Docfoc.com-ejercicios de Aplicaciòn Flujo de Fluìdos y La Ecuaciòn de Bernoulli

8/16/2019 Docfoc.com-ejercicios de Aplicaciòn Flujo de Fluìdos y La Ecuaciòn de Bernoulli

1/19

CAPITULO 7. FLUJO DE FLUIDOS Y ECUACIÒN DE BERNOULLI-(Hidráulic. I!".A. #$ui P.%

EJERCICIOS DE APLICACIÒN FLUJO DE FLUÌDOS Y LA ECUACIÒNDE BERNOULLI

A) Factores de Conversin! & L'i! ) & L* ) &+.+7,&-+ '/0&. '/ ) + L'i!0 & "l'i! ) "* ) .712 L'0

&"l'i! ) +.3 , &-2

'/0 &. *i4

'/ ) 553 "l'i!."!- C6!i4r8 u! r*id49 d4 :u;6 d4


2/19


c6!8i!uidd. E! l Fi". 4l :ud6 :u4 d4 l /4cci! & l /4cci! < c6!r*id49 c6!/8!84. L c!8idd d4 :uid6 u4 */ *6r cului4r/4cci! 4! u! ci4r86 8i4*6 dd6 4/ c6!/8!84 (/4 l4 ll G:u;6c6!/8!84%. E! 8ri!6/ d4 l r*id49 d4 / c66= >& ) >)ρA0 /4 8i4!4= ρ& A& & ) ρ< A


3/19


L r*id49 d4 :u;6 d4 *4/6 4/=

W =γ 1 A

1v1=(7.09 x 10−2 lb pie3 )(100 pulg

2 )( 1100 piesmin )( 1 pie2

144 pulg2 )(60minh )=3,249.6lb /h

.

'.- D484ri!4 l r*id49 d4 :u;6 á,i *4ri8id@ 4! L'i!@ u4*u4d4 *r6ducir/4 4! u! 8u6 d4 c4r6 4/8á!dr u4 8i4!4 u! diá48r64,84r!6 d4 &.2 *ul" .72 *ul" d4 "r6/6r 4! l/ *r4d4/@ /i l4l6cidd á,i d44 /4r . '/.S6luci!= U8ili9!d6 l d4!ici! d4 r*id49 d4 :u;6 d4 6lu4!@ /48i4!4= K ) A@ 4l ár4 4/=

A= [(1.50−2 x 0.075) x0.0254 ]2 x π 4=9.2347 x10−4 m2 0 4!86!c4/ l r*id49 d4

:u;6 4! 6lu4!= Q=(9.2347 x 10−4 m2 )(3 ms )=

2.77 x10−3 m

3

s 0 c6!ir8i4!d6

L'i!@ /4 8i4!4= Q=2.77 x 10−3 m

3

s (60000 L/min1m3/s )=166.22 L/min .

(.- D484ri!4 4l 86 r4u4rid6 d4 c6!duc86 d4 c4r6 Clir4 54/8á!dr u4 ll44 & L'i! d4 "u c6! u! 4l6cidd á,i d42.2 '/.S6luci!.- C66 K /6! c6!6cid6/@ 4l ár4 r4u4rid6 /4 *u4d4

$llr d4= K ) A0 A)K'. Pri4r6 d446/ c6!4r8ir l r*id49 d4:u;6 d4 6lu4! u!idd4/ d4 '/.

Q=3100 L

min ( 1 m

3

s

60000 L

min)=0.0516 m3s 0 4!86!c4/ 4l ár4=

A=Q

v =

0.0516m3/s

5.50m /s =9.394 x10−3 m2 . E/86 /4 d44 i!84r*r48r c66 4l

ár4 !i di/*6!il4@ *u4/86 u4 cului4r ár4 4!6r *r6duciru! 4l6cidd 6r u4 2.2 '/. P6r c6!/i"ui4!84@ d446/ u/cr4! 4l *!dic4 F d4l lir6 u! c6!duc86 4/8á!dr c6! u! ár4 d4 :u;6 ;u/86 6r u4 3.35 , &-


4/19


4l6cidd *r6ducid /4r= )K'A0 v= 0.0533m

3/s

8.213 x10−3

m2=6.50m /s @ u

l8.

.- E! l "ur@ /4 u4/8r u! i!84rcid6r d4 cl6r u4 /4 u8ili9*r 8r!/4rir cl6r d4/d4 4l :uid6 u4 :u4 d4!8r6 d4l 8u6 i!84ri6rl u4 :u4 4! 4l 4/*ci6 c6*r4!did6 4!8r4 l *r84 4,84ri6r d4l8u6 l *r84 i!84ri6r d4l c/c6 cudrd6 u4

S = 0 . 8 5 ”

S

A tA s

S e c c i ò n

t r a n s v e r s a l

E n t r a d a d ef l u ì d o a l c a s c o

S a l i d a d e

f l u ì d o d e l c a s c o

F l u j o e ne l t u b o

F l u j o e ne l c a s c o

T u b o d e c o b r e t i p o d e ! p u l " a d a

I n t e r c a m b i a d o r d e c a l o r d e c a s c o y t u b o

r6d4 l 8u6. Clcul4 lr*id49 d4 :u;6 d4 6lu4! 4! "l'i! u4 *r6ducir u! 4l6ciddd4 3 *i4/'/@ 8!86 d4!8r6 d4l 8u6 c66 4! 4l c/c6.S6luci!.- U8ili96/ l rul *r l r*id49 d4 :u;6 d4 6lu4!@ K) A *r cd *r84=% D4!8r6 d4l 8u6 d4 c6r4 8i*6 ? d4 *ul" d4 86 !6i!l= D4l*!dic4 /4 68i4!4= ED).+


5/19


c6!ir8i4!d6 "*= Qs=0.0259 pies

3

s ( 449 gal

min

1 pie

3

s)=11.665 galmin 0 El c6ci4!84

d4l :u;6 4! 4l c/c6 4!8r4 4l :u;6 4! 4l 8u6 4/= Coiente=Qs

Qt )

11.665 gal

min

6.122 gal

min

=1.905

C! CONSER*ACIÒN DE LA ENER+ÌA,ECUACIÒN DE BERNOULLI

# i v e l d e r e f e r e n c i a

F i g . E l e m e n t o d e f l u i d oe n u n c o n d u c t o

E l e $ e n t o d e lf l u i d o

vp

%

S4 *r4!di u4 l 4!4r" d4 u! /i/84@ !6 /4*u4d4 cr4r !i d4/8ruir@ /i!6 u4 *u4d4 /4r 8r!/6rd d4 u! 8i*6 68r6@ /8 4/ l l4 d4 c6!/4rci! d4 l 4!4r". Cu!d6 /4 !li9c6!duc86/ c6! :uid6/@ 4,i/84! 8r4/ 6r/ d4 4!4r"@ c66 4;4*l6

4! l Fi". E/8á l6cli9d u! ci4r8 4l4ci! (9%@ 8i4!4 u!4l6cidd (% u! *r4/i! (*%. L/ rul/ d4 4!4r" /6!=

&. E!4r" *684!cil (PE%.- E/ d4id l 4l4ci! 4/ c6!r4/*4c86 u! l!4 d4 r44r4!ci= PE % -!.0 d6!d4 Q 4/ 4l*4/6 d4l 4l44!86.


6/19



'

(p . % . v( ( (

p . % . v' ' '


-L c!8idd 868l d4 4!4r" d4 4/8/ 8r4/6r/ u4 *6/44 4l 4l44!86 d4 :uid6 /4rá l /u.

E= !E+ "E+ #E=℘γ +$%+$ v2/2 g 0 cd u!6 d4 4/86/ 8ri!6/ /4

4,*r4/ 4! u!idd4/ d4 4!4r"@ !486!-48r6 (N.% 4! 4l /i/84i!84r!ci6!l 6 4! *i4/-lir (*i4.l% 4! 4l /i/84 d4 u!idd4/ri8á!ic/.- C6!/id4r!d6 $6r 4l 4l44!86 d4 :uid6 u4 /4 u4/8r 4! l

"ur@ u4 /4 u44 d4 l /4cci!(&% l /4cci! (


7/19


4!4r" *6/4d *6r 4l :uid6 *6r u!idd d4 *4/6 d4 :uid6 u4 :u44! 4l /i/84. L/ u!idd4/ d4 l6/ 8ri!6/ /4 d! 4! !486!-48r6*6r !486! (N.'N% 4! 4l /i/84 SI 4! 4l ri8á!ic6 (l.*i4'l%. E/ d4!68r u4 4l N@ l /4 *u4d4! c!c4lr@ d4;!d6 /6l4!84 u!u!idd d4 l6!"i8ud@ 4l 48r6 (% 6 4l *i4. P6r 8!86@ l6/ 8ri!6/ /4

l4/ c6!6c4 c66 Gc49/=-El 8ri!6= *'γ /4 l4 c6!6c4 c66 c49 d4 *r4/i!.-El 8ri!6= G9 /4 l4 ll c49 d4 4l4ci!.- El 8ri!6=


8/19


&. D484ri!r u4 4l44!86/ /6! c6!6cid6/ u4 /4 4!c6!8rr.PLO DEL PROCEDI>IENTO (CONSIDERAR LA FIVURA DE C.&%&.E! l "ur *r84 d4 u! 8u4r 4l "u & MC :u4 d4 l /4cci!& l /4cci!


9/19


?N'. S4 d484ri!rá


10/19


c6!duc86 c4rrd6@ *6r l6 u4 l 4l6cidd /4rá u *4u4 A ) @ d44 4lii!r/4 /u c49 d4 4l6cidd.

-Cu!d6 6/ *u!86/ d4 r44r4!ci 4/8á! 4! 4l i/6 c6!duc86.-Si"ui4!d6 4l !áli/i/ 4! l "ur l6/ *u!86/= B@ C@ D E /4 4!cu4!8r!

d4!8r6 d4l c6!duc86 *6/44! u! ár4 d4 :u;6 u!i6r4 4l :u;6 4/4/8l4@ *6r l6 u4 l 4l6cidd /4rá l i/ l6 lr"6 d4l c6!duc86=B)C)D)E. P6r l6 u4@ /u/ c49/ d4 4l6cidd 4! 6/ ld6/ d4l 4cuci! /4r! i"ul4/ /4 c!c4lr!.

-Cu!d6 l 4l4ci! 4/ l i/ 4! 6/ *u!86/ d4 r44r4!ci.- Sil 4l4ci! 4! l6/ d6/ *u!86/ d4 r44r4!ci u/d6/ 4! l Ec. d4B4r!6ulli 4/ l i/@ 4/86/ 8ri!6/ /4 c!c4l! (9A@ 9B@ 9D%. L/ 56/4rci6!4/ !li9d/ cili8rá! l/ /i*licci6!4/ 4! l /6luci!d4 4;4rcici6/ /iilr4/ l 4;4*l6 c6!/id4rd6.

". E=e524o.- E! l "ur d4 rri 4l /i! /c "u d4l 4/8!u4@c6! l/ i// di4!/i6!4/ u4 /4 d!. Clcul4 l r*id49 d4 :u;6 d46lu4! 8r/ d4l /i! l *r4/i! 4! l6/ *u!86/ B@ C@ D E.S6luci!.- &.- cálcul6 d4 l r*id49 d4 :u;6 d4 6lu4! K@ u8ili9!d6l Ec. B4r!6ulli@ 4! 4/84 c/6 l6/ *u!86/ 4/c6"id6/ /6! A F. C66 /4di;6 !84/ 4! C.50 /4 8i4!4!@ 4! A= *A)@ A)0 4! F= *F)@ 9F )


11/19


K *4r6 !6 AB /4 clculrá d4l c6!duc86 AB ) (π'5%( %


12/19


0= p D

γ +

v D2

2 g p D

γ =

−v D2

2 g )−v'

2

2 g )−0.494m 0 /4 c6!clu4 u4 l

*r4/i! 4/ p D=γ (−0.494 m)=9.81

k&

m3 (−0.494m )=−4.846

k&

m2=−4.846 k"a= p'

! L/ *r4/i6!4/ 4! B D /6! i"ul4/ u4 l 4l4ci! l 4l6cidd/6! i"ul4/.4% Cálcul6 d4 l *r4/i! 4! E0 4/c6"i4!d6 l6/ *u!86/ A E=

p A

γ + % A+

v A2

2g=

p E

γ + % E+

v E2

2g 0 4! 4/8 Ec. *A)@ A)0 u4d=

% A= p E

γ + % E+

v E2

2 g 0 rr4"l!d6= p E=γ [ ( % A− % E )− v E

2

2 g ] 0 d4 l "ur % A− % E=

2.50m . Ti! l/ 4l6cidd4/ 4! B)C)D)E /6! i"ul4/

u4 /4 4!cu4!8r! 4! 4l i/6 ár4 c6!duc86@ 4!86!c4/ E ) B0

lu4"6v E2

2 g=

v '2

2g )0.494m . P6r l8i6=

p E=9.81 k&

m3 (2.50m−0.494 m )=9.81

k&

m3 2.006m

R4/ul8= p E=19.678

k&

m2=19.678 k"a

RESU>EN DE LOS RESUL6ADOS DEL EJE>PLO RESUEL6O!&.L 4l6cidd d4 :u;6 4! l 6uill l r*id49 d4 :u;6 d4 6lu4!4! 4l /i!@ d4*4!d4! d4 l di4r4!ci d4 4l4ci! 4!8r4 l /u*4rci4lir4 d4l :uid6 l /lid d4 l 6uill.


13/19


= = = ==

= =

=

=======

=

=

=

===

=

==

==

=

=

' 5 0 $ $ φ

( 5 0 $ $ φ

' $

0 . 4 ( $

/

1

A

F l u j o

C! >edidores *ent#ri 9 otros siste5as cerrados conve4ocidades desconocidas!,E! l "ur /4 u4/8r u! di/*6/i8i6 c6!6cid6 c66 4did6r4!8uri@ u4 /4 u8ili9 *r 4dir 4l6cidd d4 :u;6 4! u! /i/84 d4:u;6 d4 :uid6. El !áli/i/ /4 $rá c6! l Ec. d4 B4r!6ulli. E! l /4cci!B c6! diá48r6 r4ducid6 6c/i6! u4 l 4l6cidd u4!84 di/i!u l *r4/i!. S4 $ d4 d46/8rr u4 l 4l6cidd d4 :u;6d4*4!d4 d4 l di4r4!ci d4 *r4/i! 4!8r4 l6/ *u!86/ A B@ *6r l6 u4/4 u8ili9 u! !48r6 di4r4!cil 4!8r4 6/ *u!86/.E;4*l6 Ilu/8r8i6=

".El 4did6r 4!8uri 6/8rd6 4! l "ur ll4 "u 22 MC. L"r4dd 4/*4cc d4l :uid6 !68ric6 ("lic4ri! /")&.


14/19


p A+γ $ ( * )+γ $ (1m )−γ g (1m )−γ $ ( * )−γ $ (0.42m )= p' E/ d4 !68r u4 /4

c!c4l l *r4/i! 4! (%@ rr4"l!d6= p A− p'=γ $ (0.42m−1m )+γ g (1m )=γ $ (−0.58m)+γ g (1m ) @ diidi4!d6=

p A− p'γ $

=−0.58m+γ g (1m)

γ $=−0.58m+

12.36 k& m

3 (1m )

9.67 k&

m3

=−0.58m+1.278m → p A− p'

γ $=0.698m

. El ld6 i9ui4rd6 d4 l Ec. d4 B4r!6ulli /4 4lud6@ $6r /4*r6/4"uirá c6! 4l i4r6 d4l ld6 d4r4c$6@ c6! l Ec. d4c6!8i!uidd= AAA)ABB B ) A(AA'AB%0

v '=v A

( π D A

2

4

π D '2

4 )=v A

( D A

2

D '2

)=v A

(250mm

150mm

)

2

→ v'=2.777 v A → v'2=7.711v A

2

0 /4

!4c4/i8 v '2−v A

2=7.711 v A2−v A

2=6.711v A2

→ v'2−v A

2=6.711 v A2

. P6d46/

$6r 86r 4/84 r4/ul8d6@ l di4r4!ci d4 c49/ d4 4l4ci! lc49 d4 di4r4!ci d4 *r4/i! /u/8i8uirl6/ 4!

p A− p'γ

+( % A− %' )=v'2−v A

2

2 g . A/= .+31 −0.42m ) .A DE 6ORRICELLI


15/19


'.

.(

F l u j o d e u n t a n 6 u e

E! l "ur@ 4l :uid6 4/8á :u4!d6 d4l ld6 d4 u!8!u4 *6r u! 6uill li/ r4d6!d. Pr d484ri!r l 4l6ciddd4 :u;6 u4 /4 68i4!4 4! l 6uill@ /4 4/criirá l 4cuci! d4B4r!6ulli 4!8r4 u! *u!86 d4 r44r4!ci 4! l /u*4rci4 d4l :uid6 u!*u!86 4! 4l c$6rr6 u4 /4 68i4!4 d4 l 6uill=

p1

γ + %

1

+ v1

2

2g=

p2

γ + %

2

+ v2

2

2g 0 L/ *r4/i6!4/ 4! & < /6! !ul/ 4/8á!

4,*u4/8/ l 8/4r *& ) *


16/19


O8r *licci! i!84r4/!84 d4l 846r4 d4 T6rric4lli /4 u4/8r 4! l"ur /i"ui4!84@ 4! l u4 4l c$6rr6 d4 luid6 4/ l!9d6 $ci rri.El c$6rr6 lc!9 u! l8ur i"ul l 4l4ci! d4 l /u*4rci4 lir4d4l :uid6 4! 4l 8!u4. Al !l d4 l l8ur d4 4l4ci! d4l c$6rr6 l

4l6cidd 4/ c4r6=

p1

γ + %1+

v12

2g =

p2

γ + %2+

v22

2g 0 4/8 /i8uci! 4/ /iilr l

d4/rr6ll6 i!icil d4l 846r4 d4 T6rric4lli= v2=√ 2 g h 0 A$6r

4/crii4!d6 l Ec. d4 B4r!6ulli 4!8r4 l6/ *u!86/ < = p2

γ + %

2+

v22

2g=

p3

γ + %

3+

v32

2 g 0 u *


17/19


v2=√2 g[( p1γ )+h] 0 4/8 4cuci! 4/ *r4cid l 846r4 d4 T6rric4lli@8i! !84ri6r4!84 /4 8u6 v=√ 2 g h 0 4l c$6rr6 /4 4l4rá u!

l8ur $. *6r !l6"@ 4l /i/84 *r4/uri9d6 $rá u4 4l c$6rr6 /4

4l44 u! l8ur= ( p1γ )+h @ 4! 4/84 4;4rcici6@ /i d4/46/ u!l8ur d4 52 *i4/ $ ) 1 *i4/=

p1

γ =45 pies−8 pies=37 pies 0

p1=γ (37 pies )=

(62.4

lb

pie3

)(37 pies ) 1 pie

2

144 pulg2=16.03

lb

pulg2 +elat .

P6r c6!/i"ui4!84 l c49 868l *6r 4!ci d4 l 6uill 4/ ( p1γ )+h.

C! FLUJO DEBIDO A UNA CABEA EN DESCENSOA!84ri6r4!84 /4 d46/8r u4 l 4l6cidd l r*id49 d4 :u;6 d46lu4!@ u4 /4 68i4!4 d4 u! 6rici6 4! u! 8!u4@ di/i!u4 d4!4r !6 li!4l c6!6r4 4l :uid6 :u4 d4l 8!u4 di/i!u4 l*r6u!didd d4l :uid6. E! 4/84 c/6@ /4 d4/rr6llrá 4l 86d6 *rclculr 4l 8i4*6 r4u4rid6 *r cir u! 8!u40 4! 4l 4;4*l6 /4u4/8r u! 8!u4 u4 *6/44 u! 6uill li/ r4d6!d 4! 4l 6!d6@ 8r/ d4l cul /4 d4/cr" 4l :uid6.

F l u j o 6 u e s a l e d e u nt a n 6 u e c o n u n a c a b e % ad e d e s c e n s o

t

d

'

j

(

v j

Pr u! *r6u!didd d4 :uid6 dd ($%@ 4l 846r4

d4 T6rric4lli dic4 u4 l 4l6cidd d4 :u;6 4! 4l c$6rr6 4/= v ,=√ 2gh .

L r*id49 d4 :u;6 d4 6lu4! u4 */ *6r l 6uill 4/ Q= A , v ,

('/% [ (*i4/'/%. E! u! *4u4 c!8idd d4 8i4*6 d8@ 4l 6lu4!

d4l :uid6 u4 */ *6r l 6uill 6 /l4 4/ - ,=Q ( t )= A , v ,(t ) .


18/19


>i4!8r/ 8!86@ d4id6 u4 4l :uid6 4/8 /li4!d6 d4l 8!u4@ 4l!i4l d4 :uid6 di/i!u4@ dur!84 4l *4u46 i!cr44!86 d8 u!*r6u!didd 6 di/8!ci d$0 4!86!c4/ 4l 6lu4! u4 ; d4l 8!u4

4/ 6lu4! r46id6 - t =− A t h 0 4/86/ d6/ 6l4!4/ d44! /4r

i"ul4/= A , v , (t )=− A t h 0 r4/6li4!d6 *r 4l 8i4*6 d8 /4 8i4!4=

t =

−( At A , )v ,

h 0 c66 v ,=√ 2gh→t =

−( A t A , )√ 2 gh

h=

−( At A , )√ 2g

h−1/2

h . El 8i4*6

r4u4rid6 *r u4 4l !i4l d4l :uid6 d4/ci4!d d4 u! *r6u!didd $&

68r $


19/19


!84/ d4 ll4r c6 l6/ cálcul6/ u4 /4 d44! r4li9r 4! L4cuci! (&%.C.7.< E4c86 d4l 8i*6 d4 6uill.- Si l 6uill 8i4!4 u! 6r á/"ud@ 4l diá48r6 !i6 d4l c$6rr6 4/ /i"!ic8i4!84 4!6ru4 4l diá48r6 d4 l 4r8ur. El ár4 d4cud u4 /4 d44 u8ili9r

A ; 4! l 4cuci! (&% 4/ l u4 8i4!4 4l diá48r6 á/ *4u46. E/84*u!86 c6!6cid6 c66 l 4! c6!8rc8@ /4 *r4/4!8 li"4r4!84u4r d4l 6rici6- E!86!c4/ *r6,id4!84 A ; ) .+< A6

Docfoc.com-ejercicios de Aplicaciòn Flujo de Fluìdos y La Ecuaciòn de Bernoulli

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Transcript of Docfoc.com-ejercicios de Aplicaciòn Flujo de Fluìdos y La Ecuaciòn de Bernoulli