY

Page 108: Análisis dimensional

IPJ . Uu7*W. <&9D%

RPdC* ?F?=NLIG;AH?NCMGI .-3.-2 ;HzFCMCM >CG?HMCIH;F

B]jlr hjghmkg mf kakl]eY ]f ]d im]6 $%" -HG@AGL>@HKIE>GH"

dg im] gZda_YY afljg\m[aj mf [g]^a[a]fl] hYj~kalg ]f U.'1W*?f dYkaffgnY[agf]k j][a]fl]k' km]d] kmhjaeajk] dY[gfklYfl] ]d][ljgeY_f•)

la[Y' hgj dg im] k‚dg `Yq daZ]jlY\ ]f dY^‚jemdY \ae]fkagfYd \] mfY eY_falm\*B] Yim€Yd_mfgk]b]ehdgk6

=gf dgk\Ylgk6C #~j]Y\] [Y\Y YjeY\mjY$'O #\aklYf[aY]flj] dYkeak)eYk$' ] #h]je]YZada\Y\ \]d \a]d•[lja[g$' P I #[YhY[a\Y\$'hm]\]f ^gjeYjk]\gk egfgeagk ha6

;hjYar *

?kfYmdl)J]dl]ja] **

<]j_]j *

IAJ . <=D&9 #€eh]lm$

IPJ . -' IAJ . <,(+=*(+D&9

IAJ . <,'

J C O 4

< ). . - "(= ) - I I )-D . I I .A . I I .

fa - )- - ) -f' I ) -+. - I

PC !Q"&?1&N[O

L]]ehdYrYf\g ]f dYk^‚jemdYk \ae]fkagfYd ]k [gehd]lYk \] dgk v v / S 0IAJ hgj mfY ^‚jemdY \ae]fkagfYd e][~fa[Y [mYdima]jY'hm]\] ]d d][lgj ^gjeYj[mYflgk kakl]eYk \ae]fkagfYd]k ima]jY*

Ng\Yn€Y im]\Yf ^€ka[gkim] ghafYf im] dYk\ae]fkagf]k \Yf dY]k]f[aY \]dYkeY_falm\]k' q ]f ]klY [j]]f[aY k] ZYkYf hYjY Y^ajeYj im] kmkj]kh][langkkakl]eYk kgf hjanad]_aY\gk*;k€' <]j_]j YljaZmq] _jYf aehgjlYf[aY Yd`][`g \]im]' [gf kmkfgjeYk' dYl]fka‚f ]d•[lja[Y' g hgl]f[aYd' l]f_Y dYeakeY \ae]fka‚fim] dYl]fka‚f e][~fa[Y' q ;hjYar Y^ajeY im] afl]fka\Y\ \] mfY [gjja]fl] P^ WLXT^XL NZ^Lim] mfY ^m]jrY' q YljaZmq]f\g Yd[mdgeZag dYeYkY -,5 _jYegk'dd]_YYdY[gf[dmka‚f \] im] mf Yeh]jag nYd] lYflg [geg dY\•[aeY hYjl] \] mfY\afY* ; lg\Yk ]klYk hjghgka[agf]k [YZ] gZb]lYj im]' ka dY^‚jemdY \ae]fkagfYd[gehd]lY fY\Y \a[] j]kh][lg \] dY]k]f[aY \] dYkeY_falm\]k' e]fgk af^gjeY[a‚fk] dg_jYj~ lg\Yn€Y [gf ZYk]k[Yhja[`gkYe]fl] emladY\Yk*

Madgk hdYfgk kgf adaealY\gk' dY^mf[a‚f \]k[gfg[a\Y lgeYj~ ]d nYdgj[gjj]khgf\a]fl] YO+(C 9 ,' q' kYdngmf ^Y[lgj fme•ja[g' j]kmdlY6

)1 PC 'O

?d kakl]eY hjghm]klg hgj >af_d] e]j][] [ge]flYjag YhYjl]* JYjla]f\g \]dY`ah‚l]kak \] im] dYk\ae]fkagf]k `Yf \] \]\m[ajk] \] dgke•lg\gk \] e]\a\Y'YljaZmq] Y dY[Yj_Y dYeakeY \ae]fka‚f im] Y dY^m]jrY' [gf dg im] j]kmdlY'k]_ƒf k] n] ^~[ade]fl]6

;\]e~k' ]d ;f~dakak\ae]fkagfYd h]jeal] Y^ajeYjim] ]f [gf\]fkY\gj]khdYfgk_]ge•lja[Ye]fl] k]e]bYfl]k' Ymfim] l]f_Yf \ae]fkagf]k ^afalYk'dY[YhY[a\Y\ ]k hjghgj[agfYd LCTO'

=gf dY ZYk] emladY\Y' [mYdima]jYim] k]Y dY^‚jemdY \ae]fkagfYd im] k]Y*ljaZmqYYmfY \] dYkeY_falm\]k ]d•[lja[Yk' hm]\]f j]kmdlYjegfgeagk ]khmjagk*Ma m]jYd€[alg`Y[]j' hgj ]b]ehdg' U?W. <?=ZDZ%[geg hj]l]f\]f' ]flj] gljgk'<ja\_eYf q ?kfYmdl)J]dl]ja]' `mZa]jY j]kmdlY\g

U?W. <&9=D&+'

Mmhgf] dm]_gim] ]d n][lgj B la]f] \ae]fka‚f fmdY#ka m]jY [gfk][m]fl] [gf kme•lg\g \]Za]jY \Yjd] dY^‚jemdY \ae]fkagfYd =D&,$ q' kaf ]phda[Yj [‚eg' kY[YdY[gfk][m]f[aY \] im] dYh]je]YZada\Y\ eY_f•la[Y `Y \] l]f]j [geg ^‚jem)dY\ae]fkagfYd

q ]d ;f~dakak \ae]fkagfYd fg h]jealaj€Y Yn]ja_mYj[‚eg I \]h]f\] \] ?*

Uu7*W. =&9DC% $&" /GAKBU>IHMAG?C>E@AE>L?>KB>LAET?MKC?>L"[gf dg [mYd\]\m[]6

?k kYZa\g im]' ]f lg\g kakl]eY [g`]j]fl]' ]d hjg\m[lg ?u7"]k a_mYdY dYafn]jkY\]d [mY\jY\g \] dYn]dg[a\Y\ \] dYdmr*?d j]kmdlY\g Y im] dd]_Y>af_d] ]k' hgj[gfka_ma]fl]' afY[]hlYZd] q ]ddg ZYklYhYjY \]kY[j]\alYj km e•lg\g ZYkY\g ]fdY@adgkg^€Ygh]jY[agfYd*

JYjY mfY ]k^]jY \] jY\ag ]%mfa^gje]e]fl] [Yj_Y\Y [gf mfY\]fka)\Y\ \] [Yj_Y\%]f mf e]\ag \] h]je]YZada\Y\ ]' ]d ;f~dakak\ae]fkagfYd[gf dYZYk][gehd]lY \Y' hYjYdY]f]j_€Y hgl]f[aYd6

U?u7"W. <&9D'

Page 109: Análisis dimensional

.-4&

;HzFCMCM >CG?HMCIH;F pnjj* ?F?=NLIG;AH?NCMGI .-5

im] ]kl~ \] Y[m]j\g [gf ]d nYdgjim] k] gZla]f] Yd[Yd[mdYj\a[`Y ]f]j_€YmladarYf\gdYd]q \] =gmdgeZ #32$*

=gf ]d kakl]eY \ae]fkagfYd hjghm]klg hgj >af_d] j]kmdlY6

-1* =Yehg \] mf \ahgdg ]d•[lja[g*

Of \ahgdg ]kl~ [gfklalma\g hgj \gk [Yj_Yka_mYd]kq \] ka_fg [gfljY)jag' # A q ) A%im] g[mhYf k]f\gk ngdƒe]f]k [mqYk\ae]fkagf]k daf]Y)d]kkgf emq h]im]•Yk ]f [gehYjY[a‚f [gf dY\aklYf[aY' W%im] dgkk]hYjY*N‚e]k] [geg ]b] hgdYjdYj][lY im] mf] YeZYk [Yj_Yk'q [geg gja_]f]d hmflg e]\ag \]d k]_e]flg W'?d hgl]f[aYd ]f mf hmflg \]h]f\]j~ \]kmk[ggj\]fY\Yk hgdYj]k']%6>$\] dYh]je]YZada\Y\ \]d e]\ag' \] A q \] W'=gf ]klYkeY_falm\]k j]kmdlYfdgkka_ma]fl]kegfgeagk ha6

kgdm[a‚f im] [gfla]f] ]d egfgeag ]khmjag PQ\]'

-0* Cf]j[aY \] dY]d][lja[a\Y\* FP],M % S

W&A! ,ML . 6>$

M]YmfY[Yj_Y'A%\akljaZma\Y]f mfY]k^]jY \] jY\ag \' ;d [gemfa[YjC]mfYn]dg[a\Y\' a%k] [j]Y mf [Yehg ]d][ljgeY_f•la[g' [gf ]d [gfka_ma]fl][gfkmeg \] ]f]j_€Y* Ng\g hYkY[geg kadY[Yj_Yhgk]q]k] mfYeYkY' X%[mqg nYdgj\]h]f\]j~ \] dYkh]je]YZada\Y\]k' ] ? ^F' g dg im] ]k dgeakeg'\] ] q \] dYn]dg[a\Y\ \] dYdmr' ]6

q `YZj~ \] k]j6

E 9 78 [h #t' 6>" ]j ]

AWF . )-bu#-R$*

P]+

X A ] ]6 ]

< I I ( "( (= ( I I % ( ID I I % ( . IA I ( I . I

&20 ( ). . ( (

ab1&

]

A+X18&&'

N+P/]

=gf ]d kakl]eY \ae]fkagfYd \] ;hjYar j]kmdlY6

X A ] ]6 ]

< I ( ( %( (= ( ( I ( ID I % ( % ( I I

&20 ( ). . ( (&2' I % ( ( ( (

JYjY hmflgk emq Yd]bY\gk'E `Y \] k]j hjghgj[agfYd Y W%hm]k \m)hda[YjdY\aklYf[aY ]flj] dYk[Yj_Yk]imanYd]Y hgf]j \gk \ahgdgk' mfg Y

[gflafmY[a‚f \] gljg* Jgj lYflg6

>] dY mf[a‚f -bu#-R$k] hm]\] Y^ajeYjim] `Y \] k]j e~paeY hYjYCR. I'? im] -bu#-R$9 )-bu#3l ) CR$7-bu#3l+.$9 I*

FY kgdm[a‚f [gehd]lY' hYjYG- - ]%]k6

AWE . %%[gk 6>&

P]+

-2* ?d][lj‚e]ljg \] FahheYff*

P YhYj][] ]d egfgeag &2' . NP/](A% im] ]k ]khmjag hgjim] la]f] \ae]fka‚f fgfmdY]f dYZYk][gehd]lY*

?klgk ]b]ehdgk ZYklYfhYjYhjgZYj im] \]Z]f \]k][`Yjk] lg\gk dgkkakl]eYk]t im]' k] lgeY mfY ZYk] \] lj]k eY_falm\]k e][~fa[Yk hYjY j]hj]k]flYj dYk\ae]fkagf]k \] dYkeY_falm\]k ]d][ljgeY_f•la[Yk*

M]_ƒf dYl]gj€Y \] B]de`gdlr' ]flj] ]d e]j[mjag q mf ]d][lj‚dalg k]^gjeY mfY[YhY]d•[lja[Y \gZd] [gf mf kYdlg\] hgl]f[aYd #^m]jrY]d][ljg)egljar$ E

?! ; \a[`Y [YhY[gjj]khgf\] mfY [YhY[a\Y\ hgj mfa\Y\ \] km)

h]j^a[a]' im] j]hj]k]flYj]egk hgj V' ?f ]d ]d][lj‚e]ljg [YhadYjk] Y_j]_YY E

Z]d hgl]f[aYd im] k] ljYlY \] e]\aj' q k] \]l]jeafY dY\akdg[Y[a‚f' W%

im] ]d [YeZag -[j ]ph]jae]flY\g hgj dYl]fka‚f kmh]j^a[aYd\]l]jeafY]f ]d e]fak[g \] e]j[mjag* ?f ]d nYdgj\] Waf^dmaj~'Y\]e~k' ]d h]kg ]kh])[€^a[g\]d e]j[mjag' a 9 h_' q ]d jY\ag' ]%\]d [YhadYj*

Page 110: Análisis dimensional

RPCC* ?F?=NLIG;AH?NCMGI ''&''% ;HzFCMCM >CG?HMCIH;F

Mak] Yhda[Y]d ;f~dakak\ae]fkagfYd Ylg\Yk dYkeY_falm\]k e]f[agfY)\Yk' k] dd]_Yj~Ymf j]kmdlY\g]jj‚f]g' hgjim] ]flj] ]ddYkfg `Yq mfY'kafgnYjaYkj]dY[agf]k' Y kYZ]j6

d*Y ?d [YeZag im] ]ph]jae]flY dYl]fka‚f kmh]j^a[aYd]kl~ \]l]jea)fY\g hgj ]d hgl]f[aYd Yhda[Y\g'E%q hgj dY[YhY[a\Y\ hgj mfa\Y\ \] km)h]j^a[a]' V%hm]k YeZYk eY_falm\]k \]l]jeafYf dY\]fka\Y\ \] [Yj_YY[memdY\Y]f dYkmh]j^a[a]*?d ;f~dakak \ae]fkagfYd \Y6

;d j]kgdn]j ]kl] hjgZd]eY `]egk l]fa\g hj]k]fl] dYj]_dY\]d v 0' [YhalmdgPCC*k]_ƒf dY[mYdk‚dg k] \]Z]f lgeYj ]f [gfka\]jY[a‚f [Y\Y n]r dYkeY_falm\]k\] dYkim] k] hm]\Y Y^ajeYjim] mfY\] ]ddYk]k ^mf[a‚f \] dYkj]klYfl]k* ?kfYmdl)J]dl]ja] ljYlY kaemdl~f]Ye]fl] dYk[m]klagf]k d*! P .*!' [gf dg im] dd]_YY dY*

]phj]ka‚f6

im] ]k afY\eakaZd]*

>'*[j V E

< I ") '= - ) - (D "' ' "'A I ' % (

-"- ( % ( "'

t[j . VF+g " g#' U-2'-W

$)" .AGLC@>@@AAGAKBU>AGAE?>FIH AEA?MKHF>BGTMC?H"

?d [Yehg ]d•[lja[g ]f [mYdima]jhmflg \]d ]khY[agim]\Y \]^afa\g hgj]d n][lgj ?* ?d e]\ag afl]jn]f\j~ hgj kmh]je]YZada\Y\ q' hgkaZd]e]fl]'hgj dYn]dg[a\Y\ \] hjghY_Y[a‚f \] dYdmr*JYjY Yn]ja_mYj[‚eg \]h]f\]dY\]fka\Y\ \] ]f]j_€Y \] dYkj]^]ja\Yk eY_falm\]k k] hjg[]\] [geg ka_m]6

,)g[1 )*& ]

U-2'.W

(P 6 ]6 ]

< % ( ( "( (

= ( ( % ( ID "' "' ' %(

A I % ( . I

-"- ( "' % ( I

`P . )*p6+'

.*Y ?d [YeZag gL hjgng[Y mf [YeZag d[ ]f dYhj]ka‚f \]d e]j[mjag\Y\g hgj6

/*Y ?kl] [YeZag \] hj]ka‚f ]k [YmkY\] im] ]d e]fak[g ]ph]jae]fl]mfY \akdg[Y[a‚f im] \]h]f\] \]d h]kg ]kh][€^a[g' a0

JYjY ]d [Yehg eY_f•la[g k] hjg[]\] \] eg\g Yf~dg_g6

d[_&0?+&%G

U-2'/W

(X 9 u*l* ]

< %( % ( ( (

= ( I ( ID "' %( I % (

A I ( "' I

&!' ( "' % ( I

EX 9 )+h;'9+'

FY l]gj€Y \Y '- 9 9. 9 &$'#

=geZafYf\g dYk]phj]kagf]k U-2'-'. P /Wj]kmdlY6

W1 9Q F+ "g#'\[R d F

' g

FY l]gj€Y [gehd]lY #n•Yk]'hgj ]b]ehdg' JYdY[agk$#33$'[gf\m[] Y6

V # E #+gL 9 ))) F+ K)KK *$ F !

$*" 7G@>LAEA?MKHF>BGTMC?>L"

M]_ƒf dYl]gj€Y\] GYpo]dd'dYdmr]kl~ ^gjeY\Y hgj gf\Yk ]d][ljgeY_)f•la[Yk ]f dYkim] dgkn][lgj]k ? P B' im] [g]pakl]f ]f lg\g hmflg Yd[Yf)rY\g hgj dYkeakeYk' ]ph]jae]flYf [YeZagkh]ja‚\a[gk' im] k] hjghY_Yf\] mf eg\g Yf~dg_gY dYkgk[adY[agf]kY[ƒkla[Yk]f mf e]\ag ]d~kla[g*;\]e~k' dYkgf\Yk ]d][ljgeY_f•la[Yk ]b]j[]f mfY hj]ka‚f Ydj]^d]bYjk]

q' hgj lYflg'

Page 111: Análisis dimensional

((( 9FyDAKAK <Aa"Y=FKAGF9DPNAA) =D=;LJGE9?F=LAKEG (()

hdWgZXjVafj^ZgeVgZYXdcYjXidgV)=hidh XdcdX^b^ZcidhgjY^bZciVg^dhYZaViZdg}VZaZXigdbV\c|i^XVYZaVajo&WVhiVceVgV]VXZgVa\jcVhegZY^XX^d(cZh XdcVjm^a^dYZa9c{a^h^hY^bZch^dcVa)

V$ ERYNPVo[R[a_R= f ! =cigZ ZhidhYdhkZXidgZhXdZm^hiZciZh]VYZ]VWZgjcV gZaVX^•cfjZ h•ad ejZYZ YZeZcYZgYZaVheZgbZVW^a^YVYZhZ5M ]%9YZabZY^d)=a 9c{a^h^hY^bZch^dcVaXdcYjXZcbZY^ViVbZciZV5

Y$ 9R[`VQNQ QR YNR[R_TnN) ;dbd aVYZch^YVYYZZcZg\}Vi^ZcZaVb^hbV Y^bZch^•c fjZ aVegZh^•c&WVhiVg{XVbW^VgZa [VXidgcjb|g^XdZc R,3&.T5

()A/&*$$

PR,3&/T

R,3&,B

Z$ >[R_PVNQRYNYbg) =a fjZ aVhdcYVhZaZXigdbV\c|i^XVhhZVcXVeV(XZhYZZ_ZgXZgjcV egZh^•cgZkZaVfjZ edhZZc}beZij& MidYd eVhVXdbdh^Zc XVYVejcid YZaVdcYV]jW^ZhZjcV YZch^YVYYZbVhV&e&YVYVedg5

=hiV gZaVX^•cedcZ YZbVc^[^ZhidfjZ XjVafj^ZgdigVbV\c^ijY dWhZgkV(WaZZc aVgVY^VX^•c]V YZYZeZcYZgYZ4# Z5 M ]%9%

()H 7 ]!4# 6# Z$ 7 Gh (.("

2R,3&0T

:VhiV Y^hXg^b^cVgaVhigZh Y^bZch^dcZhYZaZheVX^deVgVedYZg YZYjX^gfjZadh kZXidgZh= n @ ]Vc YZ hZgeZgeZcY^XjaVgZhZcigZ h})=c Z[ZXid6h^ hZ idbVZaZ_ZPa Zc aVY^gZXX^•cYZ@&hZg{=- 1 @V 1 G&Q aVXdbedcZciZ =a ]VWg{YZXVaXjaVghZXdc Zah^\j^ZciZ XjVYgd&Zc Za fjZ [^\jgVc adh ZmedcZciZh Y^bZch^d(cVaZhdWiZc^YdhZc Zas /)

DVXdbeVgVX^•cYZR,3&/TM R,3&0TYV5

=a @A R CE(

97 * ' * ' * *9- G G ' * *9) G G '* ' *: * G ' * *@ %( ' * ( GD ' * * ( %(

2i, G G G G

edg ad fjZ&V jcV ZcZg\}VgVY^VciZJ' XdggZhedcYZg{jcV bVhV^cZgX^Va5

JZ5((i4-" R,3&1T

ejZh aViZdg}VXdbeaZiVXdcYjXZV +1 1 a)=hiV gZaVX^•c]V h^Yd\ZcZgVa^(oVYVedg =^chiZ^cVidYVhaVhZheZX^ZhYZZcZg\}V)

9a igViVgYZ[dgbVg jc bdcdb^d e^&gZhjaiVcZXjVX^dcZhcXdbeVi^WaZh&ad fjZh^\c^[^XVfjZ =a Zh^cYZeZcY^ZciZYZ@A&n Xdbd =a 7 G h^@A7 6T 7 6

-7 G&

]VWg{YZhZg=a 1 G VjcfjZ @A$G)#+" 4> L>AF>@FVINTLHF@>@JHJ CBIVHBIJJIAOG>NJLFJ"

W$ IRY\PVQNQQR]_\]NTNPVo[) Hdgad fjZ VXVWVbdhYZYZX^g&]VWg{YZhZg5Z7 ]!4# Z&]%9"#MVaVea^XVgZa9c{a^h^hY^bZch^dcVagZhjaiV5

2-P5(()N

R,3&-T

;jVcYd nV HaVcX`]VW}VYZhXjW^ZgidZabZXVc^hbd YZZb^h^•c YZ)aq ZqZg\}VgVY^VciZZ ^cigdYjX^Ydhj XdchiVciZYZVXX^•c&Vea^X•BZVch#1$Za9c{a^h^hY^bZc(h^dcVaV aVgVY^VX^•ci|gb^XV Vedn{cYdhZ Zc aViZdg}VZaZXigdbV\c|i^XVZ ^\cd(gVcYdaVZm^hiZcX^VYZY^X]VXdchiVciZ)Kjejhd fjZ aVegdYjXX^•cYZaVhdcYVhZaZXigdbV\c|i^XVhZgVYZW^YVV aV Zb^h^•c YZ ZaZXigdcZhn igVi• YZ qkZg^\jVgZakVadgYZ aVZcZg\}VY 8%%%L 8%%%#XdggZhedcY^ZciZVa ^ciZgkVadL 8%%%#Zc [jcX^•c YZaViZbeZgVijgV) @^od ^ciZgkZc^gZc Za egdWaZbVaV XdchiVciZ YZ :daiobVcc #fjZ|a aaVbVXdchiVciZYZadh\VhZheZg[ZXidh$&aVbVhV&Z' n aVXVg\V&Z&YZaZaZXqg•c&n aVhXdchiVciZhMU n Z YZakVX}d)9ea^XVXdggZXiVbZciZZa9c{a^h^hY^bZc)haGcq,Xdc jcV WVhZYZX^cXdbV\c^ijYZh& 9#:# @#1 n R' n dWi^ZcZigZh bdcdb^dh ea5

9 WZcZ[^X^dYZR,3&,M-T&XjVafj^ZgbV\c^ijY dWhZgkVWaZZc aVgVY^V(X^•cedYg{edcZghZZc [jcX^•c YZ4# 6 Q P)

Z$ C_R`Vo[ QRYN_NQVNPVo[);dc aVhbV\c^ijYZh ]' :' = Q Z&h•adejZYZ [dgbVghZjc bdcdb^d e^&edg ad fjZ ZakVadgYZaVegZh^•chZg{5 .%

2i, 1 SK-4

*!!!.%-2i- 1 (R(-(4

()]5 +.((' P R,3&.T Bjhi^[^XVV hj bdYd ZaegZhX^cY^gYZaeg^bZgd&n ad\gV Vh}YZYjX^gaVhaZnZhYZ

KiZ[Vcn YZO^Zc)

Page 112: Análisis dimensional

++- 9FyDAKAK <AE=FKAGF9D PNaA) =D=;LJGE9?F=LAKEG ++.

<ZhYZajZ\d& ZhiZ igVWV_dcd i^ZcZ b{h fjZ ^ciZg|h ]^hi•g^Xd&ejZh hZ hVWZV]dgV fjZ Zc aVhaZnZhYZaVgVY^VX^•ci|gb^XV cd ^ciZgk^ZcZceVgVcVYVc^ aVbVhVc^ aVXVg\VYZaZaZXig•c&n fjZ eVgVhj ZhijY^d]Vn fjZ gZXjgg^gVaViZdg}VXjVci^hiV)<Z idYdh bdYdh&ZaVgi}XjadYZ.ZVch ejZYZ edcZghZXdbd Z_Zbead YZVea^XVX^•cYZa9c{a^h^hY^bZch^dcVaYZbdYd ^ggZegdX]VWaZVciZhYZfjZ ]jW^ZhZh^YdZcjcX^VYdZmegZhVbZciZZaiZdgZbV YZe^)

LVbW^|c :g^Y\gdVc #--$ VWdgY•ZaegdWaZbVYZaVgVY^VX^•ci|gb^XV egZhX^c(Y^ZcYdYZaV]^e•iZh^h YZadh XjVcidh n a^b^i{cYdhZVWjhXVgaVaZnYZ KiZ[Vc&Zhid Zh&aVgZaVX^•cZcigZ aVYZch^YVYciZ\gVaYZaVZcZg\}V&b' n aViZbeZgVijgVVWhdajiV)HaVciZVaV XjZhi^•c Zc adh b^hbdh i|gb^cdh fjZ . ZVch&eZgd V[^gbVfjZ PJB aaZ\VVab^hbd gZhjaiVYd]VX^ZcYd \jVa V * aVeZgbZVW^a^YVYZa|Xig^XVYZakVX}dw);dbd ZhiVV[^gbVX^•cZhi{ Zc XdcigVYZcjZhigV iZh^h&Xdck^ZcZZmV(b^cVg aVhdajX^•c ]VaaVYVedg :g^Y\bVc)

<ZWZbdh dWhZgkVg&VciZ idYd&fjZ cd ]Vn ^cXdckZc^ZciZZc Vig^Wj^gV Z5 ZakVadg,&ejZh ZaadZfj^kVaZV ZaZ\^gjcV jc^YVYZa|Xig^XVn [dgbVg Xdc ZaaVn igZhjc^YVYZhbZX{c^XVhjc h^hiZbVXd]ZgZciZ&fjZ ejZYZ hZgZaZaZXigdhi{i^XdXZ\Zh^(bVa) Dd fjZ cd YZWZ]VXZghZZhbji^aVg aVWVhZeg^kVcYdV Z5 YZhj Y^bZch^•c)=hid Zhad fjZ ]VXZ:g^Y\bVc& n Xdc Zah^\j^ZciZ XjVYgdY^bZch^dcVa5

iZbV ZaZXigdhi{i^XdXZ\Zh^bVan Xdc Za YZ ?^dg\^&VbWdh Xd]ZgZciZhXdc aVhZXjVX^dcZh[jcYVbZciVaZh)

KZV51 7 ,+++dC6 b 7 ,&1-v aI(. Zg\*Xb. 7 ,&1-v ,+((/ .*b.

X 1 ,&.3v ,+(,1 Zg\*dC 1 ,&.3v ,+(-. .*dC)

Z 1 /&3+v,+(,+ bk Z ) Z 1 ,&1+v,+(,4 ;)

=c Zah^hiZbVZaZXigdhi{i^XdgZhjaiV5

2,5, 1 3&10vAI(K

MZc ZaYZ?^dg\^52,5

-1 2&/4v,+(.3)

-+) =cZg\}VZb^i^YVedg jc Y^edadZa|Xig^Xd)

b Z Z Z 1 Q

9 ( , , G .*- G -: * G , ,*- G *G (- ( , G (, G (-1 G G G G , (,

2,5, , G G 1 (/ (/2,5- G (- '* G * ,

dWi^ZcZadh bdcdb^dh

bR1 Q+2,5, 7 Q/+/4

2,5- 7 ((d

ZP-

=a bdbZcid Za|Xig^Xd&V 7 >R#YZjc Y^edadZ_ZXjiVdhX^aVX^dcZhh^cj(hd^YVaZhXdc jcV [gZXjZcX^Vk) KZfj^ZgZ XVaXjaVgaVZcZg\}V&J Wa'Zb^i^YVedg jc^YVYYZi^Zbed Zc jc bZY^dYZ[^c^Ydedg aVhXdchiVciZhR' =)

=a 9c{a^h^hY^bZch^dcVaXdcYjXZV5

J

a

=a X{aXjadXdbeaZid YV5

.#%#H 1 +((

1('

ZR,4&,T

/+5 (d)

.

9 Xdci^cjVX^•c&n bZY^VciZgVodcVb^ZcidhZmigV~dhVa9c{a^h^hY^bZch^dcVa&egZhX^cYZYZ 2,5- n YVXdbd hdajX^•c5

Xdc ad fjZ egZiZcYZ]VWZgYZYjX^YdaVaZnYZKiZ[Vc)<ZhYZajZ\d&aVZXjVX^•c]VaaVYVedg :g^Y\bVc ZhZgg•cZV&ejZh aVXVg\VYZa

ZaZXig•ccd [^\jgV eVgVcVYVZc aVXdchiVciZYZKiZ[Vc&hZ\€c ejZYZ kZghZZc aVZXjVX^•cR.&,TYZaXVe}ijadPNA) HZgdcd ]VXZ[VaiVXdcdXZgaVaZn ZmVXiVeVgVedYZgV[^gbVgfjZ ZagZhjaiVYdYZ:g^Y\bVc Zh^cVYb^h^WaZ&ejZh Zabdcdb^d 2,5,&

€c^Xd fjZ VegdkZX]V&cd i^ZcZ Y^bZch^•c cjaV&Zh jc bdcdb^d e^ Zhejg^d) =cZ[ZXid&hj [•gbjaV Y^bZch^dcVaZc aV WVhZXdbeaZiV Zh5

9FyDAKAK <AE=FKAGF9D) q ,0

=c Xdc[^gbVX^•cYZZhiZVhZgid&]V\Vbdh kZg fjZ 2,5, idbV Y^hi^cidhkVadgZhhZ\€c hZVZah^hiZbVYZjc^YVYZhfjZ hZ ji^a^XZ)@V\Vbdh aVegjZWVXdc Zah^h(

Page 113: Análisis dimensional

;9H}LMDG PNAAA

51/R63/- 914-;3=3:;-

#" 4>MH>DIFNOABMABG>5B@SIF@>LBG>NFPFMN>"

KjZaZV[^gbVghZfjZ =^chiZ^c]V bdY^[^XVYdaVh YZVhYZai^Zbed n YZaZheVX^d[jcY^|cYdaVhZc jcV Zci^YVYhjeZg^dg&ZaZheVX^d(i^Zbedd jc^(kZghdYZE^c`dlh`^& YZYdcYZedYg}Vc[Zg^ghZfjZ i^Zbed n ZheVX^dhdc&eVgVadh[^cZhYZaVEZX{c^XV&jcV b^hbV XdhVn fjZ& Zc XdchZXjZcX^V&YZW^ZgVciZcZgjcV b^hbV Y^bZch^•cn hZgbZY^YdhXdcjcV b^hbV jc^(YVY&edg Z_Zbead&ZahZ\jcYd)

Fd ZcigVgZbdhVfj} Zc Y^hXjh^dcZhbZiV[}h^XVh#-0$& fjZ hdc V_ZcVhVcjZhigd egde•h^id&n cdh a^b^iVgZbdhVZmVb^cVg&YZhYZcjZhigd ejcidYZk^hiV&aVhbV\c^ijYZh jhVYVhZc EZX{c^XVXdcZahdad[^c YZVkZg^\jVgh^egdXZYZd cd bdY^[^XVghj [•gbjaV Y^bZch^dcVa):VhiVg{&eVgVZaad&fjZXdch^YZgZbdhaVhbV\c^ijYZh eg^bVg^Vhn aVhaZnZh[jcYVbZciVaZh&ejZhZaaVhhdc aVhfjZ YZiZgb^cVcZah^hiZbVY^bZch^dcVa)

DVhbV\c^ijYZh eg^bVg^VhYZaVEZX{c^XVXa{h^XVhdc aVadc\^ijY&Zai^Zbed&aVbVhV&aV[jZgoVn aVZcZg\}V)DdhedhijaVYdhZc fjZ cdh ]ZbdhWVhVYdeVgVZhiVWaZXZgadhXg^iZg^dhYZ^\jVaYVYn YZhjbV hZgZ[^ZgZcVXjZgedhZc gZedhdXdcgZaVX^•cVjc h^hiZbVYZgZ[ZgZcX^VYZafjZ [dgbVeVgiZZadWhZgkVYdg)

DVXdhVXVbW^VXjVcYdhZigViVYZXdbeVgVgZcigZh}XVci^YVYZhfjZhZgZ[^ZgZcVXjZgedhVc^bVYdhYZY^hi^ciVkZadX^YVY)=c iVaXVhd&ZaXg^iZg^dYZ^\jVaYVY&fjZ ZgVdWk^dXjVcYdVbWdhXjZgedhZhiVWVcZc gZedhdgZaVi^kd&cZXZh^iVhZgedhijaVYdXjVcYdjcd YZZaadhhZbjZkZ XdcgZaV(X^•cVadigd&ejZh cd ZhZk^YZciZ&edg Z_Zbead&ZafjZ YdhXjZgedhfjZ hZbjZkZc YZY^hi^cidbdYd iZc\Vc bVhVhZfj^kVaZciZhXjVcYdhjh Z[ZXidh

Page 114: Análisis dimensional

((. 9FyDAKAK <AE=FKAGF9D PNALA) E=;yFA;9 J=D9LaNaKL9 ((/

hdWgZjc iZgXZgdhZVc \jVaZh&n ad b^hbd XVWZYZX^gYZaVhY^hiVcX^VhnYZaVhYjgVX^dcZh)

=c aVEZX{c^XVXa{h^XVhZVYb^i}Vi{X^iVbZciZfjZ iVcid aVhadc\^ij(YZhXdbd aVhYjgVX^dcZhdWhZgkVYVhZc jc XjZged ZgVc^cYZeZcY^ZciZhYZhj ZhiVYdYZbdk^b^Zcid&n fjZ ad b^hbd dXjgg}VXdcaVhbVhVhn XdcaVh[jZgoVh)=a ZmeZg^bZcidYZE^X]Zahdcn EdgaZndWa^\•VYZhZX]VgZhiZedhijaVYdn Vhjhi^ij^gadedg ZhiZdigd5FVQ\` \O`R_cNQ\_R`'b[\ R[ _R]\`\f \a_\ N[VZNQ\ QRb[N cRY\PVQNQP\[`aN[aR'ZVQR[ YNcRY\PVQNQQRb[ QR`aRYY\YbZV[\`\' \OaVR[R[b[ ZV`Z\ cNY\_' X)<^X]d YZdigd bdYd6 ZaedhijaVYdYZaV^ckVg^VW^a^YVYYZadc\^ijYZh&i^Zbedh&bVhVhn [jZgoVh&]V h^Ydhjhi^ij^Yd edg Za edhijaVYd YZ aV ^ckVg^VW^a^YVYYZ aV kZadX^YVYYZ

aVajo);dbd ZhhVW^Yd&ZhiZcjZkd edhijaVYdXdcYjXZVaVh[•gbjaVh YZigVch(

[dgbVX^•cYZDdgZcio&fjZ ^bea^XVc&Zc eg^bZgi|gb^cd& aVcZXZh^YVYYZY^hi^c\j^gZcigZaVhadc\^ijYZh&Y\' Q aVhYjgVX^dcZh&a\' Zc gZedhd&YZaVhgZheZXi^kVhXVci^YVYZh&' n a' Zc bdk^b^Zcid& ad fjZ Zfj^kVaZV YZX^gfjZ ZhiVh€ai^bVh hdc bV\c^ijYZh hZXjcYVg^Vh#%$YZ[^c^YVhbZY^VciZ

aVh[•gbjaVh5

JZheZXid YZaVbVhV&ZagZ[Zg^YdedhijaVYdgZaVi^k^hiVXdcYjXZV aVh^\j^ZciZYZ[^c^X^•cYZaVbVhVZc bdk^b^Zcid5

Z\ZM((h((

++

,((P-

fjZ iVbW^|c XjbeaZ ZagZfj^h^idYZ]dbd\ZcZ^YVYXdcY^X^dcVYV)>^cVabZciZ&aV[jZgoVh^\jZ h^ZcYdXdch^YZgVYVXdbd jc kZXidg&ad

fjZ WVhiVeVgVfjZ XdchZgkZhj XVg{XiZgYZbV\c^ijY eg^bVg^V)DVhYZ[^c^X^dcZhYZaVhbV\c^ijYZh YZg^kVYVhhjWh^hiZcZc aVEZX{c^(

XVgZaVi^k^hiV&eZgd ]Vn fjZ iZcZgegZhZciZfjZ&Zc ZaaVh&aVbVhVhZgZ([^ZgZVaXjZgedZc bdk^b^Zcid&edg ad fjZ hZg{[jcX^•c YZaVkZadX^YVY)

DV kZadX^YVYn aVVXZaZgVX^•ch^\jZc h^ZcYdYZ[^c^YVhbZY^VciZaVhZXjVX^dcZh5

Yh:' (1''&

Yi

YjVU((&Yi

)-

*''P-

XjVafj^ZgVfjZ hZVZah^hiZbVYZgZ[ZgZcX^V)9a Vea^XVgVZhiVhYZ[^c^X^dcZhaVh[•gbjaVh YZigVch[dgbVX^•cYZDdgZcio&hZdWhZgkVfjZ c^ aVhkZadX^(YVYZhc^ aVhVXZaZgVX^dcZhhZ XdbedgiVc Xdbd kZXidgZh)Kj bZY^YVcdejZYZ gZVa^oVghZYZbdYd ^cig}chZXd&h^cd V WZcZ[^X^dYZhjh gZheZXi^kVh[•gbjaVh YZYZ[^c^X^•c)

DV[•gbjaV5

X/$$$$$

fjZ hZgZ[^ZgZcV jc XjZgedfjZ hZbjZkZ Xdc aVkZadX^YVYc Vad aVg\dYZaZ_Ze n fjZ dXjeVaVedh^X^•cPa Zc ZabdbZcid Xdch^YZgVYd)

DVhegZXZYZciZhYZ[^c^X^dcZh^bea^XVcaV^ciZgkZcX^•cYZaVXdchiVciZjc^kZghVaR Zc idYd [Zc•bZcd YZbdk^b^Zcid&eZgd Zc cVYVVaiZgVcZah^hiZbVY^bZch^dcVaYZaVEZX{c^XVXa{h^XV&ejZhid fjZ XjbeaZc ZagZfj^(h^id YZ]dbd\ZcZ^YVYXdcY^X^dcVYV)K^\jZ&ejZh&]VW^ZcYdigZhbV\c^(ijYZh W{h^XVh&n hjWh^hiZaVedh^W^a^YVYYZ ZaZ\^gVgW^igVg^VbZciZigZhjc^YVYZheVgV[dgbVg h^hiZbVhXd]ZgZciZh)Fd ]Vn&edg iVcid& cXdckZ(c^ZciZZc idbVg Xdbd jc^YVYaVkZadX^YVY&R' YZaVajo&eZgd Zaadcd h^\(c^[^XVfjZ hZejZYVYZhed_VgYZhj Y^bZch^•cVY^X]VbV\c^ijY&ejZh iVabji^aVX^•c^g}VZc YZig^bZcidYZa9c{a^h^hY^bZch^dcVa)=c XdchZXjZcX^V&h^KRL7a7,&VjcfjZ hZVZ1 ,&hZg{K`L7a7KaL)=c digdhi|gb^cdh5 ZaaVRZ]\f RYR`]NPV\`VTbR[ `VR[Q\ QVZR[`V\[NYZR[aRV[QR]R[QVR[aR`)

H Zb

h^gkZidYVk}VeVgVYZ[^c^gZa}beZij&eZgdZ ZhaVbVhVZc bdk^b^Zcid)

-) =XjVX^dcZh[jcYVbZciVaZh)

HVgVadh[^cZhYZaX{aXjadY^bZch^dcVaciZgZhViVc h•ad hVWZgZc fj|hZXdck^ZgiZcaVhZ\jcYV aZnYZFZlidc n aVaZnYZaV\gVk^iVX^•c)=hiV€ai^bV&Vjc XjVcYdcd hZ Y^\VZmegZhVbZciZ&hZ XdchZgkVcVaiZgVYV&ejZh hZh^\jZ VYb^i^ZcYdfjZ aVbVhV^cZgX^Van aV\gVk^iVidg^Vhdc ^chZ(eVgVWaZh&n jcd YZadhegde•h^idh YZaViZdg}VYZaVgZaVi^k^YVY\ZcZgV(a^oVYVZhYVgXjZciVYZZhiVX^gXjchiVcX^V)

DV hZ\jcYV aZn YZ FZlidc VYfj^ZgZZc EZX{c^XVgZaVi^k^hiVjcV[dgbV Xdbea^XVYVXjVcYdhZZmegZhVZc [jcX^•c YZaVVXZaZgVX^•c)HdgZhdZhegZ[Zg^WaZgZXjgg^gVa}beZij& Xdcad fjZ hZaaZ\VVah^\j^ZciZZcjc(

#%$ HVgVb{h edgbZcdgZhgZheZXidV aVh^YZVhYZi^Zbed M ZheVX^dZc aViZdg}V)YZaV)gZaVi^k^YVY&gZb^i^bdh VaaZXidgVcjZhigd igViVYd#2,$)

Page 115: Análisis dimensional

-.+ 9FyDAKAK<AE=FKAGF9D PNAAA) E=;yFA;9 J=D9LANAKL9 -.,

X^VYd&fjZ Zh iVbW^|c k{a^YdZc EZX{c^XVXa{h^XV5?N VZ]bY`Vo[' [Yi&R`]_\]\_PV\[NY N YNcN_VNPVo['Ye&QRYnZ]Rab3

#[Yi$"! RY#bk$T #ZcigZXVci^YVYZh$)

=hiZ gZhjaiVYdeZgb^iZ V[^gbVgfjZ& eVgVXdbjc^XVg V jc XjZged jcVkZadX^YVYYZiZgb^cVYV&]Vn fjZ \VhiVgjcV ZcZg\}VfjZ cd YZeZcYZYZaV[jZgoVfjZ hZVea^fjZ&ad XjVaZhjcV bVcZgVYZZcjcX^VgZaeg^cX^e^dYZXdchZgkVX^•cYZaVZcZg\}V)

DV[•gbjaV XdbeaZiVZh5

:Pa[ 1 ZP( #,( 55 $) R/&,T

9a eVhVgVaVZXjVX^•cZcigZbZY^YVh&ZhhjeZg[ajd Za[VXidgYZegdedg(X^dcVa^YVY&ejZh aV bejah^•c n Za}beZij cd hdc bV\c^ijYZh ^chZeVgVWaZh&n gZhjaiV5

NLX1 Y#bk$) R-&,T

0) AcZgX^VYZaVZcZg\}V).) K^hiZbVY^bZch^dcVa)

<Z aViZdg}VYZEVmlZaa gZhjaiVfjZ aVajo n&Zc \ZcZgVa&aVhdcYVhZaZXigdbV\c|i^XVhedhZZc bVhV ^cZgX^Va)=c aViZdg}VYZaVgZaVi^k^YVY&ZhiVegdedh^X^•chZ\ZcZgVa^oVVidYVhaVhZheZX^ZhYZZcZg\}V)9a XVaXjaVgaVbVhV XdggZhedcY^ZciZV jcV ZcZg\}V&J' ]VWg{fjZ idbVg Zc Xdch^YZ(gVX^•caVkZadX^YVYYZaVajo&n Za9c{a^h^hY^bZch^dcVaedg h}hdad Xdc(YjXZV5

@Zbdh k^hid fjZ Zc EZX{c^XVgZaVi^k^hiVciZgk^ZcZcaVh b^hbVhbV\c^ijYZh fjZ Zc EZX{c^XVXa{h^XV)LVbW^|c ZhZab^hbd Zac€bZgd YZZXjVX^dcZh[jcYVbZciVaZh&fjZ h^\jZc h^ZcYdgZaVX^dcZhYZegdedgX^dcV(a^YVYZcigZediZcX^VhYZbV\c^ijYZh egZk^VbZciZYZ[^c^YVh)>^cVabZciZ&idYVhaVhYZ[^c^X^dcZhYZ bV\c^ijYZh hZXjcYVg^VhXjbeaZc Za gZfj^h^idYZ]dbd\ZcZ^YVY) HdYg{&ejZh&ji^a^oVghZZab^hbd h^hiZbVY^bZch^dcVafjZ Zc EZX{c^XVXa{h^XV&n iVc h•ad hZg{egZX^hdiZcZg Zc XjZciVaV^ciZg(kZcX^•c YZaVkZadX^YVYYZaVajo Xdbd XdchiVciZjc^kZghVa)

=c \ZcZgVa&aVVea^XVX^•cYZab|idYd Y^bZch^dcVaVadhegdWaZbVhYZEZX{c^XVgZaVi^k^hiVXdcYjXZV hdajX^dcZhbjn kV\Vh) NVbdh&cd dWh(iVciZ&V ]VXZgVa\jcVh Xdch^YZgVX^dcZh)

JZ5B(-("

ZR0&,T

/) ;dchZgkVX^•cYZaVZcZg\}V)

=c aVEZX{c^XVXa{h^XV&Zaeg^cX^e^dYZXdchZgkVX^•cYVWVZah^\j^ZciZkVadgeVgVaVZcZg\}VfjZ ]VW}VfjZ \VhiVgZc Xdbjc^XVgVjc XjZged YZbVhVZ aVkZadX^YVYc3

=a X{aXjadXdbeaZid YVG 1 a)?gVX^VhV ZhiV[•gbjaV hZejZYZ ^ciZgegZiVgZaVjbZcid fjZ ZmeZg^(

bZciV aVbVhV YZjc XjZged V XVjhVYZhj bdk^b^Zcid& Xdbd YZW^YdVaV^cZgX^VYZaVZcZg\}VX^c|i^XV)=c Z[ZXid&aVbVhV idiVa&iZc^ZcYdZcXjZciV R/&,T&kVaYg{5

`)3 #Z\$ZB&8-5Z\&Z Y(((((Z 5Z)

1) EVhVYZ}beZij M bVhV YZVXZaZgVX^•c)

=hiV ZmegZh^•c&Zc fjZ cd [^\jgV P' cd Zhk{a^YVZc EZX{c^XVgZaVi^k^hiV)NZVbdh fj| hZejZYZ egZYZX^gXdc gZheZXidVaVb^hbV edg Xdch^YZgVX^d(cZh Y^bZch^dcVaZh)

DVhbV\c^ijYZh VXdch^YZgVghdc Z\ n Z' ejZh aVkZadX^YVYkV ^ckdaj(dgVYVZc ZhiV€ai^bV) ;dc Zhidh YVidhn aV^ciZgkZcX^•cYZP hZ dWi^ZcZ^cbZY^ViVbZciZ

Mc XjZged YZ bVhV Z\' fjZ hZ bjZkZ Xdc aVkZadX^YVYk&hZ ]VaaVhdbZi^Yd VjcV [jZgoV&C( ;j{cid kVaYg{aVVXZaZgVX^•c&Vq

DVhbV\c^ijYZh V Xdch^YZgVghdc5 Z\' Z' [& V&n Z&ejZh aVkZadX^YVYZhi{ ^ckdajXgVYVZc Z) ;dc Z^aVhhZejZYZc [dgbVg Ydh bdcdb^dh e^&ngZhjaiV5

K^h^\j^|gVbdh ZaXg^iZg^dYZfj^ZcZh egZiZcYZcfjZ aVbVhV Zh&]\_ QRSV([VPVo['ZaXdX^ZciZYZY^k^Y^gaV[jZgoVedg aVVXZaZgVX^•c&iZcYg}VbdhfjZ

Page 116: Análisis dimensional

()( 9FyDAKAK <AE=FKAGF9D PNAAA) E=;yFA;9 J=D9LANAKL9 ())

^cigdYjX^gjcV cjZkV bV\c^ijY hZXjcYVg^V5 ,)+ DVZN`N R[ _R]\`\' Z\' fjZ ZhaV€c^XVfjZ hZji^a^oVZc EZX{c^XVXa{h^XV)HVgVZaaVhZ ejZYZc ZhiVWaZXZgadh Xg^iZg^dhYZ^\jVaYVYn YZhjbV h^c gZXjgg^gV aVbZY^YVYZdigVhbV\c^ijYZh&edg ad fjZ ZhjcVbV\c^ijY eg^bVg^V)

-)+ DVZN`N QRnZ]Rab' YZ[^c^YVedg aV[•gbjaV5fjZ edYg}VaaVbVghZtbVhV eVgVadh Z[ZXidhYZaVVXZaZgVX^•c$d&b{hh^beaZbZciZ&bVhV YZ VXZaZgVX^•c)

=a 9c{a^h^hY^bZch^dcVacVYVejZYZ YZX^gcdhVXZgXVYZaV[dgbV YZaV[jcX^•c&)Xe5edg ad fjZ ]VWgZbdhYZgZXjgg^gV aVaZn[jcYVbZciVa R-&,T&fjZ ZhXg^W^gZbdhXdbd h^\jZ5

S HH S%%%%-U#$$H

.)+ DV ZN`N QR NPRYR_NPVo['fjZ Zh jc iZchdg h^b|ig^Xd YZ[^c^Ydedg R1&-TXjVcYdhjh Z_Zheg^cX^eVaZhXd^cX^YZcXdcadhZ_ZhXddgYZcVYdh)A

[7bd(Qa

kR1&,T

9-

,((X( )" 5>NBLF>!H>M>Q BIBLDU>"

DVZXjVX^•cR0&,THVgVh^qea^[^XVgaVXjZhi^•c&i•bZhZ jc h^hiZbVYZZ_ZhXddgYZcVYdhiVaZhfjZ ZaBDBe iZc\V aVb^hbV Y^gZXX^•cn hZci^YdfjZ aVkZadX^YVY; Zc Za^chiVciZXdch^YZgVYd)=cidcXZh hZg{5 " &

J5ZP(

ZmegZhVfjZ idYVZcZg\}V&J' edhZZjcV bVhV #YZ}beZij$&Z) =hXg^iVZc aV[dgbV5BI. 1 B. !c 7 Ig 7 +&

R2&,T

n aVZXjVX^•cR1&,T&]VX^ZcYdc*P1 N&XdcYjXZV5h^\c^[^XVfjZ idYd XVbW^dZc aVZcZg\}VYZjc h^hiZbVkVVXdbeV~VYdYZjc XVbW^dYZiZgb^cVYdYZhj bVhV&XVbW^dfjZ hZg{VXjhVYdedg jcVWVaVcoVbjn hZch^WaZh^hZigViVYZjc h^hiZbVZc gZedhd&ejZh VaVjbZc(id ,Z\ YZaVbVhV^cZgX^VaXdggZhedcYZg{jc VjbZcid YZaVbVhV\gVk^(iVidg^V):VhiV&edg Z_Zbead&XVaZciVgjc XjZgedeVgVfjZ VjbZciZ YZeZhd)

=mejZhiVVh}aVXjZhi^•c& , J n a`Zl gZhjaiVchZgYdhbV\c^ijYZh eg^(bVg^VhchZeVgVWaZh&edg adfjZ cjZhigd hZ\jcYd edhijaVYdZm^\ZfjZ X-hZVjcV XdchiVciZjc^kZghVa cZajY^WaZ&n fjZYV _jhi^[^XVYVhj ^ciZgkZcX^•cZc [Zc•bZcdh YZEZX{c^XVZc fjZ Zhi{VjhZciZaVajo)

>e1 Z\Ne )"* @ q-$.*- "

n aVbVhVWjhXVYVgZhjaiVhZgjc iZchdg5

bdG G!BR$q-$.

ZN( G bdG

B7 q-

G G Z\

BR$ q-

R1&-T HZgdZhi{ \ZcZgVa^oVYVaVXgZZcX^VYZfjZ aVZXjVX^•cR2&,T]V YZ ^ciZgegZ(iVghZZc ZahZci^YdYZfjZ aVbVhVhZigVch[dgbVZc ZcZg\}V&n gZX}egdXVbZciZ&Zck^gijY YZjc eg^cX^e^dYZZfj^kVaZcX^VVc{ad\d VafjZ g^\Z aVhigVch[dgbVX^dcZhgZX}egdXVhYZXVadgZc igVWV_d)Hdg ZhdhjZaZYZX^ghZfjZ aVZcZg\}VYZaVhWdbWVhVi•b^XVhegdk^ZcZ YZ aVbVhV fjZ e^ZgYZcadh c€XaZdhVi•b^Xdh VaZhX^cY^ghZ)KZ Y^XZ&VYZb{h&fjZ aViZdg}VgZaVi^k^hiV]V gZjc^Yd Zc jcd hdad #ZcZg\}V%%bVhV 1 Xdchi$adh Ydh eg^cX^e^dhYZ XdchZgkVX^•cYZaVEZX{c^XVXa{h^XV&Za

YZaVbVhV n ZaYZaVZcZg\}V)<Z hZgX^ZgiVZhiV^ciZgegZiVX^•c&aVbVhVn aVZcZg\}Vcd hZg}VcnV ^chZeVgV(

WaZh&h^cd igVch[dgbVWaZhjcV Zc digV n& YZ VXjZgYdXdc cjZhigd edhijaVYd&edYg}Vhjeg^b^ghZedg hjeZg[ajV aVXdchiVciZY^bZch^dcVYVfjZ [^\jgV Zc R2&,T&

n ]Vn fjZ Y^hi^c\j^gZcigZaVZN`N Y\[TVabQV[NYZ*# , U N8%(")P( ,

I((( " i("&n NZN`N

a_N[`cR_`NY'Z* , U q-)

Y=c gZhjbZc)5]Vn fjZ Y^hi^c\j^gigZhZheZX^ZhYZbVhV&jcV eg^bVg^V

n dh hZXjcYVgAVh&V hVWZg5

Page 117: Análisis dimensional

-./ 9FyDAKAK <AE=FKAGF9D

Xdc ad fjZ aVZcZg\}Vn aVbVhV hZg}VcbV\c^ijYZh ]dbd\|cZVh) =aad VXVggZVg}VaVbji^aVX^•c YZaVWVhZZc Zah^hiZbVY^bZch^dcVa&n hZ YVg}VZaXdcigVhZci^YdYZfjZ jc XdcdX^b^Zcidb{h eZg[ZXidYZaVhaZnZhcVijgVaZhhZigVYj_ZgVZc jcVe|gY^YVYZZ[^XVX^VYZadh b|idYdh Y^bZch^dcVaZh)=h&ejZh&^bedgiVciZ&edcZgZc XaVgdZahZci^YdYZaVZXjVX^•cR2&,T)

HVgVedYZgV[^gbVgfjZ& Zc YZiZgb^cVYd[Zc•bZcd& jcV bV\c^ijY hZ igVch([dgbV Zc digV&Zh egZX^hdfjZ ZhiV€ai^bV VjbZciZ V ZmeZchVhYZaVeg^bZgV)=hid hjXZYZ&edg Z_Zbead&XjVcYdaVZcZg\}VX^c|i^XVYZjc XjZgedfjZ XVZVjbZc(iV iVcid Xdbd Y^hb^cjnZ aVediZcX^Va&d XjVcYdZaXVadghZigVch[dgbVZc ZcZg\}VbZX{c^XV)HZgdaVbVhV fjZ e^ZgYZcadh c€XaZdhVi•b^Xdh Zc aVhZhX^h^dcZhcj(XaZVgZhhZ ZcXjZcigV}ciZ\gVbZciZ Zc aVZcZg\}VYZhegZcY^YV)K^hZXdadXVhZjcVe^aVVi•b^XVZc jcV W{hXjaVn hZ Zk^iVhZaVhVa^YVYZZcZg\}V&cd hZ cdiVg}VaVbZcdg e|gY^YVYZeZhd&edg \gVcYZfjZ [jZhZ aVZcZg\}Va^WZgVYVZc aVe^aV)

;dc ad Y^X]dfjZYV aVXdhVZc XaVgdb^ZcigVhhZbVcZ_Vc XjZgedhbViZg^VaZhn aVZcZg\}Va^\VYVV adh b^hbdh) HZgd&h^ ^ciZgk^ZcZaVZcZg\}Vajb^cdhV&]VnfjZ ZhijY^VgaVXjZhi^•c b{h V[dcYd)

KZ\€c aViZdg}VYZaVgZaVi^k^YVY&aVZcZg\}V ciZgcVYZjc XjZged Zc gZedhdkVaZZ\P-q K^hZbjZkZ Xdc jcV kZadX^YVYc' hj bVhV #YZ}beZij$ hZXdck^ZgiZZc5

S 1 @@S$$/UHH

NA7[.- "R2&-T

edg ad fjZ aVZcZg\}VidiVa ]VWg{YZkVaZg5

YZYdcYZgZhjaiVfjZ aVZcZg\}VX^c|i^XVZhi{ YVYVedg5

:PV[ 7 ZR- ( Z\P- 7 # , ( ,$ Z\P-'NA ( q-

R2&.T

n&YZhVggdaaVcYdZc hZg^Z&hZ kZ [{X^abZciZfjZ& b^ZcigVh q 0 0 ,6

*:PV[ 1 ' Zc-q

-

;jVcYd q 1 ,&aV ZmegZh^•cR2&.ThZ Xdck^ZgiZZc :PV[ 1 XX&h^ Z\ 47 +&adfjZ edcZ YZbVc^[^ZhidfjZ idYV aVZcZg\}VYZajc^kZghd cd WVhiVeVgVfjZ jch^beaZ ZaZXig•cVaXVcXZ"aVkZadX^YVYYZaVajo)

Ddh [didcZh&d eVgi}XjaVhYZajo&hZ bjZkZc Xdc aV kZadX^YVYZ n&hZ\€c aV]^e•iZh^h YZHaVcX`(=^chiZ^c&aVajo YZ[gZXjZcX^Vc Zhi{ Xdchi^ij^YVedg [didcZhYZ ZcZg\}VO^# edg ad fjZ XVYVjcd edhZZg{jcV bVhV5

]kS/$$

X-R2&/T

n jc }beZij

]kZR 1 ((d

Z

PNBAB) E=;yFA;9 J=D9LANBKL9 -.0

DVh[•gbjaVh R2&-Tn R2&.T&ejZhid fjZ L n Z hdc [^c^idh&Zm^\Zc fjZ Zc Za[di•c hZVZ\ 1 +&eZgd ZhiV XdchZXjZcX^V&hZ\€c aV XjVa jc [di•c ejZhid ZcgZedhd hdWgZZaeaVi^aadYZjcV WVaVcoVcd YZW^ZgVeZhVgcVYV&Zh ^bedh^WaZYZXdbegdWVg&edgfjZ cd ]Vn dWhZgkVYdgXVeVoYZZ[ZXijVgiVabZY^YV)=c XVbW^d&aVbVhVX^c|i^XVZ' aVfjZ [^\jgV Zc R2&/T&i^ZcZjc hZci^YdeZg[ZXiVbZciZXaVgd)KZbVc^[^ZhiV&V aVkZo&edg hj ^cZgX^Vn edg hjh Z[ZXidh\gVk^iVidg^dh)?gVX^VhVZhidh€ai^bdh dXjggZfjZ jcV XVk^YVYaaZcVYZajo eZhVb{h fjZ h^hZZcXjZcigVV dhXjgVh&ejZh adh [didcZh X]dXVcXdc Za[dcYd Xdc b{h k^daZcX^VfjZ Xdc aVXjW^ZgiVYZaVkVh^_V) )

9 cjZhigd bdYd YZkZg&XjVcYd hZ Vig^WjnZZaYZhegZcY^b^ZcidYZZcZg\}VZc aVhgZVXX^dcZhcjXaZVgZhV aVe|gY^YVYZbVhV fjZ ZmeZg^bZciVcadh c€XaZdhVi•b^Xdh&hZ^cXjggZZc jcV [VaiVYZegZX^h^•cfjZ egdXZYZYZcd Y^hi^c\j^gZcigZbViZg^Vn ZcZg\}V&edg ad fjZ egdXZYZgZk^hVgZhidh XdcXZeidh)

LdYVaV>}h^XV&iVcid aVXa{h^XVXdbd aVXdciZbedg{cZV&hZ WVhVZc aVXaVgVY^hi^cX^•cZcigZad fjZ ZhbViZg^Vn ad fjZ ZhZcZg\}V)KZXgZ}VVciZhfjZ aVY^[Z(gZcX^VZheZX}[^XVZcigZ VbWdhZciZh gVY^XVWVZc hZgaVbViZg^V^cZgiZn eZhVYV&b^ZcigVh fjZ hZ hjedc}V V aVZcZg\}VZmZciVYZ^cZgX^Vn YZeZhd)LVaZhY^[ZgZc(X^VhhZ WdggVgdcYZhYZfjZ EVmlZaa YZhXjWg^•fjZ aV ZcZg\}Vajb^cdhV edhZZbVhV ^cZgiZn&hdWgZidYd&YZhYZfjZ hZ XdbegdW• ZmeZg^bZciVabZciZfjZ aVZcZg\}V&YZVXjZgYdXdc aViZdg}VYZaVgZaVi^k^YVYYZ=^chiZ^c&Zhi{ hdbZi^YVVaV VXX^•cYZ adh dVbedh \gVk^iVidg^dh)HgdXZYZ&ejZh& WjhXVgdigdh gVh\dh Y^([ZgZcX^VaZh)

KZ hVWZfjZ aVbViZg^VZhi{ Xdchi^ij^YVedg Xdge€hXjadhZaZbZciVaZh&egd(idcZh&ZaZXigdcZh&cZjigdcZh&ZiX)&fjZ cjcXV ejZYZc VaXVcoVgaVkZadX^YVYYZaVajo) DVZcZg\}V&edg ZaXdcigVg^d&cd ZhYZcVijgVaZoVY^hXgZiV&Xdbd hjXZYZXdcaVZcZg\}VbZX{c^XV#X^c|i^XV%ediZcX^Va$&d&h^ad Zh&Xdbd dXjggZXdcaVZcZg\}VZaZXigdbV\c|i^XV&hjh eVgi}XjaVhd [didcZh ]Vc YZbdkZghZ egZX^hVbZciZXdc aVkZadX^YVYYZaVajo) KZejZYZ&edg iVcid&Y^hi^c\j^g h^c VbW^\•ZYVYaVbViZg^VYZaVZcZg\}V)

HVgVYZhXg^W^gaVXdbedh^X^•cYZjc XjZged ZhegZX^hdZcjbZgVg aVhR`]RPVR`QRZNaR_VNYZfjZ Zhi{ Xdchi^ij^Yd&n aVhXjVci}VhYZXVYVjcV&ad XjVaZm^\ZfjZhZ YZ[^cVaVbVcZgVYZbZY^gXVci^YVYZhYZbViZg^V)

9c{ad\VbZciZ& aVZcZg\}VhZ bZY^g{ edg Va\jcd YZhjh Vig^Wjidh&ZaigVWV_dfjZ hZejZYZ gZVa^oVgXdc ZaaVd hj bVhV)

K^W^ZcZc idYd XjZged ]Vn h^ZbegZbViZg^Vn ZcZg\}V&ad fjZ ^bedgiV YZhYZZa ejcid YZk^hiVYZhj Xdchi^ijX^•c Zh aVbViZg^V)Mc XjZged h^\jZ h^ZcYdZab^hbd& VjcfjZ XVbW^Zhj g^fjZoV Zc ZcZg\}V&b^ZcigVhcd hZVaiZgZhj Xdchi^ij(X^•c bViZg^Va)Hdg ZhdejZYZ YZX^ghZfjZ bViZg^VZh VfjZaad YZfjZ Zhi{c Xdch(i^ij^Ydh adh XjZgedh)

;dck^ZcZ Y^hi^c\j^g iVbW^|c ZcigZ bViZg^Vn bVhV) DV bViZg^Vcd ^ciZgk^Z(cZ Zc >}h^XVh^cd XjVa^iVi^kVbZciZ6Zc c^c\jcV ZXjVX^•c[^\jgVc aVhXVci^YVYZhYZbViZg^V)@VhiVZc aVhZXjVX^dcZhfj}b^XVh adhY^[ZgZciZh{idbdh Zhi{c gZegZ(hZciVYdhedg hjh h}bWdadh&fjZ cd hdc b{h fjZ VWgZk^VX^dcZhYZadh cdbWgZhgZheZXi^kdh&b^ZcigVh fjZ aVeVgiZ XjVci^iVi^kVXdggZhedcYZV adh XdZ[^X^ZciZh&fjZ gZegZhZciVcbVhVhbZY^YVhZc jc^YVYZhVgW^igVg^Vh&edg Z_Zbead&Zc bdaZh)=c XVbW^d&YNZN`N RR b[N ZNT[VabQ Sn`VPN'Na_VOba\P\Zp[ N a\QN` YN` R`]RPVR`QR ZNaR_VNf N a\QN` YN` R`]RPVR QRR[R_TnN)@Vn Y^kZghVhZheZX^ZhYZ bViZg^V&eZgd h•ad ]Vn jcV ZheZX^ZYZbVhV)

Page 118: Análisis dimensional

-.1 9FyDAKAK <AE=FKAGF9D

HdYZbdh V]dgV^ciZgegZiVgaVZXjVX^•cYZ=^chiZ^c&: 1 Z'P-' Q adh ]ZX]dhfjZ aVXdc[^gbVc&YZah^\j^ZciZ bdYd5

DVbViZg^VejZYZ igVch[dgbVghZZc ZcZg\}V&n gZX}egdXVbZciZ&n Zm^hiZjcVgZaVX^•cYZegdedgX^dcVa^YVYZcigZ aVbViZg^VfjZ YZhVeVgZXZ#bZY^YVedg hjbVhVZc gZedhd$n aVZcZg\}VfjZ hZZc\ZcYgV)=c digdh i|gb^cdh5 P\[ b[N ]\_PVo[QNQNQRZNaR_VNR \OaVR[R VRZ]_R YNZV`ZN PN[aVQNQQRR[R_TVN)=h jcV gZaVX^•cYZegdedgX^dcVa^YVYZcigZ YdhbV\c^ijYZh h^beaZhfjZ cd hdc ^chZeVgVWaZh&edgad fjZ ]jZa\V Za [VXidgYZ egdedgX^dcVa^YVYZc aV ZXjVX^•cZcigZ bZY^YVh&ngZhjaiVjc eg^cX^e^dYZ XdchZgkVX^•cfjZ ejZYZ ZcjcX^VghZVh}5

=c idYd h^hiZbVXZggVYd5bViZg^V%ZcZg\}V1 Xdchi R2&0T)?gVX^VhV ZhiZeg^cX^e^dYZ XdchZgkVX^•c&aVbViZg^VVYfj^ZgZZa gVc\d YZ

bV\c^ijY [}h^XV]dbd\|cZV Xdc aV ZcZg\}V&M edYg{ bZY^ghZZc aVhb^hbVhjc^YVYZhfjZ |hiV) =c XVbW^d&cd hZejZYZ YZX^gfjZ aVbViZg^VhZV]dbd\|cZVXdc aVbVhV&edgfjZ hdc bV\c^ijYZh ^chZeVgVWaZh&MaVXdggZhedcY^ZciZgZaVX^•cYZegdedgX^dcVa^YVYZm^\ZedcZg jcV XdchiVciZjc^kZghVaZc aVZXjVX^•cZcigZbZY^YVh)LVaXdchiVciZ&hZ\€c aViZdg}VYZaVgZaVi^k^YVY&Zh^\jVa VaXjVYgVYdYZaVkZadX^YVYYZaVajo) Hdg iVcid5

R2&1Tn&V WZcZ[^X^dYZ R2&0T5

B2&2T

YdcYZ J\ ZhaVZcZg\}VfjZ hZdWiZcYg}Vh^idYVaVbViZg^VhZ igVch[dgbVhZZcZcZg\}V)

Hdg ad fjZ V]dgV hZ hVWZ&aVigVch[dgbVX^•cYZ bViZg^VZc ZcZg\}VZh jcegdXZhdYZ \ a\Q\ \ [NQN' fjZ hZ dWhZgkVXjVcYd hZ Vc^fj^aVc bjijVbZciZ jccZ\Vi•c Mjc edh^i1c&d jc egdi•c Mjc Vci^egdi•c) =c ZhiZ[Zc•bZcd MZc hj^ckZghd&aVbViZg^Va^oVX^•cYZYdh[didcZh&hZXdchZgkVcaVbVhV n Za}beZij)

=c gZhjbZc5

,) Q DV bVhV MaVZcZg\}Vcd hZ igVch[dgbVc jcV Zc digV6hdc bV\c^ijYZh^chZeVgVWaZh&a^\VYVhedg jcV gZaVX^•cYZegdedgX^dcVa^YVY)

-)u DV ZcZg\}Va^WZgVYVZc aVhgZVXX^dcZhcjXaZVgZhegdXZYZYZ aVZcZg\}VVabVXZcVYVZc adhc€XaZdhMYZaVc^fj^aVb^Zcid YZeVgi}XjaVh)

.)u DVbVhVidiVa "MZa}beZij$ hZXdchZgkVZc idYVhaVhgZVXX^dcZh)

;9H}LMDG PAP

2U:3/- /798<:/<4-9

#" :FMNBH>AFHBIMFJI>G"

9 ad aVg\dYZZhiZa^Wgd]Zbdh ^ciZciVYdegdWVgfjZ aVhY^bZch^dcZhYZaVhbV\c^ijYZh eg^bVg^Vhcd YZg^kVcYZhjh YZ[^c^X^dcZh^chigjbZc(iVaZh&h^cdYZa\gjed YZZXjVX^dcZh[jcYVbZciVaZhYZXVYViZdg}Vn YZaXg^iZg^dfjZ h^gkZeVgVhjeg^b^g aVhXdchiVciZhjc^kZghVaZhhjeZg[ajVh)HZgdVaaaZ\VgVaVbdYZgcV>}h^XVYZadhXdge€hXjadh&cdh ZcXdcigVbdhXdc aVV[^gbVX^•cgZ^iZgVYVYZfjZ hj ZhijY^dcd ejZYZ gZVa^oVghZh^cdYZhYZZaejcid YZk^hiVYZaV>^adhd[}VdeZgVX^dcVa)9h} ad V[^gbV&edgZ_Zbead&@Vaa^YVn#23$Zc Zaeg•ad\d YZhj a^Wgd)LVaVhZgX^•c&h^[jZhZX^ZgiVVXVggZVg}VaVcd kVa^YZoYZa9c{a^h^hY^bZch^dcVaZc XjZhi^dcZhXdgejhdjaVgZh&ejZh ]Zbdh k^hidXdccjbZgdhdh Z_ZbeadhfjZ&VaegdXZYZgedg k}VdeZgVX^dcVa&fjZYVc ^cYZiZgb^cVYVhaVhY^bZch^dcZh)Q XdbdhdWgZadh Xdge€hXjadhYZWZXdchigj^ghZidYVaV>}h^XViZ•g^XV&idYVaVZhigjXijgVY^bZch^dcVahZ kZcYg}VVWV_d)=h [{X^akZg fjZ cd h•ad cddXjggZiVaXVi{higd[Z&h^cdfjZ Zc ZabjcYd YZadhXdge€hXjadhg^\ZZmVX(iVbZciZ Za b^hbd h^hiZbVY^bZch^dcVafjZ Zc adh gZhiVciZhXVe}ijadhYZaV>}h^XV)

HVgVfjZ hZVVea^XVWaZZa9c{a^h^hY^bZch^dcVa&WVhiVfjZ hZXjbeaVcjZhigd eg^bZgedhijaVYd&Zc XjnVk^gijY&edg Xdch^hi^gaVhaZnZhZc gZaq(X^dcZhYZegdedgX^dcVa^YVYZcigZXVci^YVYZh&ejZYZc hZgZcjcX^VYVhh^c]VXZggZ[ZgZcX^VV c^c\€c h^hiZbVeVgi^XjaVgYZjc^YVYZh)Fd ]Vn Zc>}h^XVXdgejhXjaVgjcV hdaVaZn fjZ cd XjbeaV Y^X]dgZfj^h^id&ad fjZeZgb^iZ V[^gbVgfjZ Za9c{a^h^hY^bZch^dcVah^\jZ h^ZcYdVeqXVWaZ5NV(bdh V egdWVgfjZ hjWh^hiZh^c VaiZgVX^•cYZaVZhigjXijgVY^bZch^dcVa)

Page 119: Análisis dimensional

-.3 9FyDAKAK<AE=FKAGF9D

<Z YdhbVcZgVhhZejZYZ VaiZgVgjc h^hiZbVY^bZch^dcVa5edg gZYjX(X^•c d edg Vbea^VX^•cYZaVWVhZ)HVgVfjZ ad eg^bZgd hZVk^VWaZ&ZhegZX^hdYZhXjWg^gVa\jcV aZnfjZ gZaVX^dcZZcigZh}aVhbV\c^ijYZh W{h^XVhn Zc aVfjZ hZ ejZYV egZhX^cY^gYZaVgZheZXi^kVXdchiVciZjc^kZghVa)LVa[jZ ZaXVhdXjVcYdhZYZhXjWg^•aVaZnYZZfj^kVaZcX^VZcigZZaXVadgn ZaigVWV_d&n iVaegZiZcYZcfjZ hZViVbW^|c ZaXVhdZc >}h^XVXdgejhXj(aVgadhfjZ&Xdbd JdhZc[ZaY#24$&de^cVc fjZ&Zc k^gijY YZaViZdg}VYZaVgZaVi^k^YVY&WVhiVidbVg Xdbd jc^YVYaVkZadX^YVYYZaVajo&eVgVfjZgZhjaiZc]dbd\|cZVh n ejZYVc bZY^ghZXdcaVb^hbV jc^YVYaVadc\^ijYn Zai^Zbed&edg jcV eVgiZ&n aVbVhV&Za}beZij n aVZcZg\}V&edg digV)HZgd&h^W^Zccd ]Vn ^cXdckZc^ZciZZc idbVg Z Xdbd jc^YVYYZkZadX^YVYZaadcd ^bea^XVZafjZ hZejZYV YZhed_VgbejcZbZciZ V ZhiVbV\c^ijYYZhj Y^bZch^•c)A\jVa gVo•c ]VWg}VeVgV]VXZgO1 ,& Xdc ad fjZ ZhiV(g}VcqZaVX^dcVYdhY^bZch^dcVabZciZZai^Zbed n aVZcZg\}V&n Vh}hZedYg}VXdci^cjVg]VhiV fjZ cd fjZYVhZjcV hdaVbV\c^ijY W{h^XV&n fjZYVg}VidiVabZciZ Vggj^cVYdZa9c{a^h^hY^bZch^dcVa)=hiZ XViVXa^hbdhZZk^iVh^YZVXjZgYdXdc cjZhigd edhijaVYd n Xdc ad Y^X]dZc ZaXVe}ijadegZdZ(YZciZ&hZXdch^YZgVZ Xdbd XdchiVciZ^cZajY^WaZZc idYdh adhegdWaZbVhYZgZaVi^k}YVY)

HVgVfjZ [jZhZcZXZhVg^dVbea^VgaVWVhZ&hZg}VegZX^hd]VWZgcigdYj(X^YdjcV cjZkV bV\c^ijY fjZ cd Zhijk^ZhZgZaVX^dcVYVY^bZch^dcVa(bZciZ XdcVa\jcV YZaVhXdcdX^YVh)Fd dXjggZZhidZc >}h^XVXdgejhXjaVg&edg ad fjZ edYZbdh V[^gbVgfjZ Zh hj[^X^ZciZjcV WVhZYZ X^cXd&fjZejZYZc hZg9#:# @#Z n ># n ejZYZc gZYjX^ghZV XjVigd Zc VfjZaadhegdWaZbVhZc fjZ cd ^ciZgkZc\VaViZbeZgVijgV)

qZ Vfj} aV igVYjXX^•ca^iZgVaYZ Va\jcdh e{ggV[dh fjZ JdhZc[ZaY edcZ VaXdb^Zcod YZhj a^Wgd5

%I" tqZ YVV aV bVhV n Va}beZij aV Y^bZch^•c YZ jcV ZcZg\}V&Zh YZX^g&hZ AYZci^[^XVaVbVhV YZ XVYVeVgi}XjaVXdc hj ZcZg\}VZc gZedhd n hZ aaVbV}qeZij V aVbV\c^ijY fjZ jhjVabZciZ hZ YZh^\cVXdc ZhiZcdbWgZ5eZgd bjai^(ea^XVYVedg aVkZadX^YVYYZaVajo)w

J" t=hiZ XdckZc^d^bea^XVbdY^[^XVX^dcZhh^b^aVgZhZc aVhbV\c^ijYZh YZg^(kVYVh5Za}beZij Vc\jaVg(]VWg{YZbjai^ea^XVghZedg Z&n ZabdbZcid YZ^cZgX^Vedg R

-4 Zc e)Vgi^XjaVg&idbVbdh Xdbd XdchiVciZ[jcYVbZciVa YZ!VXX^•c!aVXdch(

iVciZ YZ<^gVd&U*-__3' bjai^ea^XVYVedg Z) ;dc Za[^c YZXdchZgkVgjcV ZmegZh^•cYZaV[dgbV NL eVgVZaXjVcid YZZcZg\}V&XVgVXiZg^oVgZbdhadhXVbW^dheZg^•Y^Xdh#XjnV kZadX^YVYYq egdeV\VX^•c hZVZ$edg hj c€bZgd X^gXjaVgYZ dcYVh P`Lj'Zhid Zh&edg Za;G;AZciZYZhj [gZXjZcX^VX^gXjaVgedg K%^

#M" tHdg digV &eVgiZ&bVciZcZbdh Za hZ\jcYd Xdbd jc^YVY YZ i^Zbed& n#q"bZcigVhcd hZ Y^\Vad XdcigVg^d$XdchZgkVgZbdhZaXb*h Xdbd jc^YVYYZkZad(X^YVY&Xdc ad fjZ aVkZadXqYVYYZaVajo VeVgZXZg{idYVk}VZmea}X^iVbZciZZc aVh[•gbjaVh Zc fjZ [^\jgZc i}Zbedh n kZadX^YVYZh)w

PAP) >zKA;9 ;GJHMK;MD9J -.4

DVaZXijgVYZZhiVha}cZVhcdh YZ_VeZgeaZ_dh)K^idYd ZaadegdXZYZYZ]VWZg]ZX]d Z 1 , #`VZ]Yf Of aNXV[TaURcRY\RVaf+, YVTUaN` b[Va +, cRY\RVaf$'xfj| ^b(edgiV Zabjai^ea^XVgedg Z adh }beZijh& hZVca^cZVaZhd Vc\jaVgZh&n fj| eVeZaYZhZbeZ~VaV Z Zc aVh[•gbjaVh Zc fjZ [^\jgZc i^Zbedh n kZadX^YVYZh8=hiZfj^iVg n edcZg aVZcd i^ZcZgVo•c YZhZg)G hZXdchZgkVh^ZbegZeVgV&YZVXjZgYdXdc cjZhigd edhijaVYd&hVakVgZa9c{a^h^hY^bZch^dcVa&d hZhjeg^bZ h^c ZmXZeX^•c)K^hZdeiV edg ZhiV€ai^bV VaiZgcVi^kV&Zai^Zbed n aVadc\^ijY VeVgZXZg{cXdbdbV\c^ijYZh ]dbd\|cZVh& n h•ad fjZYVg{c Zc EZX{c^XVYdhbV\c^ijYZh W{h^XVh&fjZ ejZYZc hZgaVadc\^ijY n aVbVhV);dc ZhiVbji^aVX^•c YZaVWVhZ&ZaXdcXZeidYZY^bZch^•c gZhjaiVXVh^c€i^a)

$" <IFA>ABM@JLKOM@OG>LBM"

;jVcYd hZ dWi^ZcZjcV ZXjVX^dc bZY^VciZ Za 9c{a^h^h Y^bZch^d(cVa&hZ hdWgZci^ZcYZfjZ h•ad Zh k{a^YVXdc jc^YVYZhXd]ZgZciZhXdcaVhZXjVX^dcZh[jcYVbZciVaZh&ejZh Va ji^a^oVgh^hiZbVh^cXd]ZgZciZh]Vn fjZ ^cigdYjX^gXdZ[^X^ZciZheVg{h^idh fjZ& edg YZeZcYZgYZ aVhjc^YVYZhVYdeiVYVh&hdc kZgYVYZgVhXdchiVciZhY^bZch^dcVYVh)<^X]d9c{a^h^h [^_VZa c€bZgd YZ jc^YVYZhW{h^XVh&eZgd YZ_VVgW^igVg^VhjcVijgVaZoVn hj XjVci}V&Xdc iVa YZ fjZ hZVcY^bZch^dcVabZciZ cYZ(eZcY^ZciZh);dc ZaadfjZYVc [^_VYVhaVhjc^YVYZhYZ idYVhaVhYZb{hbV\c^ijYZh) =cigZ adh ^c[^c^idhh^hiZbVhXd]ZgZciZh&bZgZXZc X^iVghZadh Ydh h^\j^ZciZh5

FV`aRZN RYRPa_\`amaVP\;?K5 XZci}bZigd&\gVbd& hZ\jcYd& \gVYd YZ;Zah^jh&[gVc`a^c)

FV`aRZN QR <V\_TV3bZigd& `^ad\gVbd&hZ\jcYd& \gVYd YZ ;Zah^jh&

XjadbW^d);jVafj^Zg h^hiZbVXd]ZgZciZhZgk^g}VZc >}h^XVcjXaZVg&eZgd edg YZh(

\gVX^VhZ ji^a^oVcjc^YVYZh cXd]ZgZciZh&ad fjZ ^bea^XV&cd h•ad jcVkZgYVYZgVeaV\V YZ XdZ[^X^ZciZheVg{h^idh&h^cd \gVc Xdc[jh^•c Zc adhXdcXZeidh&ejZh hZegZiZcYZ_jhi^[^XVgaVZaZXX^•cYZiVaZhjc^YVYZhXdcaVhb^hbVh gVodcZhfjZ&hZ\€c ]Zbdh ]ZX]d kZgZc ZaVeVgiVYdVciZg^dg&XVgZXZcYZ[jcYVbZcid) DVhjc^YVYZhcXd]ZgZciZhhjWh^hiZcedg Zab^hbdbdi^kd edg ZafjZ adh^c\Zc^Zgdhh^\jZc jhVcYdZaeZhdYZa^ad\gVbd Xdbdjc^YVYYZ[jZgoV)=h YZYZhZVgfjZ jc VXjZgYdciZgcVX^dcVaedc\V i|g(b^cd VZhiVh^ijVX^•cXV•i^XV)

=c >}h^XVXdgejhXjaVg&aVhadc\^ijYZhn adhi^Zbedh hjZaZcbZY^ghZZcXZci}bZigdhn hZ\jcYdh&gZheZXi^kVbZciZ&d W^ZchZgZXjggZVhjh b€ai^(eadhn hjWb€ai^eadhYZX^bVaZh)DVhhZXX^dcZhZ[^XVXZhhZb^YZc Zc O\_[R3

, WVgc1 ,+(-/ Xb!&

Page 120: Análisis dimensional

-/+ 9FyDAKAK <AE=FKAGF9D

HVgVaVbVhVhZegZXdc^oVZaZbeaZd YZaVb[VQNQZmRVPN3

, jb 7 U,U 7 ,&1042P ,+(-/ \&A6

YdcYZ;0 ZhZac€bZgd YZ9kd\VYgd) 9YZb{h&fj^ZcZh egZiZcYZcfjZ]Vn kZciV_VZc ]VXZgEMG1 ,&^cigdYjXZciVciVhjc^YVYZhYZbVhVXdbdjc^YVYZhYZZcZg\}VhZ]VaaVcZc jhd) 9a egdXZYZgVh}hZXdbZiZZab^hbdYZhVi^cdfjZ XjVcYdhZ Xdc[jcYZ aVbVhV Xdc ZaeZhd n hZidbV Xdbdjc^YVYYZ[jZgoVZa`^ad\gVbd(bVhV)KZ\€c ZhiZk^X^dhdb|idYd& hZg}V5

*, Zg\(bVhV1 ' 1 ,&,,, P ,+(-, \

P-

, B(bVhV1 ,&,,, P ,+(,/ \&

n idYVk}VfjZYV jcV cjZkV jc^YVY YZ bVhV&aV XdggZhedcY^ZciZVaRYRPa_o[(c\YaV\d Rc\YaV\#Zk$&fjZ hZYZ[^cZXdbd aVZcZg\}VfjZ Vafj^ZgZjcZaZXig•cVagZXdggZgjc igVnZXidZc ZafjZ aVXV}YVYZediZcX^VakVaZjckdai^d);dbd aVXVg\VYZaZaZXig•cZh5

Z 1 ,&1++3P ,+(,4 XdadbW^dh&hZg{5

, Zk 1 ,&1++3P ,+(,4 _ja^dh&

n aVXdggZhedcY^ZciZjc^YVYYZbVhV hZg}V5

, Zk(bVhV 1 ,&224 P ,+(.. \)

KZ]Vc YZ[^c^YdnVaVhjc^YVYZhYZadc\^ijY&YZbVhV&YZi^Zbed n YZZcZg\}V&n Xdbd h•ad ejZYZ ]VWZgZc aVWVhZigZhbV\c^ijYZh bZX{c^XVh&ZhXdhVYZVkZg^\jVgh^hZejZYZ [dgbVg Xdc ZaaVhjc h^hiZbVXd]ZgZciZ)LdbVcYd Xdbd W{h^XVVZaXZci}bZigd&ZahZ\jcYd M ZaZkdai^d&aVjc^YVYXd]ZgZciZYZ[jZgoVYZW^ZgVhZg5

A] 1 ,&1++3,+(,- Y^cVh&n aVYZbVhV5

aV41 ,&1++3,+(,- \&

fjZ cd Xd^cX^YZXdc c^c\jcV YZaVhVXijVabZciZZc jhd) =hid egjZWVfjZ Zh ^bedh^WaZ[dgbVg jc h^hiZbVXd]ZgZciZh^ hZ ^bedcZ ZaZkdai^d

PAP) >zKA;9 ;GJHMK;MD9J -/,

Xdbd jc^YVYYZZcZg\}V&Za Zkdai^d(bVhVXdbd jc^YVYYZbVhV&n hZfj^ZgZ XdchZgkVgZaXZci}bZigdn ZahZ\jcYd #d hjh b€ai^eadh n Y^k^hdgZhYZX^bVaZh$Xdbd jc^YVYZhYZadc\^ijY n YZi^Zbed&gZheZXi^kVbZciZ)

.) EV\c^ijYZh jhVYVhZc gVY^VXi^k^YVYM gVY^dad\}V)

DVnV ZbWgdaaVYVXjZhi^•cYZaVhjc^YVYZhXdgejhXjaVgZhhZXdbea^XVV€c b{h XjVcYdhZ idbVc Zc Xdch^YZgVX^•caVhbV\c^ijYZh jhVYVhZcgVY^VXi^k^YVYn gVY^dad\}V)

DV NPaVcVQNQ'0# d edYZg Zb^h^kdYZ jc XjZged gVY^VXi^kdZh&edgYZ[^c^X^•c5

6 a}b X';1'a(&B X'X

YF1''&

Qa

YdcYZX'; ZhZac€bZgd YZ{idbdh fjZ hZigVch[dgbVcZc Zai^Zbed X'X%Kj jc^YVYXd]ZgZciZZc Zah^hiZbVXZ\Zh^bVaYZW^ZgVhZgaVVXi^k^YVYYZjc XjZgedfjZ hZYZh^ciZ\gVVgVo•cYZjc {idbd XVYVhZ\jcYd&n edYg}VaaVbVghZb^Xgdgji]Zg[dgY#jgY$&nV fjZ hZ]V YZ[^c^YdZagji]Zg[dgY #gY$Xdbd aVVXi^k^YVYYZjc XjZgedZc ZafjZ hZegdYjXZjc b^aa•c YZYZh^c(iZ\gVX^dcZhXVYVhZ\jcYd) <Zh\gVX^VYVbZciZ&cd ]Vn \gVcYZhZheZgVcoVhYZfjZ Zagji]Zg[dgY egZkVaZoXV&ejZh h^\jZ jh{cYdhZZaPb_V\' fjZ ZhjcVjc^YVY cXd]ZgZciZ5

, Xjg^d1 .&2 P ,+,+ [DgY)

DVNPaVcVQNQR`]RPnSVPNhZYZ[^cZbZY^VciZaV[•gbjaV5

6I/$$( Z"

YdcYZS ZhaVbVhVYZaXjZged)Kj jc^YVYXd]ZgZciZZc Zah^hiZbV;?K&YZW^ZgVhZgZa[DgY*\&eZgdhZjhV ZaXjg^d*\gVbd&

DVP\[`aN[aR _NQVNPaVcNZh&edg YZ[^c^X^•c5

, YF3''/ YZ"

M hZb^YZZc K(a)

>^cVabZciZ&aV`RZVcVQNZhi{ YZ[^c^YVedg aV[•gbjaV5

G Ac- U +&14.

1 1n hZb^YZZc hZ\jcYdh)

9FyDAKAK <AE=FKAGF9D) ( ,1

Page 121: Análisis dimensional

+-+ 9FyDAKAK <AE=FKAGF9D

K eVhVbdhVaVhbV\c^ijYZh fjZ hZjhVc Zc gVY^dad\}VXdcZaegde•h^idYZYdh^[^XVgaVgVY^VX^•c&hZigde^ZoVXdciVaZhY^[^XjaiVYZh&fjZ XdcdXZbdhgVY^•ad\dhZb^cZciZhfjZ Xdc[^ZhVccd ]VWZgad\gVYdZciZcYZgaVYZ[^c^X^•cYZagdZci\Zc) =c digd aj\Vg #3+$]Zbdh igViVYdYZedcZg Zc XaVgdaVhYZ[^c^X^dcZhYZYdh^h&n XVhh^bjai{cZVbZciZ VeVgZX^ZgdcaVhJZXdbZc(YVX^dcZhAciZgcVX^dcVaZhhdWgZMc^YVYZhJVY^da•\^XVh&fjZ Xd^cX^YZcZciZgVbZciZXdc cjZhigVhXdcXajh^dcZh)9fj} cdh a^b^iVgZbdhV YZ[^c^gaVYdh^hhjb^c^higVYVn aVYdh^hVWhdgW^YV)

9a YZ[^c^gaVYdh^hhjb^c^higVYV&3# hZYVedg hjejZhid fjZ ad fjZ ^c(iZgZhVYZaVgVY^VX^•ceVgVadh[^cZhiZgVe|ji^XdhZhhj edYZg^dc^oVciZ&nfjZ WVhiVXdcdXZghj kVadgZc ZaV^gZZc XdcY^X^dcZhcdgbVaZh)=a edYZg^dc^oVciZZh&edg YZ[^c^X^•c&aVXVg\VidiVa fjZ aaZkVcXdch^\dadh^dcZhYZXVYVh^\cd a^WZgVYdhedg aVgVY^VX^•cZc aVjc^YVYYZkdajbZc YZV^gZZc XdcY^X^dcZhcdgbVaZhn Zc aVjc^YVYYZi^Zbed5

HdYZg dc^oVciZ( q&Ia

n aVYdh^hhjb^c}higVYVZhZaegdYjXid YZaedYZg^dc^oVciZedg Zai^ZbedYZ^ggVY^VX^•c5

' Y)B

Kj [•gbjaV Y^bZch^dcVaZh5

E3G1 ?(.D

n hj jc^YVYZc Za h^hiZbVXZ\Zh^bVaZh ZagdZci\Zc) =c Zah^hiZbVYZ?^dg\^&aVjc^YVYhZg{. ) ,+. kZXZhbVndg)

DV Ydh^hVWhdgW^YVhZ YZ[^cZXdbd aV ZcZg\}VVWhdgW^YVedg XVYV\gVbd YZiZ_^YdV XdchZXjZcX^VYZaV^ggVY^VX^•c)Kj jc^YVYXd]ZgZciZZc Zah^hiZbV;?K& YZW^ZgVhZgZaZg\_\&eZgd hZji^a^oVZagZe&fjZ ZhjcVjc^YVY^cXd]ZgZciZ5

, gZe ( 3. Zg\_\)

9XijVabZciZ&hZ jhV ZagVY5, gVY1 ,++ Zg\_\)

&" 0JMFMBI COI@FVIABG>>@NFPFA>A" ABG>AFMN>I@F>"

HVgVedcZg YZbVc^[^Zhidadh^cXdckZc^ZciZhYZaZbeaZd YZjc^YVYZh^cXd]ZgZciZh&igViZbdh YZgZhdakZgZah^\j^ZciZ egdWaZbV)KZY^hedcZYZjc XjZgedXjnVVXi^k^YVYkVaZ0# n hZhVWZfjZ Zc XVYVYZh^ciZ\gVX^•c

PAP) >zKA;9 ;GJHMK;MD9J +-,

Zb^iZ jcV hdaVeVgi}XjaVXdcjcV ZcZg\}VJ) KZXdcdXZZaXdZ[^X^ZciZidiVaYZVWhdgX^•c&C6&YZY^X]VheVgi}XjaVhZc ZaV^gZ&n hZhVWZfjZ XVYVdcaaZkVjcV XVg\VR' n fjZ Zc aVegdYjXX^•cYZXVYVeVgZ_VYZ^dcZhhZXdchjbZ&edg i|gb^cd bZY^d&jcV ZcZg\}VZ5) ^Ij| Ydh^hhZdWiZcYg{XVYVjc^YVYYZi^Zbed Zc jc ejcid fjZ Y^hiVWYZaXjZgedgVY^VXi^kd HVgVcd iZcZgfjZidbVg Zc Xdch^YZgVX^•caVgVY^VX^•chZXjcYVg^V&hZhjedcZ fjZ aVgVY^V(X^•chZegdeV\V Zc ZakVX}d)

;dc aVhbV\c^ijYZh X^iVYVh&Za9c{a^h^hY^bZch^dcVaXdcYjXZV5

9Wa 6 J C6 _ R

9 %) G ( ' * * G: G G * G G G@ '* ' * %( G G GD * G G G G *

-0' * ' * G G ) ' *-0( G G G * * G

Jd5((Z5

0M ! J$3PX 7 2 K= N9W#(Z5( )

;dbd aVYdh^h]V YZkVg^VgZc gVo•c^ckZghVYZaXjVYgVYdYZaVY^hiVcX^V&n hZgegdedgX^dcVaV aVZcZg\}V&J' YZXVYVeVgi}XjaVgZhjaiV5

px 1 R 0MN9Ca R3_-

=a X{aXjadXdbeaZid&hZ\€c hZkZ [{X^abZciZ&XdcYjXZV aVgZaVX^•c5

fjZ Zhk{a^YVXdc XjVafj^Zgh^hiZbVYZjc^YVYZhXd]ZgZciZh)HZgd&Zc aV&eg{Xi^XV&0 hZZmegZhVZc Xjg^dh&R Zc Zah^hiZbV;?K=& C6Zc Xb(a&CMT

EZk& Z5 Zc Zk&g Zc Xb&n hZe^YZaVYdh^hZc gdZci\Zch_]dgV)=cidcXZh&]Vn fjZ ^cigdYjX^gcjbZgdhdh XdZ[^X^ZciZheVg{h^idh&n aV[•gbjaV hZXdc(k^ZgiZZc5

.&2< ,+,+ < ,+1 < .1++

/2i

9 0MN9C

R3_-

Page 122: Análisis dimensional

-// 9FyDAKAK <AE=FKAGF9D

fjZ&Xdbd R 1 /&3+ P ,+(,+ j) Z)Z)n Z1 .- Zk&YV5

6J3 7 ,&04" aG3[D '+'! a)

_

=hiV [•gbjaV YVaVYdh^hZc gdZci\Zch&M cd ejZYZ hZgji^a^oVYVh^cdb^Y^ZcYd[D Zc Xb(E&6 Zc Xjg^dh&J Zc EZk&WZc Xb MaZc ]dgVh)

'" <I MFMNBH>ABOIFA>ABM@JEBLBINBMK>L>G>2UMF@>ABGJM@JLKWM@OGJMQ ABG>L>AF>@FVI"

;jVcYd igVh bZY^d h^\ad YZ ^cXdbegZch^1c ]V ad\gVYd egZkVaZXZgZa h^hiZbVYZ ?^dg\^ Zc =aZXigdbV\cZi^hbd& hZg}VYZZheZgVgfjZ hjh kZciV_Vh[jZhZc iVb(W^|c gZXdcdX^YVhedg adh fjZ Xjai^kVc aV>}h^XVYZadh Xdge€hXjadhn YZaVgVY^V(X^1c&eZgd&edg YZh\gVX^V&cd kVc aVhXdhVhedg ZhiZ XVb^cd)

<dh gVodcZhhjZaZc VYjX^ghZZc XdcigV YZah^hiZbV YZ ?^dg\^) McV Zh aV YZfjZ hjh jc^YVYZhhdc YZhbZhjgVYVhh^ hZ XdbeVgVc Xdc aVhXVci^YVYZhfjZ hZbVcZ_Vc Zc ZabjcYd hjWVi1b^Xd6aVdigV Zh fjZ Zajhd YZjc^YVYZhZheZX^VaZh&iVaZhXdbd Za Zkdai^d&[VX^a^iVZa aZc\jV_Z n h^bea^[^XVadh X{aXjadh)DV eg^bZgVgVo1c cdh eVgZXZWVaVY}&ejZh XjVafj^Zg h^hiZbV YZ jc^YVYZh]V YZ YVgc€bZ(gdh bjn \gVcYZh d bjn eZfjZ~dh Va ji^a^oVgadeVgV bZY^g aV kZadX^YVYYZ aVajo n aVhY^bZch^dcZhYZadhc€XaZdhVi1b^Xdh)DVhZ\jcYV Zh[€i^a h^hZXdch^YZgVcadh WZcZ[^X^dhfjZ gZedgiV aVhjegZh^1c YZXdZ[^X^ZciZheVg{h^idh&ad b^hbd Zc aVhZXjVX^dcZhegde^VhYZaV>}h^XVVi•b^XV fjZ Zc aVhfjZ h^gkZc&edg Z_Zbead&eVgVZaX{aXjadYZadh VXZaZgVYdgZhYZeVgi}XjaVh)

=c gZVa^YVY&adh igVhidgcdh fjZ egdYjX^g}VaVVYdeX^•c YZah^hiZbV YZ ?^dg\^hZ gZYjXZcV iZcZg fjZ XVbW^VgZc aVhiVWaVhYZgVY^h1idedhaVhZcZg\}VhZmegZ(hVYVhZc Zkdai^dhd Zc bZ\VZkdai^dh edg hjh Zfj^kVaZciZh Zc _ja^dh&n V ^cigdYj(X^gcjZkVh jc^YVYZhYZ Ydh^h&V hVWZg5

Mc^YVYYZ Ydh^hhjb^c^higVYV5

XjadbW^d, 1 .v adVgdZci\Zch)

FK

Mc^YVYYZ Ydh^hVWhdgW^YV5

, _ja^d U ,+/ Zg\ U ,-0((( ( ( gZe)`\ \

<ZhYZajZ\d& hZ ejZYZc [dgbVg ^c[^c^idh h^hiZbVhXd]ZgZciZh&ejZh ZhVgW^igV(g^VaV ZaZXX^1cYZ XjVigd jc^YVYZh&h^c XdciVg Za \gVYd YZ iZbeZgVijgV) HZgdhjXZYZfjZ& h^hZ VYdeiVZaZkdai^deVgVaVjc^YVY YZZcZg\}V&_jciVbZciZ Xdc ZahZ\jcYd n XjVafj^ZgVYZadh b€ai^eadh YZX^bVaZhYZabZigd& c^c\jcV YZaVhjc^(YVYZhYZbVhV VXijVabZciZ Zc jhd Zh Xd]ZgZciZ)Q&h^hZ VYdeiV Zakdai^d Xdbdjc^YVY YZediZcX^VaZa|Xig^Xd&_jciVbZciZ Xdc ZaZkdai^dXdbd jc^YVY YZZcZg\}V&cd hZ ejZYZ VYdeiVgZa`^ad\gVbd& c^ c^c\jcd YZhjh Y^k^hdgZhYZX^bVaZh&Xdbdjc^YVY YZbVhV)

PAP) >zKA;9 ;GJHMK;MD9J -/0

9 i}ijad YZXjg^dh^YVY&YVbdh VXdci^cjVX^1cjc h^hiZbVYZjc^YVYZhXd]ZgZc(iZh Zc fjZ hZidbV ZaZkdai^d Xdbd jc^YVY YZZcZg\}Vn Zc ZafjZ idYVhaVhgZaV(X^dcZhZcigZ aVhcjZkVh jc^YVYZhn aVhYZah^hiZbV)YZ ?^dg\^ hZ ZmegZhVcXdcVjm^a^dYZ jc hdad c€bZgd5

N 1 ,&1+- ,+(,4&

fjZ Zh ZakVadgYZaVXVg\VZaZbZciVaZmegZhVYVZc XjadbW^dh)

H[VQNQROm`VPN`3

Ddc\^ijY5 bZigd)L^Zbed5 hZ\jcYd)EVhV5N \gVbdh);Vg\V Za|Xig^XV5N XjadbW^dh)

H[VQNQRQR_VcNQN`3

:VhiV iZcZg V aVk^hiV Za XjVYgdYZ[•gbjaVh Y^bZch^dcVaZh&eVgVaaZ\VgV aVXdcXajh^1cYZfjZ& Zc ZhiZh^hiZbV&aVhjc^YVYZhYZediZcX^Va&ciZch^YVYYZaXVb(ed Za|Xig^XdZ ^cYjXX^1cbV\c|i^XV hdc aVhb^hbVh fjZ Zc Zah^hiZbV YZ ?^dg\^6aVhYZ[jZgoV&ZcZg\}V&}beZij& ^cYjXX^1cZaZXigdhi{i^XV&bdbZcid YZadh Y^edadhZa|Xig^Xdn bV\c|i^Xd& XVeVX^YVY&^ciZch^YVYYZ aV Xdgg^ZciZn edYZg ^bVcVYdg&hZ dWi^ZcZcbjai^ea^XVcYd edg Za c€bZgd N aVhgZheZXi^kVhjc^YVYZhYZ ?^dg\^6[^cVabZciZ&aVjc^YVY YZgZh^hiZcX^VZh N kZXZhbZcdg fjZ Zad]b^d)

(" 7IA> >MJ@F>A>> OI> K>LNU@OG>BI HJPFHFBINJ"

KZ\€c aV]^e•iZh^hYZaYjfjZ #VciZheg}cX^eZ$Ddj^h YZ:gd\a^Z&idYVeVgi}XjaVZc bdk^b^Zcid aaZkVVhdX^VYdjc [Zc•bZcd dcYjaVidg^dXV(gVXiZg^oVYdedg hj adc\^ijY YZdcYV 9) =hiV bV\c^ijY ]V YZ fjZYVgYZiZgb^cVYVedg aVbVhVZc gZedhd&Z\' n edg aVkZadX^YVY&c' Xdc aVZkZcijVaeVgi^X^eVX^•cYZaVhXdchiVciZhjc^kZghVaZhU M R3

3 Z\ c U

? , G , -@ G , G ,@ G G , ,

-5' , , , ,

[/cR

0/HO \!\"%Z\c R

KZejZYZ V]dgViZcZg Zc XjZciV fjZ Za XdX^ZciZc*R ^ciZgk^ZcZiVch•ad Zc aViZdg}VYZaVgZaVi^k^YVY&n fjZ h^gkZeVgVeVhVgYZaVbVhVZc

Page 123: Análisis dimensional

(*, 9FyDAKAK <AE=FKAGF9D

gZedhd&Z\' V aV bVhV Zc bdk^b^Zcid& Z) KZg{&ejZh5

U317'(

ZcR1),T

KZ\€c <Z :gd\a^Z&Zh G 1 ,);dbW^cVcYd R1&,TXdc aVZXjVX^•cYZ=^chiZ^c&

Z51 WTK-1 ]k&

gZhjaiVeVgVaVkZadX^YVYYZegdeV\VX^•c5

X-

A 1 3; 1 +()c

DViZdg}VXdbeaZiV XdcYjXZV G 1 ,)

)" 4> COI@FVIABJIA>M"

@VhiVV]dgV&ZaXVb^cdfjZ eVgZXZb{h egdbZiZYdg eVgVaaZ\VgVjcViZdg}VYZadh [Zc•bZcdh XdgejhXjaVgZhZhZafjZ eVgiZ YZaVZXjVX^•cYZKX]gdY^c\Zg5

U 2+* U-' % qd*( I"C" 7 +&,X ,'X(S

R2),T

Zc aVfjZ O ZhaVXdchiVciZYZHaVcX`&S aVbVhVYZaXdge€hXjad&n B hjZcZg\}VediZcX^Va)=c XjVcid V aVfjZ ejY^|gVbdh aaVbVgegdiV\dc^hiVYZaVZXjVX^•c&aV[jcX^•c G*&hZa^b^iVKX]gdY}c\ZgVYZX^gfjZ h^gkZeVgVYZiZgb^cVgjc}kdXVbZciZ Za ZhiVYdYZah^hiZbV)=h idYVk}VdW_ZidYZY^hXjh^•chj h^\c^[^XVYd[}h^Xd&eZgd Za9c{a^h^hY^bZch^dcVaejZYZ YZX^gcdhVa\d bjn ^ciZgZhVciZVXZgXVYZaVb^hbV) =c aVZXjVX^•cR2&,TaVY^bZc(h^•c YZd* fjZYV ^cYZiZgb^cVYV&eZgd hjXZYZfjZ aVh€c^XVhhdajX^dcZhVXZeiVWaZhhdc aVhcdgbVa^oVYVh&d hZVVfjZaaVhZc fjZ hZXjbeaZ fjZ

3-$(4

YdcYZ+*%ZhaV[jcX^•c XdbeaZ_VXdc_j\VYVYZG*&n Q(_3ZhZaZaZbZcid YZkdajbZc) KZ\€c Zhid&]VWg{YZhZg5

R+*+*%T1 ?(.'

&(((

PAP) >zKA;9 ;GJHMK;MD9J (*-

YZYdcYZgZhjaiVfjZ ZaegdYjXid YZ+*+*%edg jcV bV\c^ijY XjVafj^ZgV&'gZegZhZciVaVYZch^YVYYZaVb^hbV5

H 1 ^\*\*%)

*" 9>AFJ @GSMF@JABGBGB@NLVIBI BGP>@UJ"

KZhjedcZ fjZ idYVaVbVhV&Z\' YZaZaZXig•cZhYZW^YVV hj ZcZg\}VediZcX^Va&Zhid Zh&VaigVWV_dfjZ Zh egZX^hdgZVa^oVgeVgVXdcYZchVgaVXVg\V&R' Zc jcV Zh[ZgVYZgVY^d&_' edg ad fjZ ]VWg{YZYZeZcYZgYZaVhXdchiVciZhYZakVX}d&Z5 n X);dc aVhbV\c^ijYZh bZcX^dcVYVhh•ad ejZYZ[dgbVghZjc bdcdb^d e^&n gZhjaiV5

R-

_ 1 G ((d R3&,TZ5gcX(

DV b^hbV [•gbjaV& ZbaNaV`ZbaN[QV`' h^gkZeVgVZaegdi•c)

+" 1IBLDU>BGB@NLJMNSNF@>ABGJMIW@GBJM>NVHF@JM"

K^ZcigZ adh cjXaZdcZhcd hZZ_ZgX^ZgVcb{h [jZgoVhfjZ aVhegZk^hiVhedg aVaZnYZ;djadbW& ZaigVWV_dcZXZhVg^deVgVgZjc^g D egdidcZh Zc jcc€XaZdVi•b^Xd YZgVY^d?# YZeZcYZg{YZaVXVg\VZaZbZciVa&R' YZagV(Y^d&_\' YZacZjig•c n YZaVhXdchiVciZhYZakVX}dZ5 n P)

C R ? Z

? ( 7 * %) *: * 7 7 '* 7

@ %( 7 7 ( '*D 7 * 7 ( 7

/KO * %( * * 7

R-

# _\ $d5 Z5J I2 D ? %

KZ\€c :Zi]Z n :VX]Zg #3,$&Zc Zah^hiZbVZaZXigdhi{i^XdZh5

. R-

C 7 ( D!D $ *# '&$ ,

eZgd&hZ\€c ]^X^bdh kZg Zc digd aj\Vg "-,#$aV[•gbjaV XdggZXiVZh5

d5h#h(h$)0 E _\

Page 124: Análisis dimensional

(*. 9FyDAKAK <AE=FKAGF9D

,+) >jZgoVYZDdgZcio)

V6 fj| [jZgoVhZ]VaaVhdbZi^Ydjc ZaZXig•cfjZ hZbjZkZ Zc jc XVb(ed bV\c|i^Xd8

<Za XVbed WVhiVg{XdcdXZgZakZXidg:& fjZ ZhZagZhedchVWaZYZaVhVXX^dcZhedcYZgVaZh)=a ZaZXig•c[^\jgVg{ edg hj XVg\V&R' Medg hj kZad(X^YVY&c)

K^XdcadhYVidhegZXZYZciZhhZVea^XVZa9c{a^h^hY^bZch^dcVacd Xdc(h^YZgVcYdb{h fjZ jcV bV\c^ijY ZheVX^VaZc aVWVhZ&hZdWi^ZcZjc bd(cdb^d e^5

N2i, 1 ''&

RcE

fjZ eZgb^iZ V[^gbVgaVegdedgX^dcVa^YVYYZCXdc M N Xdc :& eZgd fjZcVYVY^XZgZheZXidYZaVedh^X^•cgZaVi^kVYZZhidhigZhkZXidgZh)

HVgV]VaaVgaVXjVci}Vn aVY^gZXX^•cYZ aV [jZgoV&]Vn fjZ ]VaaVghjh Xdb(edcZciZh ,," ,-" Ah&Xdc gZaVX^•cV jc h^hiZbV YZ Z_ZhXddgYZcVYdh)L•bZhZ ZaZ_ZPa Zc aVY^gZXX^•cYZaVkZadX^YVY&Xdc ad fjZ hZg{c- 1 kV 1 G&Q Za eaVcdPa e- YZbdYd fjZ XdciZc\V ZakZXidg:& Xdc ad XjVa&:h 1 G)Mi^a^oVcYdaVh[•g(bjaVh Y^bZch^dcVaZhYZas /&XVe}ijadPNAA&hZkZ fjZ Xdc aVhX^iVYVhbV\c^ijYZhn aVhXdbedcZciZh ,, M,- YZaV[jZgoV cd hZ ejZYZ [dgbVg c^c\€c bdcdb^d e^&ad fjZ h^\c^[^XVfjZ Y^X]VhXdbedcZciZh cd YZeZcYZcYZNa" Q Xdbd ,, 7 ,- 7 Gh^kE1 G&ad b^hbd dXjgg^g{VjcfjZ kE 1*1 G)HVgVaViZgXZgVXdbedcZciZ hZi^ZcZ5

ad fjZ egjZWVfjZ aV[jZgoV Zh eZgeZcY^XjaVgVaeaVcd YZiZgb^cVYdedg c M :Q kVaZ5

C1 <MZ 'F :)DV iZdg}VXdbeaZiV YV 7 1 a)

=h YZ cdiVg fjZ& edg ji^a^oVgjc h^hiZbV Y^bZch^dcVaZc fjZ Rr)r)T1 ,& aV[•gbjaV Y^bZch^dcVaYVYVedg Zaegde^d DdgZcio Zh^cXdggZXiV&hZ\€c ]^od cdiVgKdbbZg[ZaY&ejZh [^\jgV Zc ZaaV@ Zc aj\Vg YZ:)

PAP) >zKA;9 ;GJHMK;MD9J (*/

,,) JVY^dYZXjgkVijgVYZaVigVnZXidg^VYZjc ZaZXig•cZc jc XVbed bV\c|i^Xd)

<Za egdWaZbVVciZg^dggZhjaiVfjZ&h^ZaXVbed Zh]dbd\|cZd& aV[jZg(oVhZg{XdchiVciZn&Xdbd ZhcdgbVa VaVigVnZXidg^V&|hiV ]VWg{YZhZgX^gXjaVg)9YZb{h&idbVcYd adhZ_ZhXdbd Zc ZaegdWaZbVVciZg^dg&gZhjaiVfjZ h•ad^ciZgk^ZcZaVXdbedcZciZ 7- YZ:& ZhidZh&aVfjZ ZheZgeZcY^Xj(aVgVk)

_ c &- Z Z

9 , , G G G: G G , , GG G ( , ( , G G> G G , G ,

2iE , ( , , , ,

SZ_ 7 +(()

P7

DViZdg}VYVG 7 ,)

,-) 1G Zhe}c)

DVheVgi}XjaVhZaZbZciVaZhedhZZc jc }beZij Vc\jaVg #Zhe}c$&Xdbdh^ \^gVhZcZc idgcd YZh} b^hbVh) 9Yb^i^ZcYd fjZ hj XdbedgiVb^ZcidbZX{c^XdfjZYV YZiZgb^cVYdedg hj bdbZcid YZ^cZgX^V&n iZc^ZcYdZcXjZciVaVedh^WaZciZgkZcX^•cYZaVhXdchiVciZhjc^kZghVaZhUMR' gZhjaiVjc hdadbdcdb^d e^6MaVhdajX^•cZh5

3 1 <O#

fjZ cd YZeZcYZYZabdbZcid YZ^cZgX^VYZaVeVgi}XjaV)DViZdg}VY^XZfjZ G Zhjc b€ai^ead ZciZgdd hZb^ZciZgdYZ,*- gg)

HdYZbdh V]dgVgZhdakZgZah^\j^ZciZ egdWaZbV)x;j{cid kVaZZaVjbZcid& YYZ'fjZ ZmeZg^bZciVaVbVhV YZjcV eVgi}XjaVXjVcYd hj Zhe}c eVhVYZakVadgG Va

kVadg]*-2i8KZVS aVbVhV Zc gZedhd YZaVeVgi}XjaV&fjZ hjedcYgZbdh Zh[|g^XV)K^WZh

d ) {ZagVY^d&Za bdbZcid YZ^cZgX^VgZheZXidYZjc Y^{bZigd XjVafj^ZgV&hZg 5

9a \^gVgaVeVgi}XjaVZc idgcd YZ jcd YZ hjh Y^{bZigdh Xdc jc }beZij Vc\j(

Page 125: Análisis dimensional

-0+ 9FyDAKAK <AE=FKAGF9DPAP) >zKA;9 ;GJHMK;MD9J -0,

aVgU*-,,3' aV[gZXjZcX^V]VWg{YZhZgiVa fjZ5

U-,,3c> 1 ''&

-,,3

iVciZhjc^kZghVaZh=G Q O#aVeg^bZgVeVgVidbVg XjZciVYZaVh[jZgoVhYZ;djadbW&n aVhZ\jcYVedg Z[ZXidYZaVXjVci^oVX^•c)

DViZdg}VYV5

X R ‚d U Z

9 G G %) - G: G G '* * *G '* G - '* GD G * - G G

,,3, * %* - ) ' *

M Z\d5((

Z]

X 1 G Z\R/

# Z\ $4 -U. 08 Z )d ]

X5Z\R/

2:\-U. #, 5 55$

d hZV5

>*+&*?

MaVZcZg\}VX^c|i^XVYZgdiVX^•ckVaYg{5

=c XdchZXjZcX^V&ZaVjbZcid gZaVi^kdYZbVhV hZg{5

#%" 1G H>DIBNVIAB.JEL"

KZ]V VkZg^\jVYdfjZ aVheVgi}XjaVhedhZZcjc bdbZcid bV\c|i^Xd&CE#cd Xdc[jcY^gXdcaVeZgbZVW^a^YVYbV\c|i^XV$&fjZ ]VWg{YZYZeZcYZgYZZ' R' O%DV[•gbjaV Y^bZch^dcVaYZCEZh >CE?1 B@$-7>#n Za9c{a^h^hY^bZch^dcVaXdcYjXZV5

G RUCE1 '(

S

DVXdchiVciZq 7 X*P' YdcYZP ZhaVkZadX^YVYYZaVajo&hZaaVbVXdch(iVciZ YZJnYWZg\)

#'" 1G MFMNBH>ABG>M@JIMN>INBMOIFPBLM>GBM"

c 7 X #U, UU , $"- T-

T 1 ,&-&.&)))

=a jc^kZghd Zhi{ Xdchi^ij^Ydedg Xdge€hXjadh#ZaZXigdcZh&egdidcZh&cZjigdcZh&ZiX)$fjZ hZXVgVXiZg^oVcedg hj bVhVn edg hj XVg\VZa|Xig^XV)9 aVhnVcjbZgdhVh ZheZX^ZhYZXdge€hXjadhXdggZhedcYZcbVhVhY^kZghVh&eZgdh•adhZXdcdXZjcV XV)g\VZaZbZciVa&aVYZaZaZXig•c)=hiVhXVci^YVYZhejZYZc Xdch^YZgVghZXdbd XdchiVciZhjc^kZghVaZh&n ZaaVh&_jciVbZciZXdc aVhXdchiVciZhjc^kZghVaZhegde^VbZciZ Y^X]Vh&hdc adh h^aaVgZhXdcfjZ ]Vc YZXdchigj^ghZaVhiZdg}Vh[}h^XVh)

=a 9c{a^h^hY^bZch^dcVaeZgb^iZV[^gbVgfjZ&Zc XVYViZdg}V&Zac€bZgdYZ XdchiVciZhjc^kZghVaZhY^bZch^dcVabZciZ cYZeZcY^ZciZhcd ejZYZZmXZYZgYZaVbjai^ea^X^YVYYZaVWVhZgZheZXi^kV)NZgZbdh&VYZb{h&fjZh^ZbegZejZYZ [dgbVghZjcV WVhZXdc XdchiVciZhjc^kZghVaZhZmXajh^kV(bZciZ&YZYdcYZgZhjaiVfjZ XjVafj^ZgdigV]VWg{YZhZg[jcX^•c bdcd(b^V YZaVhfjZ hZidbZc eVgVXdchi^ij^gaVWVhZ)DVhXdchiVciZhjc^kZg(hVaZh&edg Xdch^\j^ZciZ&ejZYZc Xdch^YZgVghZXdbd kZXidgZhZc jc ZheV(X^dkZXidg^VaXdc iVciVhY^bZch^dcZhXdbd kVa\VaVbjai^ea^X^YVYYZaVWVhZ&Zhid Zh&X^cXdZc ZaXVhdb{h \ZcZgVa)=c XdchZXjZcX^V&[\ ]bRQR

DViZdg}VYVG 1 ,*/2i& Xdcad fjZ&Zc ZaXVhdYZaZaZXig•c&hZi^ZcZ5

NR11 +&4-1) *)'+, Vbe < b(&

fjZ ZhZabV\cZi•c YZ:d]g)

#&" 4> @JIMN>INBAB9QA?BLD"

DV hZg^ZYZ:VabZg Zc Za ZheZXigdYZa]^Yg•\Zcd Zhi{ YVYVedg aVZXjVX^•c5

n hZigViVYZXVaXjaVgaVXdchiVciZQ%=c ZaegdWaZbV ciZgkZcYg{caVhbVhVhSU n SV YZaZaZXig•cn YZaegdi•c&aVXVg\VZaZbZciVa&M#n aVhXdch(

Page 126: Análisis dimensional

(+( 9FyDAKAK<AE=FKAGF9D PAP) >zKA;9 ;GJHMK;MD9J (+)

UNOR_Zm` QRPV[P\P\[`aN[aR` b[VcR_`NYR`bR `RN[ QVZR[`V\[NYZR[aRV[QR(]R[QVR[aR`)F•iZhZ fjZ fjZYV YZiZgb^cVYdZa c€bZgd YZ XdchiVciZhW{h^XVh&eZgd]Vn a^WZgiVYZc hj ZaZXX^•c#%$)

=c aVEZX{c^XVXj{ci^XVn gZaVi^k^hiVWVhiVcigZh bV\c^ijYZh W{h^(XVh&fjZ ejZYZc hZg5aVbVhV&Z' YZjcV eVgi}XjaVZaZbZciVa6aVkZadX^YVYYZaVajo&P' n aVXdchiVciZYZHaVcX`&O#ejZh ZaYZiZgb^cVciZYZaVbVig^o

=a kVadgYZac€bZgd [^_d*K* YZeZcYZYZaVeVgi}XjaVfjZ hZXdch^YZgZ&n XgZXZYZhYZZaZaZXig•c]VhiV Zaegdi•c eVhVcYdedg aVnV aVg\VhZg^ZYZbZhdcZh) =c idYd XVhd&gZhjaiVcc€bZgdh bjn eZfjZ~dh&V adh fjZ&edg V]dgV&cd hZejZYZ Vig^Wj^gc^c\€c h^\c^[^XVYd)

=c =aZXigdbV\cZi^hbd ]Vn fjZ Vbea^VgaVWVhZXdcjcV cjZkV Xdch(iVciZ&fjZ ejZYZ hZgaVXVg\VZaZbZciVa&R) =c XdchZXjZcX^V&XjVafj^ZgdigV XdchiVciZjc^kZghVa]VWg{YZhZg[jcX^•c bdcdgc^V YZZ' P' Un R)@Z Vfj} YdhZ_Zbeadh5

+ 2 ' (: , G ,@ +(, (,

Z Z U

ZhY^hi^cidYZXZgd&ad fjZ egjZWVfjZ Y^X]VhXdchiVciZhhdc Y^bZch^dcVa(bZciZ ^cYZeZcY^ZciZh)

;jVafj^Zg [jcX^•c bdcdb^V YZ S# K# O# hZg{jcV cjZkV XdchiVciZjc^kZghVaYZcVijgVaZoVbZX{c^XV&n edYgZbdh [dgbVg XdchiVciZhjc^(kZghVaZhfjZ iZc\Vc jcV [•gbjaV Y^bZch^dcVaXjVafj^ZgV)K^&edg Z_Zbead&hZigViVYZXVaXjaVgjcV adc\^ijY d jc i^Zbed Zc jc egdWaZbVZc fjZ ^ciZg(kZc\Vc iVc h•ad eVgi}XjaVhYZbVhVZ' Za9c{a^h^hY^bZch^dcVaYVXdbdhdajX^•cYdhcjZkVh XdchiVciZhjc^kZghVaZh&V hVWZg5

=a c€bZgd *K+ fjZ [^\jgV Zc aVZmegZh^•cYZaVXdchiVciZY^Za|Xig^XVYZakVX}dZhi{ gZaVX^dcVYdXdc aVP\[`aN[aRQRR`a_bPab_NSV[NYZKdbbZg[ZaY&fjZ Zc Zah^hiZbVZaZXigdhi{i^Xd#Z5d 7 ,$ hZZhXg^WZVh}5

Ua\ 1 Ra$$($

ZR

-,aR-

0< 7 (( 7 2 -4 ,+(,

PU " '

VaeVhdfjZ&XdcaVWVhZXdbeaZiV&Zh5

Uad7 PP(3()

ZR "

R-0< 7 ((( 7 2&-4 aG(h

-Z5dX]

n&edg iVcid5

Ddh c€bZgdh MRn MaejZYZc hZgXjVaZhfj^ZgV&eZgd h^]jW}ZgZVa\jcVgVo•ceVgVfjZ cd [jZhZc bZcdgZh fjZ jcd& gZhjaiVg}VfjZ Zc ZaegdWaZbVXdch^YZgVYdcd edYg}Vc^ciZgkZc^gadc\^ijYZh c^ YjgVX^dcZhc[Zg^dgZhVUWZPn UWZP-'gZheZXi^kVbZciZ);dc egdidcZh d cZjigdcZh&edg Z_Zbead&gZhjaiV5

**K- 1 '' 1 13&0)

(&!

>^cVabZciZ&Zc LZgbdY^c{b^XV]VXZ[VaiVdigV XdchiVciZjc^kZghVaZc aVWVhZ&XdchiVciZfjZ ejZYZ hZgaVYZ:daiobVcc)

ad7 ,&..+4" ,+(,. Xb6 a\ 1 /&/.411 ,+(-/ h)

#(" 4JMIWHBLJMOIFPBLM>GBM"DVXdchiVciZYZaV\gVk^iVX^•c&5# ZhYZ}cYdaZejgVbZciZ bZX{c^XV&

edg ad fjZ ]VWg{YZhZg[jcX^•c bdcdb^V YZZ' P'O%=c Z[ZXid5

UP< 1 ,ia ((d

Z-

=c aV?ZdbZig}V YZ=jXa^YZh&aVgVo•c ZcigZ aVX^gXjc[ZgZcX^Vn ZaY^{bZigd&XjVcYdVbWVhbV\c^ijYZh hZ b^YZc Xdc jcV b^hbV jc^YVY&Zhjc c€bZgd [^_d&Zac€bZgd *K& fjZ ejZYZ Xdch^YZgVghZXdbd jcV Xdch(iVciZ YZY^bZch^•c cjaV egde^VYZaZheVX^dZjXa^YZd)

=c >}h^XVhZbVcZ_Vc XdchiVciZhjc^kZghVaZhXdc aVhfjZ hZejZYZc[dgbVg bdcdgc^dh e^ Xjndh kVadgZh&h^hZji^a^oVjc h^hiZbVXd]ZgZciZYZjc^YVYZh&hZg{c c€bZgdh [^_dh&fjZ hZ ejZYZc YZcdb^cVgc€bZgdh jc^(kZghVaZh)LVaZhhdc&edg Z_Zbead&adhc€bZgdh ,ia" ,i- Q ,ih&fjZ ]Zbdh ]VaaV(Yd Zc ZaVeVgiVYdVciZg^dg)

#%$ ?j^Yd :ZX`( #-.$ hZ]V dXjeVYdZc ZaegdWaZbVYZaVXdcZm^•cZcigZ aVhXdchiVciZhjc]5ZghVaZh&eaVciZVcYdXdggZXiVbZciZaV XjZhi^•c n ]VX^ZcYdkZghj VaXVcXZ)iZqgA;d)HZgdeVgiZ YZaVV[^gbVX^•c\gVij^iV YZfjZ aVWVhZ]V YZZhiVg;+5)6ihiaiMa8Vedg aVhigZh bV\c^ijYZh&adc\^ijY&bVhV n i^Zbed&edg ad fjZhjq XdchaYZgV8aGcZh8bjn ^c\Zc^dhVhedg X^Zgid&VXZgXVYZac€bZgd YZXdchiVciZhjcAkZghVaZhY^bZch^dcVabZciZ^cYZeZcY^ZciZhXVgZXZcYZ [jcYVbZcid)

Page 127: Análisis dimensional

-0/ 9FyDAKAK<AE=FKAGF9D PAP) >zKA;9 ;GJHMK;MD9J -00

=a c€bZgd gZ YZaV?ZdbZig}VejZYZ XVaXjaVghZXdcidYVaVegZX^h^•cfjZ hZYZhZZbZY^VciZYZhVggdaadhZc hZg^ZYZYjX^YdhYZadhedhijaVYdh[jcYVbZciVaZhYZaV?ZdbZig}V)=c XVbW^d&adhc€bZgdh jc^kZghVaZhYZaV>}h^XV]Vc YZXVaXjaVghZVeVgi^gYZadhkVadgZh]VaaVYdhZbe}g^XVbZciZeVgVaVhXdchiVciZhjc^kZghVaZh)Hdg Z_Zbead&Zac€bZgd 2iV hZXVaXjaVg{XdcadhkVadgZhYZ[,6r& O#R n R ZmegZhVYdhZc jc h^hiZbVXjVafj^ZgVYZjc^(YVYZhXd]ZgZciZh)

=h YZcdiVg fjZ Va\jcdh c€bZgdh jc^kZghVaZhhZVaiZgVcXjVcYdaVhbV\c^ij(YZhfjZ Zc Zaadh[^\jgVc hZb^YZc Xdc jc^YVYZhXd]ZgZciZhXdc digd h^hiZbVYZZXjVX^dcZh&Zhid Zh&XjVcYd hZ XVbW^VZa[VXidgcjb|g^Xd VgW^igVg^dfjZ [^\jgVZc |hiVh) Ddh c€bZgdh [" V1 ,/&03 m ,+(,. n [" / 1 /&11 P ,#$.2&edg Z_Zbead&hZ]Vc dWiZc^YdXdc jc^YVYZhXd]ZgZciZhXdc aVhZXjVX^dcZhZaZXigdbV\c|i^XVhgVX^dcVa^oVYVh&Zc Xjnd XVhdZh ‚d 1 =g) K^hZ]jW^ZgVcji^a^oVYdaVhjc^YVYZhcdgVX^dcVa^oVYVh&]VWg}VfjZ ]VWZgidbVYd ‚d 1 /c=g n hZg}V5

EjX]d hZ]V ZheZXjaVYdVXZgXVYZah^\c^[^XVYdYZZhidhc€bZgdh jc^kZghVaZh)>^c`ZaWjg\ #3-$&YVcYdedg hjejZhid fjZ h•ad ]Vn jcV adc\^ijY jc^kZghVa&ZagVY^dYZacjXaZ•c #_\ 1 ,&., P ,+(,. Xb$&YdhbVhVh ZaZbZciVaZh#aVYZaZaZXig•cn aVYZaegdi•c$ n idbVcYd Zc XjZciV aVXVg\VZaZbZciVan aVhXdchiVciZhjc^(kZghVaZhZ&=G" 5 n O#YZYjXZfjZ ]Vn XjVigd c€bZgdh jc^kZghVaZh5

LN M,,/&03 P ,+(,.

#//&11 P ,+.2

#/

;dbd Zc kZo YZa[VXidg#/ hZejZYZ edcZg digd XdZ[^X^ZciZcjb|g^Xd XjVafj^Z(gV&gZhjaiVfjZ Y^X]dhc€bZgdh jc^kZghVaZhejZYZc idbVg ZakVadgfjZ hZ YZhZZ)=hid egjZWVjcV kZo b{h aV[ji^a^YVYYZVig^Wj^gaZhhZci^Yd[}h^Xd)

Z-

[". 1 ''' 1 ,/&03 P ,+(,.6:\UP

#)" <I MFMNBH>ABOIFA>ABMOIFPBLM>GBM

HVgV[dgbVg jc h^hiZbVYZjc^YVYZhXd]ZgZciZh&ejZYZc ZaZ\^ghZVgW^igVg^V(bZciZ X^cXdjc^YVYZh&fjZ ejZYZc hZgigZhbZX{c^XVh&Za\gVYd YZiZbeZgVijgVn jcV ZaZXigdbV\c|i^XV)DV ZaZXX^•cejZYZ hZg]ZX]V YZbVcZgV fjZ VYfj^ZgVcZakVadg* digVhiVciVh XdchiVciZhjc^kZghVaZh)

HVgVaVhbV\c^ijYZh bZX{c^XVhhZ Y^hedcZYZXjVigd XdchiVciZhjc^kZghVaZh&5# Z&;0 = O#n Xdbd h•ad hZ gZfj^ZgZcigZh&edYZbdh XdckZc^gZc egZhX^cY^gYZ

aVeg^bZgV);dc aVhXdchiVciZhZ&;0# U hZejZYZc [dgbVg igZhbdcdb^dh e^ fjZ iZc\Vc&

gZheZXi^kVbZciZ&aVb^hbV Y^bZch^•c fjZ aVadc\^ijY& aVbVhV n Zai^Zbed& nfjZ hZg{c aVhjc^YVYZhXd]ZgZciZhZc Zah^hiZbVfjZ ZhiVbdh [dgbVcYd5

n Xdbd XdbZciVg^dV\gZ\V5

!#0 eZhVgYZaVhV\jYVh hj\Zhi^dcZh YZ=YY^c\idc n YZdigdh&[VaiVjcV iZdg}VfjZ Zmea^fjZ hVi^h[VXidg^VbZciZaVgVo•c YZhZgYZZhiVhXdchiVciZhYZY^bZc(h^•c cjaV) F^ h^fj^ZgV]Vn jcVc^b^YVY VXZgXVYZ X•bd hZ ]V YZ VWdgYVgaVXjZhi^•c Xdc edh^W^a^YVYZhYZ|m^id) =h YZhjedcZg fjZ aVhbVndgZh Y^[^XjaiVYZhhjg_Vc VaigViVgYZ Zmea^XVgX•bd hVaZjc c€bZgd iVc ZcdgbZ Xdbd Za ["/ 1

1 /&11 P ,+.2&ejZh Zh ^ckZgdh}b^afjZ iVa c€bZgd gZhjaiZ YZ gZaVX^dcZhZcigZbV\c^ijYZh Vi•b^XVh)=hid ]V hj\Zg^Yd aV ^YZVYZ Xdch^YZgVgadXdbd egjZWVZk^YZciZYZaVXdcZm^•cZcigZ adh YVidhVhigdc•b^Xdhn adh Vi•b^Xdh) DVhXdch^(YZgVX^dcZhYZ =YY^c\idc& <^gVX&=giZa&5dgYVc n digdh hZgk^g{ceVgV V\joVgZa^c\Zc^d YZfj^Zc igViZ YZVWdgYVgZaegdWaZbV)w

=c gZVa^YVY&ejZYZc dWiZcZghZc[^c^YVYYZc€bZgdh jc^kZghVaZh&ejZh ejZ(YZc XdbW^cVghZYZ ^c[^c^idhbdYdh aVhXdchiVciZhjc^kZghVaZhYZ bVcZgV fjZgZhjaiZc bdcdb^dh e^&edg ad fjZ& N ]_V\_V'gZhjaiV^cVXXZh^WaZZaegdWaZbVYZXVaXjaVgiZ•g^XVbZciZidYdh Zaadh)9 cjZhigd bdYd YZ kZg&aV XjZhi^•c YZWZeaVciZVghZZc adh h^\j^ZciZh i|gb^cdh5 9NQN` PV[P\P\[`aN[aR b[VcR_`NYRQVZR[(`V\[NYZR[aRV[QR]R[QVR[aR`'PNYPbYN_a\QN`YN`^bR `R R[PbR[a_N[R[ Y\` QV`aV[a\`PN]VabY\QRYN;n`VPN)

=a 9c{a^h^hY^bZch^dcVaV[^gbVfjZ XjVafj^ZgXdchiVciZjc^kZghVa]V YZhZg[jcX^•c bdcdb^V YZVa\jcVh YZaVhXdchiVciZhfjZ hZidbVc Xdbd W{h^XVh&XdcadfjZ ZaegdWaZbVhZgZYjXZV]VaaVgZagZheZXi^kd[VXidgcjb|g^Xd)

HgdWaZbVhYZZhiZi^ed ]Vc h^YdnV gZhjZaidhbZY^VciZaVhbdYZgcVhiZdg}Vh&n Vh}hZhVWZ&edg Z_Zbead&XVaXjaVgaVhXdchiVciZhYZKiZ[Vc&YZO^Zc&YZJnYWZg\&ZiX|iZgV&eZgd digdh Zhi{c edg gZhdakZg)>VaiV&edg Z_Zbead&jcV iZdg}VfjZ eZg(b^iV XVaXjaVgaVhgZaVX^dcZhZcigZaVhbVhVhYZaVhY^hi^ciVheVgi}XjaVhZaZbZciV(aZh6aVXdchiVciZYZaV\gVk^iVX^•cZc [jcX^•c YZjcV bVhV ZaZbZciVa&n YZaVhXdchiVciZhZn U4aVheZgbZVW^a^YVYZhYZakVX}dZc [jcX^•c YZZ&X&U' ZiX)

Mc^YVYYZadc\^ijY5UA_ 1 ,&..+4v ,+(,. Xb)

Mc^YVYYZbVhV5 ,&1042 P ,+(-/ \)

Mc^YVYYZi^Zbed5 UA_ 1 /&/.411 P ,+(-/ h)X-

=a kVadgYZa\gVYd fjZYV YZiZgb^cVYdh^hZ]VXZX 1 ,)

Mc^YVYYZiZbeZgVijgV5-

MPMM1 ,&+3 ,+,- +;)XA_

=c =aZXigdbV\cZi^hbd hZ ejZYZ idbVg Xdbd jc^YVYaVXVg\VYZaZaZXig•c&d W^ZchZejZYZ ^\jVaVgV , XjVafj^ZgVYZaVheZgbZVW^a^YVYZhYZakVX}d&aVZa|X(ig^XVd aVbV\c|i^XV) @Vn&ejZh&kVg^Vhedh^W^a^YVYZheVgV[dgbVg h^hiZbVhjc^(kZghVaZhYZjc^YVYZhXd]ZgZciZh)

HdYg}VXgZZghZfjZ Zc aV[dgbVX^•c YZ ZhiVhjc^YVYZh&fjZ ]Zbdh aaVbVYdjc^kZghVaZh&cd ]Vn cVYVVgW^igVg^d&h^cd fjZ& edg YZX^gadVh}&ZhiVg}VcbejZhiVh

Page 128: Análisis dimensional

-01 9FyDAKAK<AE=FKAGF9D

edg aV b^hbV cVijgVaZoV)F d Zh Vh}&h^c ZbWVg\d&edg aVhgVodcZhfjZ YVbdhV Xdci^cjVX^•c5

=h VgW^igVg^dZa idbVg Xdbd jc^YVY YZbVhV aV^ckZghVYZaVXdchiVciZ YZ9kd\VYgd&ejZh ZhiVXdchiVciZgZhjaiVYZVig^Wj^gXdckZcX^dcVabZciZZakVadg,1V aVbVhV YZa h•ided ,1 YZadm}\Zcd)

DV jc^YVYYZadc\^ijY XVgZXZYZhZci^Yd [}h^Xd)K^hZ Y^k^YZedg -& gZhjaiVaVaaVbVYVadc\^ijY YZdcYVYZ;dbeidc eVgVZacZjig•c& h^c fjZ Zaadfj^ZgVYZX^gfjZ iVaadc\^ijY YZdcYVXdggZhedcYZVVa\d gZVa)=c hj aj\Vg hZ]jW^ZgVedY^YdidbVg ZagVY^dXa{h^XdYZaZaZXig•cXVaXjaVYdXdc aV[•gbjaV R3&,T)

LVbW^|c hZ edYg}VidbVg Xdbd jc^YVY YZadc\^ijY aVY\[TVabQSb[QNZR[aNYYZ @Z^hZcWZg\&YZ[^c^YVedg5

R-

R1'''&gcX-Z5d

;GFKL9FL=K MFAN=JK9D=K

#GRPU[VPNYARd` 7bYYRaV['ANaV\[NY7b_RNb \S FaN[QN_`'dXijWgZYZ ,41.$YdcYZZ n R hdc&gZheZXi^kVbZciZ&aVbVhV n aVXVg\VYZaZaZXig•c)HZgd&\jVa(bZciZ& hZejZYZ idbVg XjVafj^ZgdigV eVgi}XjaV&n cd ]Vn gVo•c eVgVXdch^YZgVgXdbd b{h [jcYVbZciVa jcV YZ aVhbjX]Vh adc\^ijYZh Vh}YZ[^c^YVh)9YZb{h&]Zbdh k^hid Zc ZaVeVgiVYdVciZg^dgfjZ ZakVadgYZZ5d kVg}VhZ\€c hZji^a^XZcaVhjc^YVYZhgVX^dcVa^oVYVhd aVhcd gVX^dcVa^oVYVh)

LVbedXd Zh[{X^a]VaaVgZah^\c^[^XVYdYZaVjc^YVYYZi^Zbed& fjZ hZedYg}Vhjhi^ij^g edg ZaeZg}dYdYZgdiVX^•cYZaZaZXig•cZc idgcd YZh}b^hbd& XVaXjaVYd

Xdc R,-&,T)=c [^c&ZaidbVg aVhXdchiVciZhZ&;0 n U eVgV[dgbVg aVWVhZYZaVhbV\c^(

ijYZh bZX{c^XVhZh XdhVVgW^igVg^V);jVafj^ZgV YZ aVhiZgcVh[dgbVYVhXdc 5#Z&;0 n U XdcYjX^g}VV jc cjZkd h^hiZbV YZ jc^YVYZhjc^kZghVaZh&n cd ]VngVo•c eVgVXdch^YZgVgjcd YZ ZaadhXdbd eg^k^aZ\^VYd&hZ\€c hZ ]^od kZg Zc Zas 3&XVe}ijad NAA)

NZadX^YVYYZaVajo5;Vg\V ZaZbZciVa5

EVhVYZaZaZXig•c5

EVhVYZaegdi•c5

Mc^YVYYZbVhV Vi•b^XV5

EVhVYZacZjig•c5

=aZXig•c(kdai5;dchiVciZ YZaV\gVk^iVX^•c5;dchiVciZ YZadh\VhZh5;dchiVciZ YZ:daiobVcc5;dchiVciZ YZHaVcX`5;dchiVciZ YZKiZ[Vc5;dchiVciZ YZO^Zc5;dchiVciZ YZ9kd\VYgd5

9FyDAKAK <AC=FKAGF9D) q ,2

d 1 -&4424-0 P ,+3 b K(a&

R 1 ,&1+-,+ P ,+(,4 ;)

O4&,+4, P ,+(., ;)Z (Z ( 0&/3042 P ,+(/ j)

U S ,&12-0- P ,+(-2 `\)be ( E,&++2-211. j)

*j 1 '' YZaVbVhV YZa{idbd YZac€Xa^YdcX)

,-U S ,&12/3- P ,+(-2 `\)

*GG ' E,&++3110/ j)

ZN 1 ,&1+-,+ P ,+(,3 5&< 1 1&12+ P ,+(,, bK `\(, K(a)

E 1 3&.,/. P aGK5 #bda(`\g7 uC(,)X 1 ,&.3+0/ P ,+(-. 5 uC(a)U 1 1&1-01 P ,G(K/ 5 P h&V 1 0&1142 P ,+(3 `\ K(. uC(/)O 1 -&3423 P aG(h b uC)

A6 1 1&+--0- P ,++ #bda(`\_g!)

Page 129: Análisis dimensional

A4C3D 5;E363D

(& 8AFC;7C1 BPhWZQM0VIT`\QY]MLMTI =PITM]Z!9L`_STP] GTWWL]^#BL]n^# (///&>L^ XPXZ]TL^ Z]TRTYLWP^^ZY OP WZ NZXTPYeZ^OPW[L^LOZ ^TRWZ&

)& C7J@A>6D1 BZIV-$ @W`$AWK$!(.+ !(//*"# [lR& 0*,&*& D;C A>;G;7C >A6971 <I\]ZM! */ !(///"# [lR& )/(&+& 9& 8& 8;EK97C3>61 >PQT$;IO$! ). !(//0"# [lR& *)*&,& 3& H& Ck5=7C1 >PQT$;IO$! ). !(//."# [lR& ('+&-& <&:& <73@D1>ZWK$@W`$AWK$!.- !(0',"# [lR& ,+,&.& >AC6 C3J>7;9:1 L" 8V^M-\QOI\QWV-WV =IXQTIZQ\`$>PQT$;IO$! #$%#!"

M" <I\]ZM! 0, !(0(,"# [lR& --&/& 6& C;34AF5:;@D=J1 >]JTQKI\QWVdLMT 8V[\Q\]\0MZWL`VIUQY]M!?Z^Nq# (0()&0& ?& B>3@5=1 DWZTM[]VOMVlJMZ LQMBPMWZQMLMZEQQZUM[\ZIPT]VO!>PT[eTR

!(0'-"# [lR& (,0&('& 3& 7;@DE7;@10VV$ LMZ>PF-$!*, !(0(("# [lR& -/-&((& 7& 4F5=;@9:3?1 >P`-$ @M^$!+ !(0(+"# [lR& *+,& <I\]ZM! 0- !(0(,"# [lRT%

YL^ )'/ d *0-&()& 3& ?hEC3>1 7WUWOMVMQ\hM\AQUQTQ\]LMMV0MZWL`VIUQY]M!BL]n^ !(/0)"&(*& ?& 3& G3D5:J1 =WU%X\M[@MVL]-LMT 0KILMUQM!((+ !(/0)"# [lR& (+(-# 0 ((,

!(/0)"# [lR& ,0.&(+& >7G;%5;G;E3 d 3?3>6;1 :M[QWVMLQ;MKKIVQKI@IaQWVITM!(# 4ZWZYTL&

(,& 8& 7:C7@87DE%383@3DD<7H31 ;I\P$ 0VV$! .. !(0(-"# [lR& ),0&(-& C&D3@<F3@1 BMWZiILMTI[ UIYVQ\]LM[Ni-QKI[ -C- H]ULIUMV\W[ITYhJZQKW[!

@M^$LMTI 0KIL$ LM=QMVK$!OP ?LO]TO# _&*0&(.& C&5&EA>?3@1 >P` -$@M^$!* !(0(+"2 0 !(0(."# [lR& ),&(/& A& 6& 5:bA>DA@1 BZIQ\hLM>PY[QY]M!PR`YOL POTN&Q]LYNP^L#_&( !(0()"#

[lRTYL *()&(0& <& B3>35;AD1 ;IOVQ\]LM- ` ]VQLILM[MTMK\ZWUIYVh\QKI[!?LO]TO !(0+("#

[lRTYL ('&)'& C7;5:7@435:1 >P[RM!7IVL[WWZ\MZJ]Kj!4P]WnY!(0*)"&)(& 6;7DD7>D:ACDE1 ;lTTMZ#>W]QTTM\1!:MPZJ]KPLMZ>P`[QS! !(0)0"# [lR& (0,&))& B& H& 4C;69?3@1 3QUMV[QWVIT0VIT`[Q-! JLWP# FYTaP]^T_d B]P^^& 7cT^_P

`YL _]LO`NNTpYP^[LoZWL [`MWTNLOL[Z] WLFYTaP]^TOLO @LNTZYLWOPE`N`XlY# CP[qMWTNL3]RPY_TYL&

A4C3D 5;E363D ),0

)*&)+&),&)-&

?& 9F;6A 475=1 8V\ZWL]K\QWVI TI \PhWZQMLM[Y]IV\I! 5ZTXM]L !(0+)"&8C&C`^^Z1 @MW]MLM[?]M[\QWVM[AKQMV\QNQY]M[!() !(0,("# [lR& +'&<&B3>35;AD1 4TTMVO]IQMLMTI 5i[QKI` -C XMK]TQIZHQTW[WRQI!?LO]TO !(0,*"&?& B>3@5=1 AKQMV\QNQK0]\WJQWOZIXP`$E]LO& TYRWP^LOP 8C3@= 93J@AC#

>ZYO]P^ !(0,'"&9& 4FC@;DEA@4CAH@1 >ZWK$>P`-$ AWK$!,* !(0+("# [lR^& +(/ d +*)&D;C 3CE:FC 766;@9EA@1 BPMVI\]ZM WN\PMXPF-_IT _WZTL!(0)/"# [lRT%

YL ),)&H& :7;D7@47C91 GMQ\1KPZQN\N$>PF-$!('( !(0*-"# [lR& ,**&<&B3>35;AD1 8V^M[\QOIKQkV` XZWYZM[W!(- !(0+,"&H& :7;D7@47C9& 3NLOPXTL OP 5TPYNTL OP DLUZYTL&1MZ!L$ UI\P#XPF-$#

9TI[-M! /, !(0,*"&B&aG&4C;69?3@1 4VKQKTWXMLQI1ZQ\gVQKI!PO&OP (0,(& 3]_TN`WZ3QUMVMQW#

VIT 0VITF-Q-$4& >7G;1 ;I\PMUI\QKIM VW\IM$1WT$LMT8V[\!LM;I\$! CZ^L]TZ !3]RPY_TYL"#

-# ( !(0+-"# [lR& (&:& 6;@9>71 >PQT$;IO$! ** !(0+)"# [lR^& *)(%*. !(0+-"# [lR& -+&63>K7>>1 >PQT$;IO$! *- !(0+,"# [lR& +/,&B&B; 53>>7<31 ;I\PMUI\QKIM VW\IM!3]RPY_TYL"#ZN_`M]P#(0,)&?& >&4F>>A5=1 0U$ &">PF-$!)) !(0,+"# [lR& )0(&<&:& =77@3@1 0U$ \$>PF-$!)) !(0,+"# [lR& ,.)&D5AEE 4>3;C1 >ZWK!@W`$AWK$!(/0 !(0+."# [lR& -0& 4--IQ- QV@PMWTWO`!

4]T_T^S CSPZWZRT^_5W`M#>ZYO]P^ !(0+."&:& H3>>AE1 7IVLJ]KP LMZ>P`-QS!**!(0)-"&<&C7J B3DEAC1 =]Z-&KiKTQKWLM;I\MUg\QKI[ !(0)+"# [lR& +&7& >A767> J B3@6FCA1 0VITM- LMTI AWKQMLIL=QMV\iNQKI0ZOMV\QVI!')*

!(0+)"&6F@53@DA@1>ZWK!>P[Q[!AWK$!>ZYO]P^ !(0+("# [lR& ,*&:& 6;@9>71 >PQT$;IO$ +' !(0+0"# [lR& 0,&H& f&1 BMWZiIOMVMZITLMTI[ UIYVQ\]LMcNi[QKI[CZ^L]TZ !3]RPY_TYL"

!(0+(Q&

<& B3>35;AD1 BMZUWLQVgUQKI` UMKgVQKIM[\ILQ[\QKI!?LO]TO !(0+0"# [l%RTYL(/'&

>34A57EE31 4TM\\ZW\MKVQKI!(0*)"# [lR& (-)0&D7>HJ@1 1ZQ\$&"0XXTQML>P`-QK[!+ !(0*,"# [lR& )')&?34E;@AE%>393C671 0VITY[M3QUMV[QWVMlM$0XXTQKI\QWV-I TI ;hKIVQY]M

LM[NT]QLM-$=NNQKM<I\QWVITL e\]LM- M\ LM@MMPMZKPM[0MZWVI]\QY]M-!BL]n^ !(0+/"&

>;BB?3@@1 =WUX$@MVL$0K$AM$!('+ !(//."# [lR& ('.'&:& 7& :F@E>7J1 3QUMV[QWVIT0VITF-Q-!>ZYO]P^ !(0,)"&76& 9F;>>3F?71 :I UM-]ZM$E]LO&OPWL]_ZOP CF@97 !,*"&9L`_STP] GTWWL]^&

BL]n^&5&CF@971 4VK$;I\P$ EQ--$!_&G# [lR& (&3& DA??7C87>61 DWZTM[]VOMVlJMZ \PMWZM\Q[KPM>P`[QS! !(0+/"# [lR& (0&H& 6& :3C=;@D d 8& 7& 4CAH@1 0U$ =PMU$AWM$!+( !(0(0"# [lR& +00&>A:@DE7;@1 EQML$0VV$! ,* !(/0+"# [lR& ('-)2 ,+ !(/0,"# [lR& .(*& G$>P`-$

=PMU$!-+ !(0'/"# [lR& -/-2 /+ !(0(*"# [lR& +('&<&B3>35;AD1 ;MKgVQKINi[QKI!?LO]TO !(0-*"&

).&)/&

)0&*'&*(&

*)&

**&

*+&*,&*-&*.&*/&*0&

+'&+(&

+)&

+*&++&+,&

+-&

+.&+/&+0&

,'&,(&

,)&

,*&,+&,,&,-&

,.&

Page 130: Análisis dimensional

"# A4C3D 5;E363D

,/& 8& >38;E31 0MZWLQVgUQKIIXTQKILI$;& @&E&0$! ?LO]TO !(0+,"&,0& E&;D@3C6;1 2QMVKQI` BhKVQKI!]Pa&OPW5&OP P^_`OTLY_POP TYRPYTP]Z^#OP

4`PYZ^ 3T]P^"#U`YTZ!(0+)"&-'& 7& >A767> B3>F?4A d 7& C&Dg43EA10V$ LMTI AWKW2QMV\W0ZOMV\QVI!(/*

!(0+)"# [lR& )))&-(& 53C3E:hA6ACJ1 ;I\P$ 0VV$! -. !(0'0"# [lR& *,,& GmL^P_LXMTmYPWL]_nN`WZ

OP >3@6h PY PW7IVLJ]KP LMZ>P`1QS!;I !(0)-"&-)& <&B3>35;AD1 :I[ KQMVKQI[!34ZN&7^[& [L]L PWB]ZR]P^Z OP WL 5TPYNTL^"#

)( !(0,("&-*& >&>3@63F d 7& >;8D:;EK1 A\I\Q[\QKIT>P`1QK[!_]LO&TYRWP^L"#AcQZ]O!(0*/"&

-+& 6& C;34AF5:;@D=J1 <I\]ZM! /, !(0(,"# [lR& ,0(&-,& >& :AB81 3QM<I\]ZEf-[M 8f[KPIN\MV!/ !(0)'"# [lR& ('0& GmL^P _LXMTmY

8& C7;5:71 BMWZiILMTW[?]IV\I! 5LW[P!(0))"# [lR& (,-&--& 5&CF@971 >P`[$ GMQ\[KP$!(. !(0(-"# [lR& )')&-.& B&DEC3@7A10\\Q$@$0KK$[KQ!BWZQVW!,0 !(0(.%(0(/"# [lR& (/,&-/& B&D&7[DE7;@1 0U$ &"WN>P`[$! )) !(0,+"# [lR& +')&-0& 3& DA??7C87>61 >P`[$ GMQ\[KP$!*- !(0*,"# [lR& /(+& 0VV$ L$ >P`[$! )+

!(0*0"# [lR& **,&.'& 7& B7CF553 d 8&67?;5:7>;D1 7MT^$>P`[$ 0K\I! )- !(0,*"# [lR& *)0&.(& <&B3>35;AD1 @MTI\Q^QLIL$<]M^I BMWZiI!7^[L^L%5LW[P"#?LO]TO !(0-'"&.)& <&3& DEC3EEA@14TMK\ZWUIOVM\QKBPMWZ`$?N9]Lb%:TWW!(0+("# [lR& )+(&.*& 8& 3BC3;K1 <]M^W[Q[\MUILM]VQLILM[MThK\ZQKI[!>ZR]ZoZ !7^N`PWL;YO`^%

_]TLW"&.+& 7D@3F>E%B7>E7C;710VIT`[M LQUMV[QWVVMTTMM\;h\ZWTWOQM$AWKW@$LM[8VO$

M\LM[ 8VL][\ZQMT[!+ !(0,("&.,& ?& 47C97C1 2$ @$0KIL$ [[/ )*,# BL]n^ !(0,)"# [lR& )*,&.-& <&B3>35;AD1@M^$5IK$ 2$ :Q[JWI! ( !(0,)"# [lR& (*0&..& <&B3>35;AD14TMK\ZQKQLIL` UIOVM\Q[UW!?LO]TO !(0,0"# [lR& ),+&./& 6& :3>>;63J1 8V\ZWL]K\WZ`V]KTMIZ>P`1QK[!HTWPd!@`PaL JZ]V" !(0,'"&.0& >& CZ^PYQPWO1<]KTMIZHWZKMM!@Z]_S :ZWWLYOB`MWT^STYR5Z&#3X^_P]OLX

!(0+/"# [lR& I;G&/'& <&B3>35;AD1 2CV$ 2WV\$:Q[JWI! , !(0,("# [lR& (.*&/(& 47E:7 7 435:7C1 @M^$;WLMZV>P`[$! / !(0*-"# [lR& 0-&/)& H& 8;@=7>4FC91 0\WUQK>P`1QK[!;K6ZI_#7QTT !(0,'"# [lR& *+(&

i@6;57 3>834hE;5A

&

3N_TaTOLO1)+(&3P]ZOTYlXTNL1(**&3WL^1(*-&3WNLYNPOP `Y []ZdPN_TW10*3YPYpXP_]Z1 (-'&3[]LTe# )(,# )(-# )(/&3_Xp^QP]L# (.,&3aTpY1 (*-&

4

4LNSP]1 )+.&4LWXP]!DP]TP"1),'&4L]Y !FYTOLO"1)*/&4L^P1 +0&4L^P^ P^_]TN_L^1-(&

X`_TWLOL^1-*# /+# (.(&% ^`[P]LM`YOLY_P^1-(# /-&% `YTaP]^LWP^1/0&4PNV !9&"1(+# ),)&4P]RP]1 )(,# )(-&4P_SP1 )+.&4TZ_ !FYTOLO"1)'-&4T]RP1),/&4ZS]1 ),'&4ZW_eXLYY1(..# (/'# (0(&4ZXML^1 (+*&4Z`^^TYP^\1 (,/# (-'# (-/# (/)&4]TORXLY1 ('# (+# (.# *'# .'# //# (W'#

()+# (-/# (.)#)(.#))+&

4]ZRWTP1)+,&4`NVTYRSLX1('# WW#.'# (-/# )(,&4`WWZNV1*,&4`]YT^_ZY 4]ZbY1 (,&

P5LnOLWTM]P1/*&% PY XPOTZaT^NZ^Z1()*&5lWN`WZNZY`YTOLOP^1,0&

5LWZ]1(-*&% P^[PNnQTNZ1(-,&5LXMTZ OP ML^P1,/&5LX[Z TXLYLOZ]1(0-&5LY_TOLO#OPQTYTNTpY1).&% OP ^`^_LYNTL1(--&5L[TWL]TOLO1((.&5L]RL PWmN_]TNL1(0,&5L_PYL]TL1(')&5P]Z LM^ZW`_Z1(+0&5ZPQTNTPY_POP OTWL_LNTpY1(-,&5ZPQTNTPY_P^[L]l^T_Z^1 +-&5ZSP]PYNTLOP WL^YTOLOP^1+-# +0&5ZXT^TpYD&F& @&1)''&5ZX[]P^TMTWTOLO#(+(# (-,&5ZX[_ZY !>ZYRT_`O"1),-&5ZYOPY^LOZ]1)(.&5ZYO`N_TaTOLO_m]XTNL1(,*# (.*# (/*&5ZY^P]aLNTpYOP WLPYP]RnL1)*'&% OP WLXL^L1 )*-&5ZY^_LY_POP 3aZRLO]Z1 +'# ++# (./&% OP 4ZW_eXLYY1+'# ++# (..# ))*&

Page 131: Análisis dimensional

!%! i@6;57 3>834hEW5A

5ZY^_LY_POTYlXTNL1+(# +,&OP6T]LN1)*/&PWPN_]ZXLRYm_TNL1+(# +,# )((&OP8L]LOLd1+W&OPWZRL^P^#(-.&OPWLR]LaT_LNTpY1*0# ++#-'# ),)&OPBWLYNV1+'# +,# (//&\`nXTNL1*)# .)# (0+&]LOTLN_TaL1)+(&OPDZXXP]QPWO1),)&OP D_PQLY1+(# (0(&OPHTPY1+(# (0)&

5ZY^_LY_PNL]LN_P]n^_TNL^1*/&OPWm_P]1+'# +,&TYOT^[PY^LMWP^1+-&^`[P]QW`L^1+-# /.# 0'&`YTaP]^LWP^1*0# +*# ),(# ),.&

5Z]]TPY_PPWmN_]TNL1(0,&5]T_P]TZOPP\`TaLWPYNTL1)/&5`LY_Z OPLNNTpY1(/.&5`]TZ1 )+(&

"#

5SbZW^ZY#()&

6

6LWePWW1)-&6PNLX[P]TZ1)'/&6PN]PXPY_ZWZRL]n_XTNZ1('*&6PY^TOLOOPPYP]RnL1))(&6TL[L^ZYP^&((,&6nLe 4PUL]LYZ10'6TP^^PW^SZ]^_1(*&6TXPY^TpY#NZXZaPN_Z]&-'&

OPWLLNPWP]LNTpY10.&OPWlYR`WZ1-+&!5ZYNP[_ZOP"1,*&OPWLNZY^_LY_POP3aZRLO]Z1 (/'&% NL[TWL]1((.&NZY^_LY_POPWLR]LaT_LNTpY10.&OP WL XLRYT_`OP PWPN_]ZXLRYm_T%

NL^1(00# )(+&OPWXpO`WZOP]TRTOPe1(()&Y`WL1-*&OPWL[]P^TpY1(',&OPWL_PX[P]L_`]L1 (-/# (.0&

6TXPY^TpYOPW_]LMLUZ10.&% OPWLaPWZNTOLO10.&% OPWLaT^NZ^TOLO1())# (*+&6TYRWP1)-# ,.# -,# --# )(,# )(/&6T[ZWZPWmN_]TNZ1)(0# )),&6T^N]TXTYLNTpYOP WL OTXPY^TZYPP^%

[LNTLWP^10'# (*+# )(*&6T^_]TM`NTpYOP4ZW_eXLYY1(/'&% OP?LcbPWW1(/(&6Z^T^]LOTLN_TaL1)+*&

'

7N`LNTpYOP>L[WLNP1((0&7N`LNTZYPQn^TNL^1*.&

Q`YOLXPY_LWP^10-&OPWZRL^P^1(-/&SZXZRmYPL^1))&NZYWZRL]T_XZ^1.)&OP?LcbPWW1(00# )')&

7OOTYR_ZY1(,# (-# ),+&7S]PYQP^_%?QLYL^^UPbL1((# .'&7TY^_PTY1WA#)()&7WL^_TNTOLO1(',&7WPN_]pXP_]ZOP>T[[XLYY1 )(0&7WPN_]pY1)+.# )+0&7WPN_]pY%aZW_TZ1)*/&7YP]RnLNTYm_TNL10/&% TY_P]YL1(-+&

% WTM]P1(-.&7YQ]TLXTPY_Z1(.'&7Y_LW[nL1(++# (-.&% WTM]P1(-.&7Y_P^ NZX[L]LMWP^1),&7Y_]Z[nL1 (-+&7[^_PTY1(0*&7\`TaLWPY_PXPNlYTNZOPWNLWZ]1*0#

++# (-*&7^NLWLOP3aZRLO]Z1 (+-# (,(&

OP5`]TP1 (+/# (,(&OP6L;_ZY1(+,&OPQ]nZ1(,)&OP=PWaTY1(,(&OP D_PQLY1(,(&_P]XZOTYlXTNL1(+/# (,(&

7^NLWLLM^ZW`_L^1(+/&% `YTaP]^LWP^1(+/# (,(&7^YL`W_%BPW_P]TP1)(,# )(-# )(.# ))(&

Z

i@6W57 3>834hE;5A !%"

7^[nY1 )+0&7^_LOZ^NZ]]P^[ZYOTPY_P^1(.+&7^_P]]LOTlY1)',&7c[ZYPY_P OPWSTO]pRPYZ1*)# .+&7c[ZYPY_P^ OTXPY^TZYLWP^10&

8

8LN_Z]P^OPNZYaP]^TpY1,0# )'.&% OPQZ]XL1.0&8LYYTYR1()-&8L]LOLd !5ZY^_LY_POP"1+(&8P]XT1 (/+&8TM]LYP`_]L1 ('-&8TWZ^ZQnLZ[P]LNTZYLW1(*#)(.&8TYVPWM`]R#),+&8T_e9P]LWO1('&8WPcTpY1('/&% NT]N`WL]1('-&

8W`N_`LNTZYP^1(/'&8Z_ZYP^1)*+&8p]X`WL OTXPY^TZYLW1()# ,-&8Z`]TP]1 0# ()& ,-# -.# (,*# (-*&8]LYVWTY!FYTOLO"1)'-&8`P]eL# OPQTYTNTpY10,&% NPY_]n[P_L1(''&% OP>Z]PY_e1)+/&8`YNTpYOPZYOL^1)+-&8`YNTZYPSZXZRmYPL^1)(# ,)&

(

9LWTWPZ1(+&9L`^^1 )(,&% !EPZ]PXL OP"1)'+&% !FYTOLOOP"1)'.&9Z_L#^LWTOL[Z] NL[TWL]P^1()'&% !GTM]LNTZYP^OP`YL"1 ((0&9`TWWL`XP10'&

)

:LWWTOLd1)*.&:L]VTY^1()(&:PLaT^TOP1)''&:PT^PYMP]R1(-&:mWTNP1(+)&:PWXSZW_e1(*(# )(0&

:P]_e1 )(,&:TO]pXP_]Z1 (*(&:ZXZRPYPTOLO!B]TYNT[TZOP"1-.&:Z[Q1 (0(&:`Y_WPd10'# (''# (*+# (*/&

(

;R`LWOLOOPNLY_TOLOP^1)/&;XLYLNTpY1)(,&nX[P_`1 )*'&;X[`W^TpY1)*'&

;YO`NNTpYPWmN_]TNL1(0,&% XLRYm_TNL1(0-&;YP]NTL1)*(&

% OPWLPWPN_]TNTOLO1)(/&% OPWLW`e1)))&;Y_PY^TOLOPWmN_]TNL1(0,&;^YL]OT1(+,# (/0&;^ZXZ]QT^XZOP OTXPY^TZYPd aPN_Z%

]P^1-'&

<

<PLY^1('# (0(# )(,# ))*&

+

=l]XlY !GZY"1()/&=PPYLY1*,&=PWaTY1(,# ((0&=WPTY1((&

,

>LMZNP__L!B]ZMWPXLOP"1/(&

>LQT_L1(*-&>LXTYL]1(),&>LYOL`1(-/&>PYe1)'+&>PaT1)-# .(# 0'&>PaT 5TaT_L1!! >Pd OP3X[L]P1 (0/&

OP5Z`WZXM1(0/&OP8L]LOLd%9L`^^1(0.&OP:ZZVP1 */# (',&OP=P[WP]100&

Page 132: Análisis dimensional

!%# i@6;57 3>834hE;5A

>Pd OP>L[WLNP1(0/&OPCZbWLYO1(0/&

% OP D_PQLY1))*&% OPHTPY1(/0# (0(# ))*&>PdP^ Q`YOLXPY_LWP^1*,&% OPWLR]LaT_LNTpY1*0&>TQ^ST_e1(-/&>T[[XLYY1 /-&>ZORP1('&>ZPOPW1-+# (+,&>pRTNL[Z^T_TaT^_L1(*# )-&>ZYRT_`OOP5ZX[_ZY1 ),-&% Q`YOLXPY_LWOP:PT^PYMP]R1),-&>Z]PY_e1)()# ))/&>Z^NSXTO_1(..&

-

?LRYP_pYOP4ZS]1 ),'&?LRYT_`OP^#OPQTYTNTpY1).&

LOT_TaL^1)/&[Z] OPQTYTNTpY1*(&OP]TaLOL^1*(&

OTXPY^TZYLWXPY_PTYOP[PYOTPY_P^1,/&Q`YOLXPY_LWP^1*'&TY^P[L]LMWP^1+,&[]TXL]TL^1*'&^PN`YOL]TL^1*(&]PWL_TaL^1-,&

?L]_TYZ_%>LRL]OP1/,&?L^L1 )**&

OPLNPWP]LNTpY1)*(# )**&R]LaT_L_Z]TL1*0# 0,&OPnX[P_`1 )*(# )**&TYP]NTLW1*0# 0,&WZYRT_`OTYLW1)*(&

PY]P[Z^Z1 0-# )**&_]LYaP]^LW1)*(&

?L_P]TL1)**&?LcbPWW1()# ),# (0-# ))(&% !FYTOLOOP"1)'.&?PNlYTNLP^_LOn^_TNL1(-.&% ]PWL_TaT^_L1)).&?POTOL^1)0&

LM^ZW`_L^1,*&OT]PN_L^1*)&TYOT]PN_L^1**&

?POTOL^]PWL_TaL^1,*&?m_]LW1('&?TNSPW^ZY1))/&?TYVZb^VT1)).&?pO`WZ OP]TRTOPe1('-# (()&% OPJZ`YR1 ('-&?ZW1(--&?ZXPY_Z XLRYm_TNZ1)(,&?ZYZXTZ^ OPOTXPY^TpYY`WL1..&% P^[`]TZ^1/,&?Z]WPd1))/&?ZaTXTPY_ZNT]N`WL]1(''&

% OPWZ[WLYP_L^100&?`W_T[WTNTOLOOPWLML^P1,(&

.

@P`_]ZYP^1(/+&@Pb_ZY!>Pd OPPYQ]TLXTPY_ZOP"1(.'&@TNSZW^ZY1(*(&@qNWPZL_pXTNZ^#PYP]RnL1)+.&@qXP]Z 23OPWL9PZXP_]nL1)''&

OP?LNS1 (+(&

OPXZWP^1(-,&OPB]LYO_W1(,/&OPCPdYZWO^1()+# (,/&% #OT^N]TXTYLNTpY1(*0&OP D_]`SLW1(+'&

@qXP]Z^ `YTaP]^LWP^1),*&

@`__TR1-,&

ZAM^P]aLMWP^1),&AP]^_PO!FYTOLO"1)'-&AWL!GPWZNTOLOOPWL^"1((0&AYOLL^ZNTLOL1)+,&% _m]XTNL&1(,.&AYOL PWPN_]ZXLRYm_TNL^1))(&% ^`[P]QTNTLWP^1(*(&A^NTWLNTZYP^LXZ]_TR`LOL^1('*&

OP`Y Wn\`TOZPY`Y _`MZ1())&[P]TpOTNL^1(')&

1

BLWZXL]P^1(,/&BLYOPZ1((+&

i@6;57 3>834hE;5A

BmYO`WZNpYTNZ1('(&% PWl^_TNZ1('0&% ^TX[WP1/'# /,&BP]XPLMTWTOLOPWmN_]TNL1+(# +,# )'-&% XLRYm_TNL1+(# +,&BP]XT_TaTOLO1+(# +,# (0-# )'-&BP]`NNL1)'(&X7. *)# .+&BT5LWWPUL1)/&BWLYNV1('# (*# (,# (..# (/.#))*&% !7N`LNTpYOP"1(0(&

BZOP]TZYTeLY_P1)+)&BZT^P`TWWP1()-&BZ^_`WLOZ[]TXP]Z1 *,&% ^PR`YOZ1+*#+-&B]LYO_W1().# ()/&B]P^TpY1(',&% OPWL]LOTLNTpY1(0*# )))&B]TYNT[TZOPP\`T[L]_TNTpY1(./&% OP^TXTWT_`O1.0&% OP^`[P][Z^TNTpY1(0,&B]ZMWPXL&OP4Z`^^TYP^\1 (.)&B]Z[LRLNTpYOPWNLWZ]1(,,&B]ZdPN_TW!3WNLYNPOP`Y"1 0*&

/

CLNTZYLWTeLNTpYOP :PLaT^TOP1 )''#)')&

CLO#)+)&CLOTLNTpY1(/.&CLOTLN_TaTOLO1)+(&

CLOTZOPWPWPN_]pY1)+.&CLOTZWZRnL1)+(&CLWPTRS1('# ((*# ((0# (,0# (-'# (.)&CmRTXPYWLXTYL]1(),&% _`]M`WPY_Z1()-&CPRWL [L]L [WLY_PL]WZ []ZMWPXL^1

/)&CPTNSPYMLNS1(*&CPXZWTYZOP=l]XlY1 (+'&CPZWZRnL1*-# -,&CP[1 )+)&CP^ZYLOZ]P^1(*(&CP^Z]_PP^[T]LW1(('&CPd BL^_Z]1-+# (+,&CPdYZWO^1('# ()+&

!%$

CTLMZ`NSTY^Vd1('# ()0# (.)&CZPY_RPY!FYTOLO"1)+)&CZ^PYQPWO1)*.&CZ_LNTpYOP`YL [WLNLPY`YL NZ]]TPY%

_P1()/&CrNVP]1 ('&C`YRP1 0'# (0)&C`^^PWW1*'&C`^^Z1 (+# (-0&C`_SP]QZ]O!FYTOLO"1)+(&CdOMP]R1),'&

^DlML_Z1(+,&DLNV`]1(0+&DLY <`LY1 ((# )(# )*& ).# +,# -'#

-/&DNZ__4WLT]1-,&DNS]-OTYRP]!7N`LNTpYOP"1)+-&DPWbdY1/)&DPXTaTOL1)+(&

DP`OZ[P]nZOZ1('*&DnXMZWZOPWLPN`LNTZYP^1,*&DTXTWT_`O1(**&DT^_PXL59D71 )',&

59D?1 )'-&% OP9L`^^1 )('&% OP9TZ]RT1+*# ,*# )'*&DZWTOPeOP WL NZY^_]`NNTZYP^1((*&DZXXP]QPWO1(0-&D_ZVP^1()+&% !EPZ]PXL OP"1)'+&D_]LYPZ1(0*&D_]L__ZY1)(*&D_]`SLW1(+'&D`XL [Z] LN`X`WLNTpY1)/&

% aPN_Z]TLW1)0&D`^_LYNTL!5LY_TOLOOP"1(--&

E

EL_P1()(&EPX[P]L_`]L1 )0# (+,# (-/&EPY^TpY1('-&EPZ]PXL&OP 9L`^^1 )'+&

OP[T1 -.# -/&% OPD_ZVP^1)'+&

Page 133: Análisis dimensional

"## i@6;57 3>834hE;5A

5EP^WL1)'+&EP_]ZOP1(0+&ETPX[Z WZNLW1)()&EZWXLY1(*# (-/&EZ]^TpY1(()&E`MP]nL^#(),&E`MZ^ NL[TWL]P^1((.&E`]MTYL^1(++&

4

FYTOLOXl^TNL1)*/&FYTOLOP^1)0&

NZSP]PY_P^1+.# )'*&NZ][`^Z`WL]P^1)*0# )++&OP9TZ]RT1+-# ,*# )'*&]LOTZWpRTNL^1)+)&`YTaP]^LWP^1),,&

FYTpY ;Y_P]YLNTZYLWOP 8n^TNL1+0#(--&

GL^NSd1((# (+&GPN_Z]P^YT_L]TZ^10(&GPWZNTOLOOPWNLWZ]1(,,&

OPWLW`e1+'# +,&% OPWLZYOL PWPN_]ZXLRYm_TNL^1))(&% OPWZYTOZ1(*'&GPY_TWLOZ]P^1(+*&GTM]LNTZYP^OPWLRZ_L^1((0&GTM]LNTZYP^OP`YL N`P]OL1(((&GT^NZ^TOLO1())# (*+&% NTYPXl_TNL1(),&% OPWZRL^P^1(.*# (/*&GZW`XPYOP`Y [L]LWPWP[n[POZ10*&GLY OP] HLLW^1(.+&

6

HPMP] !FYTOLO"1)'0&

i@6;57 97@7C3>BlRTYL^

BCj>A9A&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&.

;@ECA6F55;j@&& &&&&&&&&&&&&&&&s s &&&&&s s &&s &&s &&&&&s s &&&&&&&&&&& 0

B3CE7 BC;?7C3

8F@63?7@EAD 67> 3@g>;D;D 6;?7@D;A@3>

53BTEF>A (&% @M[]UMVLMTI \MWZiILMTI PWUWOMVMQLILLMN]VKQWVM[' LMMK]IKQWVM[$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ )(

(& >L^ Q`YNTZYPSZXZRmYPLRPYP]LWTeLOL^#[lR& )(& % )&

7N`LNTZYPSZXZRmYPL^#))&

53BiEF>A Y&%:W[ MV\M[LMTI 5i[QKI$$$$$$$$$$$$$$$$$$$$$$$$$$$$ (*

(& AM^P]aLMWP^#[lR& ),& % )& >Z^ PY_P NZX[L]LMWP^#),&%*&?LRYT_`OP^ d NLY_TOLOP^#).& % +& 7W N]T_P]TZOP TR`LW%OLO#)/& % ,& >L OPQTYTNTpYOP^`XL# )/& % -&FYTOLOPd XP%OTOL^#)0& % .& ?LRYT_`OP^ []TXL]TL^ d ^PN`YOL]TL^#*'& %

/& ?POTOL^OT]PN_LP TYOT]PN_L^#*)&

53BTEF>A Y;&%>ZQUMZXW[\]TILW$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ *,

(&>L YL_`]LWPeLOP WL WPdP Q`YOLXPY_LWP^OP WL8n^TNL#[lRTYL *,& % )& >L^ PN`LNTZYPOP WL8n^TNL#*.& % *&5ZY^%

_LY_P^NL]LN_P]n^_TNL^d NZY^_LY_P^YTaP]^LWP^#*.&

53BTEF>A ;G& % AMO]VLWXW[\]TILW$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ +*

(&A[TYTZYPLNP]NLOPWLNZY^_LY_P^`YTaP]^LWP^#[lR& +*&%)& ?LRYT_`OP^TY^P[L]LMWP^#++&% *&7Y`YNTLOZOPWPR`YOZ[Z^_`WLOZ#+-& % +&DT^_PXL OP `YTOLOP NZSP]PY_P^#+-&%

Page 134: Análisis dimensional

"#% i@6;57 97@7C3>

,& 4L^P OP `Y NZYU`Y_ZOP XLRYT_`OP^#+0&% -&?POTOL^LM%^ZW`_L d ]PWL_TaL^#,*& % .& >Z^ ^nXMZWZOP WL PN`LNnZYP^Qn^TNL^#,*&

53BTEF>A G&% 4T KWVKMX\WLMLQUMV[QkV $

(&8p]X`WL^ OTXPY^TZYLWP^#[lR& ,,& % )&5LXMTZ OP ML^P#,/& % *& 8LN_Z]P^ OP NZYaP]^TpY#,0& % +& 3YLWZRnLPY_]POTXPY^TZYPd aPN_Z]P^# -'& % ,& 4L^P^ ^`[P]LM`YOLY_P^ dML^P^P^_]TN_L^#-(& % -& 4L^P^ X`_TWLOL^#-*& % .& >L^ XLR%YT_`OP OPOTXPY^TpYY`WL#-*&% /&?LRYT_`OP ]PWL_TaL^#-+&%0&>L^ ^P`OZXLRYT_`OP OP WLCPZWZRnL#-,&

53BTEF>A G;& % 4T \MWZMUILMXQ $

(&:ZXZRPYPTOLOOPWLQp]X`WL Qn^TNL^#[lR& -.& % )&EPZ%]PXL OP [T# -/& % *& >L^ PN`LNTZYPNZY WZRL]T_XZ^#.)& %+&>L NZY^_LY_P\`nXTNL# .)& % ,& 7WPc[ZYPY_P OPWSTO]pRP%YZ# .+&

B3CE7 D79F@63

3B>;535;A@7D

53BTEF>A G;;& % ;WLW LM[QWVIT $

U\MIZ TW[XZWJTMUI[LM IVgTQ[Q[LQUMV#

(&DT^_PXL P [WP_Z OP XZYZXTZ^OP OTXPY^TpYY`WL#[l%RTYL..& % )& f(L []lN_TNL[L]L QZ]XL] `Y ^T^_PXLNZX[WP_ZOP XZYZXTZ^ (# ./& % *&;YQZ]XLNTpY\`P [`POP ZM_PYP]^PNZYPW3Yl & OTXPY^TZYLW&B]TYNT[TZOP^TXTWT_`O#.0& % +&CP%RWL[L]L &OY_PL]WZ []ZMWPXL^#/)& % ,& >L^ ML^P^OPQTNTPY%_P^#/+&% -& >L^ ML^P^ `[P]LM`YOLY_P^d WL NZY^_LY_P^ %[P]QW`L^#/-& % .& BL[PW\`P OP^PX[PoLY WL NZY^_LY_P^YT%aP]^LWP^#//& % /&>L^ ML^P^ YTaP]^LWP^#/0&% 0&6T^N]TXTYLNTpYOP WLOTXPY^TZYPOPWP^[LNTZ#0'& % ('& GZW`XPYOPW[L]LWP%WP[n[POZ#0)& % f(& 3WNLYNPOP `Y []ZdPN_TW#0*&

53BTEF>A G;;;& % 3QVgUQKI LM[kTQLW[ZiOQLW[ $

(&?LRYT_`OP^ []TXL]TL^#[lR& 0,& % )& 7N`LNTZYP Q`YOL%XPY_LWP^#0-& % *&DT^_PXLOTXPY^TZYLW#0.& % +&>L PYP]RnLNZXZ XLRYT_`O[]TXL]TL# 0/& % ,& CPaZW`NTpYOP WZ N`P][Z^NPWP^_P^#00&% -&8`P]eL NPY_]n[P_L#(''& %.& EPY^TpYZ]TRTYLOL[Z] `Y XZaTXTPY_ZNT]N`WL]#(''& % /& BmYO`WZNpYTNZ#('(&%0&A^NTWLNTZYP^[P]TpOTNL^#(')& % ('& 5L_PYL]TL#(')& % ((&A^NT%WLNTZYP^LXZ]_TR`LOL^#('*&

i@6;57 97@7C3> "#&

BlRTYL^BlRTYL^

,,

53BiEF>A ;I& % ;MKgVQKI LM[kTQLW[LMNWZUIJTM[$$$$$$$$$$$$$$$$$$$ (',

(& DT^_PXLOTXPY^TZYLW#[lR& (',& % )&8WPcTpYNT]N`WL]OP`YL ML]]L#('-&%*& 8WPcTpYOP `YL ML]]L^ZXP_TOLL `YL 4ZWLQ`P]eL# ('/& % +&BmYO`WZPWl^_TNZ#('0& % ,& BP]nZOZ OP `Y]P^Z]_P PY P^[T]LWL^ZNTLOZL `Y aZWLY_P#(W'&% -&8]PN`PYNTLOPWLaTM]LNTZYP^Q`YOLXPY_LWP^OP`YL N`P]OL#(((& % .&7YP]%RnLOP WL aTM]LNTZYPQ`YOLXPY_LWPOP `YL N`P]OL# (((& %/& EZ]^TpYOP `YL&ML]]L#(()& % 0&DZWTOPeOP WL NZY^_]`NNTZ%YP^# ((*& % ('& BLYOPZ#((+& % ((& 6TL[L^ZYP^#((,&

-.

53BTEF>A I& % ;MKgVQKI LM,T]QLW[$$$$$$$$$$$$$$ $$$$$$$$ $$$$$$$$ ((.

(&DT^_PXLOTXPY^TZYLW#[lR& ((.& % )&5L[TWL]TOLO#((.& %*&3^NPY^ZOP Wn\`TOZPY _`MZ^ NL[TWL]P^#((.& % +&DLW_ZOP[]P^TZYP^PY WL `[P]QTNTPOP `Y Wn\`TOZ#((/& % ,& GPWZNTOLOOP WLZWL^#((0& % -&GTM]LNTZYP^OP`YL RZ_L#((0& % .& BP^ZOP WL RZ_L^ OP^[]PYOTOL OPWPc_]PXZ OP `Y _`MZ NL[TWL]#()'& % /& GT^NZ^TOLO#())& % 0& A^NTWLNTZYP^OP `Y WT\`TOZPY `Y _`MZ PY F# ())& % ('& 5LnOLOP `YL P^QP]LPY `Y XPOTZaT^NZ^Z#()*& % WW&7WYqXP]Z OP CPdYZWO^#()+& % ()& 5T]N`%WLNTpYOP QW`TOZ^[Z] _`MP]nL^#(),& % (*& CZ_LNTpYOP `YL[WLNLPY `YL NZ]]TPY_PQW`TOL#()/& % (+& GPWZNTOLOOP []Z%[LRLNTpYOPWZYTOZ#(*'& % (,& AYOL^^`[P]QTNTLWP^P^_LNTZYL%]TL^#(*(& % (-& CP^ZYLOZ]P OP :PWXSZW_e#(*(& % (.& :nO]p%

XP_]Z OP @TNSZW^ZY#(*(&

.. (**53BTEF>A I;& % 0MZWLQVgUQKI $

(&7W[]TYNT[TZOP^TXTWT_`Od WLOT^N]TXTYLNTpYOP WLOTXPY%^TZYP OPWP^[LNTZ#[lR& (**&% )& 6TXPY^TZYP OP WLaT^NZ^T%OLO#(*+&% *&3WL^OP LaTpY#(*-& % +&E]lY^T_Z OPW]mRTXPYWLXTYL]LW]mRTXPY_`]M`WPY_Z#(*0&% ,& CPXZWTYZOP =l]%XlY# (+'& % -& ;YQW`PYNTLOP WLNZX[]P^TMTWTOLO&7W YqXP]ZOP ?LNS# (+(& % .& :mWTNP#(+)& % /& 4ZXML^ d aPY_TWLOZ%]P^# (+*&% 0&E`]MTYL^#(++&

0,

53BTEF>A I;;& % BMUXMZI\]ZI $$$$$$$$$$m$$$$$$$ ! ! $!

(&>L^ P^NLWLNZYaPYNTZYLWP^#[lR& (+,& % )& >L P^NLWLOP3aZRLO]Z# (+-& % *& A_]L^ P^NLWL^YTaP]^LWP d LM^ZW`_L^#(+/& % +&>L P^NLWL_P]XZOTYlXTNL#(+0&% ,& CPWLNTpYPY_]PWL OTaP]^L^P^NLWL^`YTaP]^LWP^#(+0&

(+,

53BTEF>A I;;;& % =WVL]K\Q^QLIL\hZUQKI $

(&>PdP^ Q`YOLXPY_LWP^#[lR& ;&,*&% )& DT^_PXLOTXPY^TZ%YLW#(,+& % *&B]Z[LRLNTpYOPWNLWZ]PY `Y XPOTZTYOPQTYTOZ#(,,& % +&B]Z[LRLNTpYOPWNLWZ]PY `YL ML]]L#(,,& % ,&GPWZ%

(,*

Page 135: Análisis dimensional

"$ i@6;57 97@7C3>

NTOLOOP[]Z[LRLNTpYOPWNLWZ]#(,-& % -&E]LY^XT^TpYOPWNLWZ][Z] _`MP]nL^#(,.& % .& 7YQ]TLXTPY_ZOP `Y ^pWTOZPY `YLNZ]]TPY_PWn\`TOL#(,/& % /& 3YPXpXP_]Z OP LWLXM]PNL%WTPY_P#(-'&

53BTEF>AI;G& % BMZUWLQVgUQKI $

(&5LWZ]#[lR& (-*& % )&7YP]RnLTY_P]YLd PY_]Z[nL#(-+& %*&DT^_PXLOTXPY^TZYLW#(-,& % +&GL]TLMWP^TYOP[PYOTPY_P^dNZY^_LY_PNL]LN_P]n^_TNL^#(-,& % ,& 5ZY^_LY_POP WZ RL^P^[P]QPN_Z^#(-.& % -& >L OTXPY^TpYOP WL_PX[P]L_`]L# (-/& %.& 7N`LNTpYOP WZRL^P [P]QPN_Z^#(-/& % /& 7YQ]TLXTPY_ZOP`YL P^QP]L#(.'& % 0&5L^Z^ PY \`P P^ aTLMWPWLML^PX`_TWL%OL#(.(& % ('& DZW`NTpYOPW[]ZMWPXLOP 4Z`^^TYP^\# (.)& %((& CPWLNTpYPY_]P WLaT^NZ^TOLOd WLNZYO`N_TaTOLO_m]XTNLOP `Y RL^ [P]QPN_Z#(.*& % ()& >Pd OP WZ P^_LOZ NZ]]P^[ZY%OTPY_P^#(.+& % (*& 6T^_]TM`NTpYOP []P^TZYP^PY WLL_Xp^%QP]L#(.,&

53BTEF>AIG& % ;MKgVQKI MM\ILQ[\QKI $

(& >L NZY^_LY_POP 4ZW_eXLYY#[lR& (..& % )& B]TYNT[TZOP P\`T[L]_TNTpY&5ZY^_LY_POP 3aZRLO]Z# (./& % *&>Pd OPOT^_]TM`NTpYOP 4ZW_eXLYY#(/'& % +&8W`N_`LNTZYPP^_LOn^%_TNL^#(/'& % ,&>Pd OPOT^_]TM`NTpYOP?LcbPWW#(/(& % -&B]P%^TpYOP `YL XL^L RL^PZ^L#(/)& % .& GT^NZ^TOLOOP WZ RL%^P^# (/*& % /& 5ZY &TN_naTOLO_m]XTNLOP WZ RL^P^#(/*&%0&6PY^TOLOOP WP]LNTpYOP WZ YP`_]ZYP^#(/+&

53BTEF>A !QkV\hZUQKI UMKgVQKIK]IV\Q[\I $

(&@PNP^T &(&OP`YL Y`PaL NZY^_LY_P`YTaP]^LW#[lR& (/.& %

)& >L NZY^ ]_P OP BWLYNV#(//& % *&>Pd OP D_PQLY# (0'& %+1 7N`LNT &OPWZ]OCLdWPTRS#(0(& % ,& >Pd OP HTPYd PN`L%NTpYOP &LYNV#(0(& % -&B]P^TpYOP]LOTLNTpY#(0*& % .&5ZY^%_LY_P\`nXTNL#(0+&

53BTEF>AIG;;& % 4TMK\ZbUIOVM\Q-UW $

(& ?LRYT_`OP []TXL]TL^#[lR& (0,& % )& >PdP^ Q`YOLXPY%_LWP^#(0.& % *&DT^_PXLOTXPY^TZYLW#(00& % +&>L ]LNTZYLWT%eLNTp&YOP :PLaT^TOP#)''& % ,& DT^_PXLOP 9TZ]RT#)'*&%-& D;^_PXL^ NPRP^TXLWP^#)',& % .& 8LN_Z]P^ OP NZYaP]^TpY)'.& % /& DT^_PXLOP 9L`^^# )('& % 0&6T^N]TXTYLNTpYOP WL^fXPY^TZYP^ OPWP^[LNTZ#)(*& % ('& ?LRYT_`OP^ ^PN`YOL%]TL^#)(+& % ((& A_]Z^ ^T^_PXL OTXPY^TZYLWP^#)(,& % ()& 5ZY%OPY^LOZ][WLYZ#)(.& % (*& 7YP]RnL [Z_PYNTLWOP WL NL]RL^

"$!i@6;57 97@7C3>

BlRTYL^BlRTYL^

PWmN_]TNL^#)(.& % (+&;YP]NTLOPWLPWPN_]TNTOLO#)(/& % (,& 5LX%[Z OP `Y OT[ZWZPWmN_]TNZ#)(0& % (-& 7WPN_]pXP_]ZOP >T[[%XLYY#)(0& % (.& 6PY^TOLOOP PYP]RnLPY PWNLX[Z PWPN_]Z%XLRYm_TNZ#))(& % (/& AYOL PWPN_]ZXLRYm_TNL^#))(& % (0&>L]LOTLNTpY_m]XTNLNZXZQPYpXPYZZYO`WL_Z]TZ#))*& % )'& 7YP]%RnLPXT_TOL[Z] `Y OT[ZWZPWmN_]TNZ#)),&

(-*

53BTEF>AIG;;;& % ;MKgVQKIZMTI\Q^Q[\I $

(&>L^ XLRYT_`OPOP WL?PNlYTNL]PWL_TaT^_L#[lR& )).& %)& 7N`LNTZYP Q`YOLXPY_LWP^#))0& % *& DT^_PXLOTXPY^TZ%YLW#)*'& % +&5ZY^P]aLNTpYOP WLPYP]RnL#)*'& % ,& ;YP]NTLOP WLPYP]RnL#)*(& % -& ?L^L OP nX[P_` d XL^L OP LNPWP]L%NTpY#)*(& % .& ?L_P]TL#XL^L d PYP]RnL#)**&

)).

(..

53BTEF>AI;I& % 5QMQKIKWZX][K]TIZm$$$$$$$$$$$$$$$$$$$$$$$$$$$$$

(&DT^_PXLOTXPY^TZYLW#[lR& )*.& % )&FYTOLOPNZ][`^N`%WL]P^#)*0& % *&?LRYT_`OP^`^LOL^ PY ]LOTLN_TaTOLOd ]LOTZ%WZRnL#)+(& % +&6Z^T^ PY Q`YNTpYOP WLLN_TaTOLOd OP WLOT^%_LYNTL#)+)& % ,& FY ^T^_PXLOP `YTOLOP NZSP]PY_P [L]LWL8n^TNLOPWZNZ][q^N`WZd OPWL]LOTLNTpY#)++&% -& AYOLL^ZNTLOLL `YL [L]_nN`WLPY XZaTXTPY_Z#)+,& % .& >L Q`Y%NTpYOP ZYOL^#)+-& % /& CLOTZNWl^TNZOPWPWPN_]pYPY PWaLNnZ#)+.& % 0& 7YP]RnL PWPN_]Z^_l_TNLOP WZ YqNWPZL_p%XTNZ^#)+.& % ('& 8`P]eL OP >Z]PY_e# )+/& % ((& CLOTZOPN`]aL_`]L OPWL_]LdPN_Z]TLOP`Y PWPN_]pYPY`Y NLX[Z XLRYm%_TNZ#)+0&% ()& 7WP^[nY#)+0& % (*& 7WXLRYP_pYOP 4ZS]#),'& % (+&>L NZY^_LY_POPCdOMP]R#),'& % (,& 7W^T^_PXLOPWL NZY^_LY_P^`YTaP]^LWP^#),(& % (-& >Z^ YqXP]Z^ `YTaP]^L%WP^#),*& % (.& FY ^T^_PXLOP `YTOLOP^YTaP]^LWP^#),,&

)*.

(/.

5ZY^_LY_P^YTaP]^LWP^ & ),.

),/

)-(

AM]L^NT_LOL^ &

nYOTNPLWQLMm_TNZ &

(0,

((