Problemas Primera Unidad Fluidos II

REDES ABIERTASEjemplo

DATOS DE ENTRADASTUBO LONGITUD DIAMETRO

1 De A-U1 13002 De U1-B 7603 De U1-C 5404 De U1-U2 2360

5 De U2-D 11506 De U2-E 1350

Calculo del diametro del tubo A-U1Al asunir alturas entonces se obtien dh, y usar frmula de velocidadHT Longitud Dimetro

30 1300 0.3530 1300 0.430 1300 0.4530 1300 0.530 1300 0.5530 1300 0.630 1300 0.630 1300 0.630 1300 0.6

DATOS DE ENTRADASTUBO LONGITUD DIAMETRODe A-U1 1300De U1-B 760De U1-C 540De U1-U2 2360

De U2-D 1150De U2-E 1350

Calculo del diametro del tubo U1-BAl asunir alturas entonces se obtien dh, y usar frmula de velocidad

HT Longitud Dimetro30 760 0.1530 760 0.230 760 0.2530 760 0.330 760 0.330 760 0.330 760 0.3

Calculo del diametro del tubo U1-cAl asunir alturas entonces se obtien dh, y usar frmula de velocidadHT Longitud Dimetro

50 760 0.1550 1300 0.250 1300 0.250 1300 0.2

Tener cuidado con los caudales que salende los nudos

caudales COTAS que salen Ks viscosidA= 150 m 0.31 0.0003 0.00000114B= 90 m 0.31 0.0003 0.00000114C= 70 m 120 0.0003 0.00000114U1 120 0.0003 0.00000114U2 75 0.0003D= 12 m 330 0.0003 0.00000114E= 0 m 255 0.0003 0.00000114

Asumiendos cotas para los nudosU1= 120U2= 75Altura Dh 2g Ks/3.7D VELOC Q =caudal suma(hm)

30 19.62 0.00023166 2.86480432 0.27474977 1.547720930 19.62 0.0002027 3.11391284 0.39006118 1.8285869930 19.62 0.00018018 3.35070284 0.53121121 2.1172617330 19.62 0.00016216 3.57703437 0.70011505 2.4129534730 19.62 0.00014742 3.7943321 0.89860124 2.7150223

27.2849777 19.62 0.00013514 3.81692386 1.07577709 2.7474494727.2525505 19.62 0.00013514 3.81463804 1.07513284 2.7441597527.2558402 19.62 0.00013514 3.81486999 1.07519822 2.7444934927.2555065 19.62 0.00013514 3.81484646 1.07519159 2.74445964

caudales COTAS que salen Ks viscosidA= 150 m 0.31 0.0003 0.00000114B= 90 m 0.31 0.0003 0.00000114C= 70 m 120 0.0003 0.00000114U1 120 0.0003 0.00000114U2 75 0.0003D= 12 m 330 0.0003 0.00000114E= 0 m 255 0.0003 0.00000114

Asumiendos cotas para los nudosU1= 120U2= 75

Altura Dh 2g Ks/3.7D VELOC Q =caudal suma(hm)30 19.62 0.00054054 2.19798965 0.03871814 0.9110747530 19.62 0.00040541 2.64068764 0.08269577 1.3150334130 19.62 0.00032432 3.04099827 0.14879985 1.7439541730 19.62 0.00027027 3.41029765 0.24029298 2.1932457430 19.62 0.00027027 3.41029765 0.24029298 2.19324574

27.8067543 19.62 0.00027027 3.28220912 0.23126774 2.0315860327.968414 19.62 0.00027027 3.29181885 0.23194485 2.0434997

Asumiendos cotas para los nudosU1= 120U2= 75Altura Dh 2g Ks/3.7D VELOC Q =caudal suma(hm)

50 19.62 0.00054054 2.84576209 0.05012881 1.5272140150 19.62 0.00040541 2.60625002 0.08161733 1.2809579550 19.62 0.00040541 2.60625002 0.08161733 1.2809579550 19.62 0.00040541 2.60625002 0.08161733 1.28095795

Tener cuidado con los caudales que salen

Km3.72.52.24.5

4.25

Km3.72.52.24.5

4.25

Problema de diseo de Tubera en sLa tubera de descarga de la Planta de Tratamiento de aguas residuales del Municipio de San Migueltiene una longitud de L=150mts, y por ella debe pasar un caudal mximo de 120 lts/seg. La altura mnima de operacin es 2.2 m y en la tubera se tienen prdidas menores por entrada Km1=0.5, por un codo, K=0.8por uniones Km3=10x0.8, por salida Kms=1.0Calcular el dametro de la tubera comercial de PVC requerida si la temperatura del agua es 14CDATOS DE I Longitud 150 Mts L

caudal 120 m3/seg QDifrencia de aZ2 2.2 mts Z2Viscosidad deViscosidad 0.00000117 m2/seg ver tablaRugosidad absKs= 0.00015Prdidas de CKm 9.4Gravedad g= 9.81Densidad 998.20 Kg/m3

ProcesoSuponer un dimetro inicia 0.15Suma de Prdida Menores 3.30

H Dametro Ks/d hf Vam m

m variable variable2.2 1.50E-01 1.00E-03 2.2000 -0.4155192.2 2.00E-01 7.50E-04 2.2000 -0.4798002.2 2.50E-01 6.00E-04 2.2000 -0.5364332.2 3.00E-01 5.00E-04 2.2000 -0.5876332.2 3.00E-01 5.00E-04 1.3730 -0.4642212.2 3.00E-01 5.00E-04 1.6899 -0.5150272.2 3.00E-01 5.00E-04 1.5687 -0.4962132.2 3.00E-01 5.00E-04 1.6151 -0.5034982.2 3.00E-01 5.00E-04 1.5974 -0.5007232.2 3.00E-01 5.00E-04 1.6042 -0.5017872.2 3.00E-01 5.00E-04 1.6016 -0.5013802.2 3.00E-01 5.00E-04 1.6026 -0.5015362.2 3.00E-01 5.00E-04 1.6022 -0.501476

DATOS DE I Longitud 45caudal 0.00049

Difrencia de aZ2 25Viscosidad deViscosidad 0.00000114Rugosidad absKs= 0.00015Prdidas de CKm 0Gravedad g= 9.81Densidad 0.00

ProcesoSuponer un dimetro inicia 0.01Suma de Prdida Menores 0.00

H Dametro Ks/dm

m25 1.27E-02 1.18E-0225 2.52E-02 5.95E-0325 3.77E-02 3.98E-0325 5.02E-02 2.99E-0325 6.27E-02 2.39E-0325 7.52E-02 1.99E-0325 8.77E-02 1.71E-0325 1.00E-01 1.50E-0325 1.13E-01 1.33E-0325 1.25E-01 1.20E-0325 1.38E-01 1.09E-0325 1.50E-01 9.99E-0425 1.63E-01 9.22E-04

La tubera de descarga de la Planta de Tratamiento de aguas residuales del Municipio de San Migueltiene una longitud de L=150mts, y por ella debe pasar un caudal mximo de 120 lts/seg. La altura mnima de operacin es 2.2 m y en la tubera se tienen prdidas menores por entrada Km1=0.5, por un codo, K=0.8

0.00049Calcular el dametro de la tubera comercial de PVC requerida si la temperatura del agua es 14C

H= Suma hf- suma (Km)V2/2GVb-1 Vb-2 Velocidad Area Caudal Q>= Qd suma

m/seg Hmvariable variable 3.14 D2/4 variable

0.000270 0.000094 1.429 0.0177 0.0252 no 0.34330.000203 0.000061 1.717 0.0314 0.0539 no 0.49580.000162 0.000044 1.977 0.0491 0.0971 no 0.6577

0.000135 0.000033 2.217 0.0707 0.1567 si 0.82700.000135 0.000042 1.741 0.0707 0.1231 si 0.51010.000135 0.000038 1.937 0.0707 0.1369 si 0.63130.000135 0.000039 1.865 0.0707 0.1318 no 0.58490.000135 0.000039 1.893 0.0707 0.1338 no 0.60260.000135 0.000039 1.882 0.0707 0.1330 no 0.59580.000135 0.000039 1.886 0.0707 0.1333 no 0.59840.000135 0.000039 1.885 0.0707 0.1332 no 0.59740.000135 0.000039 1.885 0.0707 0.1333 no 0.5978

0.000135 0.000039 1.885 0.0707 0.1332 no 0.5977

Mts L 0.0254m3/seg Q 0.00049mts Z2m2/seg ver tabla

Kg/m3

H= Suma hf- suma (Km)V2/2Ghf Va Vb-1 Vb-2 Velocidad Area Caudalm m/segvariable variable variable variable 3.14 D2/4

25.0000 -0.744124 0.003192 0.000606 1.801 0.0001 0.000225.0000 -1.048198 0.001609 0.028507 1.595 0.0005 0.000825.0000 -1.282076 0.001075 0.000000 3.806 0.0011 0.0042

25.0000 -0.810318 0.000808 0.000144 2.448 0.0020 0.004825.0000 -0.905603 0.000647 0.000103 2.830 0.0031 0.008725.0000 -0.991774 0.000539 0.000079 3.183 0.0044 0.014125.0000 -1.071035 0.000462 0.000063 3.513 0.0060 0.021225.0000 -1.144821 0.000405 0.000051 3.825 0.0079 0.030225.0000 -1.214132 0.000360 0.000043 4.122 0.0100 0.041125.0000 -1.279694 0.000324 0.000037 4.406 0.0123 0.054225.0000 -1.342057 0.000294 0.000032 4.679 0.0149 0.069725.0000 -1.401648 0.000270 0.000028 4.942 0.0177 0.0876

25.0000 -1.458806 0.000249 0.000025 5.197 0.0208 0.1080

0.0381

1er AproOjo

2da aprox

Q>= QsumaHmvariable

nononosi 1er Aprosi Ojosinonononononono 2da aprox

Caudal 2.1 ltscota capt 2500 msnmcota Rese 2450 msnm 50Longit. 380 msnm

Pendiente 0.13157895 m/mS(0.57) 0.31472863

2.839*HF 0.90135133Q/2.8639*hF 6.67241488

D= 2.01829538

Usando Monograma Hazen - Williams

se Tiene = 0 1 1/2" 25002450

Q= 2.1Hf 0.13157895hf(0.21) 0.65317439Q(0.38) 1.23089612

0.873936241.33798303

TUBERIAS EN SERIE

Datos de IngresoH1= 2540H2= 2511.5Diferencia de cotas 28.5

Dimetro Longitud Km Material Ksm m

Tubera I 0.6 423 4.2 concreto 0.0003Tubera II 0.5 174 3.4 PVC 0.000015Tubera III 0.3 373 5.3 PVCTubera IV 0.25 121 7.5 PVCViscosidad 1.14E-006Prdida por friccion PRIMERA ITERACIONPRIMERA TUBERAL1/D1(5) 5439.8148L2/D2(5) 5568L3/D3(5) 153497.94L4/D4(5) 123904

288409.76hf1= 0.5375502 m para la frmula

Dametro Ks/d hf Va Vb-1m

m variable variable variable6.00E-01 5.00E-04 0.5376 -0.244621 0.000135

Velocidad V1-1 9.20E-01Cuadal en la Tuber 1 2.60E-01 m3/sCaudal que sale 0.06Caudal que Pasa 2.00E-01Dametro 5.00E-01Velocidad V2-1 1.02E+00Dametro

f Nmero de Denomin denominadato Ks/d Rreynoldsasumido DATO CALCULADO

0.001 0.000015 446,753 7.47781403 7.477814030.01788342 0.000015 446,753 8.67007418 8.67007418

0.01330315 0.000015 446,753 8.55211496 8.552114960.01367266 0.000015 446,753 8.56309691 8.563096910.01363761 0.000015 446,753 8.56206861 8.562068610.01364089 0.000010 446,753 8.58488083 8.584880830.01356849 0.000010 446,753 8.58269202 8.582692020.01357541 0.000010 446,753 8.5829018 8.58290180.01357475 0.000010 446,753 8.58288169 8.58288169

Hf2-1 2.50E-01 0.250000 mHm2-1 1.80E-01 0.180000 m

Cuadal en la Tuber 1 2.60E-01 m3/sCaudal que sale1 0.06Caudal que sale2 0.074Caudal que Pasa T3-1 1.26E-01Dametro 3.00E-01Velocidad V3-1 1.78E+00


0.001 0.000015 469,087 7.51922149 7.519221490.017687 0.000015 469,087 8.70428902 8.70428902

0.01319877 0.000015 469,087 8.58802164 8.588021640.01355857 0.000015 469,087 8.59876432 8.598764320.01352471 0.000015 469,087 8.59776615 8.597766150.01352785 0.000010 469,087 8.62154088 8.621540880.01345334 0.000010 469,087 8.61927478 8.619274780.01346042 0.000010 469,087 8.61949052 8.619490520.01345974 0.000010 469,087 8.61946998 8.61946998

Hf3-1= 2.71E+00 2.700000 mHm3-1 8.58E-01 0.858000 m

Cuadal en la Tuber 1 2.60E-01 m3/sCaudal que sale1 0.06Caudal que sale2 0.074caudal que sale 3 0.06Caudal que Pasa T4 6.60E-02Dametro 2.50E-01Velocidad V4-1 1.34E+00


0.001 0.000015 294,855 7.12348302 7.123483020.01970676 0.000015 294,855 8.375036 8.3750360.01425695 0.000015 294,855 8.24258918 8.242589180.01471881 0.000015 294,855 8.25568743 8.255687430.01467214 0.000015 294,855 8.25438325 8.254383250.01467678 0.000010 294,855 8.27039127 8.270391270.01462002 0.000010 294,855 8.26877045 8.268770450.01462575 0.000010 294,855 8.26893442 8.268934420.01462517 0.000010 294,855 8.26891783 8.26891783

Hf4-1= 6.52E-01 0.652000 mHm4-1= 6.91E-01 0.690000 m

Perdida Total H1= 6.0600 M enor que H=28.5

SEGUNDA ITERACIONDatos de IngresoH1= 2540H2= 2511.5Diferencia de cotas 28.5


Tubera I 0.6 423 4.2 concreto 0.0003Tubera II 0.5 174 3.4 PVC 0.000015Tubera III 0.3 373 5.3 PVCTubera IV 0.25 121 7.5 PVCViscosidad 1.14E-006Prdida por friccionPRIMERA TUBERAL1/D1(5) 5439.8148L2/D2(5) 5568L3/D3(5) 153497.94L4/D4(5) 123904

288409.76hf2= 0.4232505 m

0.5375502 0.4232505 0.96080073 para la frmula



Velocidad V1-2 1.24E+00Cuadal en la Tuber 1 3.50E-01 m3/sCaudal que sale-1 0.06Caudal que Pasa T2 2.90E-01Dametro 5.00E-01Velocidad V2-2 1.48E+00


0.001 0.000015 446,753 7.47781403 7.477814030.01788342 0.000015 446,753 8.67007418 8.670074180.01330315 0.000015 446,753 8.55211496 8.552114960.01367266 0.000015 446,753 8.56309691 8.563096910.01363761 0.000015 446,753 8.56206861 8.562068610.01364089 0.000010 446,753 8.58488083 8.584880830.01356849 0.000010 446,753 8.58269202 8.582692020.01357541 0.000010 446,753 8.5829018 8.58290180.01357475 0.000010 446,753 8.58288169 8.58288169

Hf2-2= 5.25E-01 mHm2-2 3.78E-01 m

Cuadal en la Tuber 1 3.50E-01 m3/sCaudal que sale1 0.06Caudal que sale2 0.074Caudal que Pasa T3 2.16E-01Dametro 3.00E-01Velocidad v3-2 3.05E+00Dametro


0.001 0.000015 803,909 7.97279653 7.972796530.01573181 0.000015 803,909 9.07381973 9.073819730.01214562 0.000015 803,909 8.97629703 8.976297030.01241097 0.000015 803,909 8.98450647 8.98450647

0.0123883 0.000015 803,909 8.9838124 8.98381240.01239021 0.000010 803,909 9.02109224 9.021092240.01228802 0.000010 803,909 9.01780972 9.017809720.01229696 0.000010 803,909 9.01809825 9.018098250.01229618 0.000010 803,909 9.01807289 9.01807289

Hf3-2= 7.27E+00 m

Hm3-2 2.52E+00 m

Cuadal en la Tuber 1 3.50E-01 m3/sCaudal que sale1 0.06Caudal que sale2 0.074caudal que sale 3 0.06Caudal que Pasa T4 1.56E-01Dametro 2.50E-01Velocidad v4-2 3.18E+00Dametrohf2


0.001 0.000015 696,641 7.85296637 7.852966370.01621558 0.000015 696,641 8.97727458 8.977274580.01240826 0.000015 696,641 8.87474611 8.874746110.01269662 0.000015 696,641 8.88361027 8.88361027

0.0126713 0.000015 696,641 8.88284033 8.882840330.01267349 0.000010 696,641 8.91596502 8.91596502

0.0125795 0.000010 696,641 8.91298242 8.912982420.01258792 0.000010 696,641 8.91325056 8.913250560.01258716 0.000010 696,641 8.91322645 8.91322645

Hf2= 3.13E+00 mHm2 3.86E+00 m

Perdida Total H= 18.4377 todava es menor a 28.5

TERCERA ITERACIONDatos de IngresoH1= 2540H2= 2511.5Diferencia de cotas 28.5


Tubera I 0.6 423 4.2 concreto 0.0003Tubera II 0.5 174 3.4 PVC 0.000015Tubera III 0.3 373 5.3 PVCTubera IV 0.25 121 7.5 PVCViscosidad 1.14E-006Prdida por friccionPRIMERA TUBERA

L1/D1(5) 5439.8148L2/D2(5) 5568L3/D3(5) 153497.94L4/D4(5) 123904

288409.76hf= 0.1897893 mnuevo hf 0.5375502 0.4232505 0.18978934 1.1505901 prar la formula



Cuadal en la Tuber 1 3.84E-01 m3/sCaudal que sale 0.06Caudal que Pasa T2-3 3.24E-01Dametro 5.00E-01Velocidad v2-3 1.65E+00Dametro


0.001 0.000015 446,753 7.47781403 7.477814030.01788342 0.000015 446,753 8.67007418 8.670074180.01330315 0.000015 446,753 8.55211496 8.552114960.01367266 0.000015 446,753 8.56309691 8.563096910.01363761 0.000015 446,753 8.56206861 8.562068610.01364089 0.000010 446,753 8.58488083 8.584880830.01356849 0.000010 446,753 8.58269202 8.582692020.01357541 0.000010 446,753 8.5829018 8.58290180.01357475 0.000010 446,753 8.58288169 8.58288169

Hf2--3= 6.54E-01 mHm2-3 4.71E-01 m

Cuadal en la Tuber 1 3.84E-01 m3/sCaudal que sale1 0.06Caudal que sale2 0.074Caudal que Pasa 3-3 2.50E-01Dametro 3.00E-01Velocidad v4-3 3.53E+00

Dametrof Nmero de Denomin denomina

dato Ks/d Rreynoldsasumido DATO CALCULADO

0.001 0.000015 929,307 8.09339437 8.093394370.01526647 0.000015 929,307 9.17002338 9.170023380.01189212 0.000015 929,307 9.07759175 9.077591750.01213553 0.000015 929,307 9.08515243 9.085152430.01211534 0.000015 929,307 9.08453151 9.084531510.01211699 0.000010 929,307 9.12649165 9.126491650.01200583 0.000010 929,307 9.12288391 9.122883910.01201533 0.000010 929,307 9.12319351 9.123193510.01201451 0.000010 929,307 9.12316694 9.12316694

Hf3-3= 9.49E+00 mHm3-3= 3.37E+00 m

Cuadal en la Tuber 1 3.84E-01 m3/sCaudal que sale1 0.06Caudal que sale2 0.074caudal que sale 3 0.06Caudal que Pasa T4-3 1.90E-01Dametro 2.50E-01Velocidad v4-3 3.86E+00Dametro


0.001 0.000015 847,119 8.01643911 8.016439110.01556098 0.000015 847,119 9.10875183 9.108751830.01205264 0.000015 847,119 9.01306498 9.013064980.01230991 0.000015 847,119 9.02103845 9.021038450.01228816 0.000015 847,119 9.02037123 9.020371230.01228998 0.000010 847,119 9.05928449 9.059284490.01218463 0.000010 847,119 9.05588698 9.055886980.01219377 0.000010 847,119 9.05618309 9.056183090.01219297 0.000010 847,119 9.05615727 9.05615727

Hf2= 4.49E+00 mHm2 5.70E+00 m

Perdida Total H= 24.7643

CUARTA ITERACIONDatos de IngresoH1= 2540H2= 2511.5Diferencia de cotas 28.5



288409.76 0.425 0.538hf= 0.0704597 m

0.5375502 0.4232505 0.18978934 0.0704597 1.2210497



Cuadal en la Tuber 1 3.95E-01 m3/sCaudal que sale 0.06Caudal que Pasa 3.35E-01Dametro 5.00E-01Velocidad v2 1.71E+00Dametrohf2


0.001 0.000015 446,753 7.47781403 7.477814030.01788342 0.000015 446,753 8.67007418 8.670074180.01330315 0.000015 446,753 8.55211496 8.552114960.01367266 0.000015 446,753 8.56309691 8.56309691

0.01363761 0.000015 446,753 8.56206861 8.562068610.01364089 0.000010 446,753 8.58488083 8.584880830.01356849 0.000010 446,753 8.58269202 8.582692020.01357541 0.000010 446,753 8.5829018 8.58290180.01357475 0.000010 446,753 8.58288169 8.58288169

Hf2= 7.03E-01 mHm2 5.06E-01 m

Cuadal en la Tuber 1 3.95E-01 m3/sCaudal que sale1 0.06Caudal que sale1 0.074Caudal que Pasa 2.61E-01Dametro 3.00E-01Velocidad v2 3.70E+00Dametrohf2


0.001 0.000015 973,201 8.13163138 8.131631380.01512323 0.000015 973,201 9.20030538 9.200305380.01181396 0.000015 973,201 9.10950013 9.109500130.01205066 0.000015 973,201 9.11685731 9.116857310.01203122 0.000015 973,201 9.11625889 9.11625889

0.0120328 0.000010 973,201 9.15981543 9.159815430.01191864 0.000010 973,201 9.1560997 9.15609970.01192831 0.000010 973,201 9.15641607 9.156416070.01192749 0.000010 973,201 9.15638913 9.15638913

Hf2= 1.03E+01 mHm2 3.69E+00 m

Cuadal en la Tuber 1 3.95E-01 m3/sCaudal que sale1 0.06Caudal que sale2 0.074caudal que sale 3 0.06Caudal que Pasa 2.01E-01Dametro 2.50E-01Velocidad v2 4.10E+00Dametrohf2

f Nmero de Denomin denomina

dato Ks/d Rreynoldsasumido DATO CALCULADO

0.001 0.000015 899,792 8.06660638 8.066606380.01536803 0.000015 899,792 9.14874332 9.14874332

0.0119475 0.000015 899,792 9.05517587 9.055175870.01219569 0.000015 899,792 9.06287976 9.062879760.01217496 0.000015 899,792 9.06224287 9.062242870.01217667 0.000010 899,792 9.10311766 9.103117660.01206757 0.000010 899,792 9.09958417 9.099584170.01207694 0.000010 899,792 9.09988906 9.099889060.01207613 0.000010 899,792 9.09986275 9.09986275

Hf2= 5.02E+00 mHm2 6.44E+00 m


QUINTA ITERACIONDatos de IngresoH1= 2540H2= 2511.5Diferencia de cotas 28.5



288409.76 0.425 0.538hf= 0.0248991 m

0.5375502 0.4232505 0.18978934 0.0704597 0.0248991

Dametro Ks/d hf Va Vb-1

mm variable variable variable

6.00E-01 5.00E-04 1.2459 -0.372422 0.000135Cuadal en la Tuber 1 3.99E-01 m3/sCaudal que sale 0.06Caudal que Pasa 3.39E-01Dametro 5.00E-01Velocidad v2 1.73E+00Dametrohf2


0.001 0.000015 446,753 7.47781403 7.477814030.01788342 0.000015 446,753 8.67007418 8.670074180.01330315 0.000015 446,753 8.55211496 8.552114960.01367266 0.000015 446,753 8.56309691 8.563096910.01363761 0.000015 446,753 8.56206861 8.562068610.01364089 0.000010 446,753 8.58488083 8.584880830.01356849 0.000010 446,753 8.58269202 8.582692020.01357541 0.000010 446,753 8.5829018 8.58290180.01357475 0.000010 446,753 8.58288169 8.58288169

Hf2= 7.20E-01 mHm2 5.18E-01 m

Cuadal en la Tuber 1 3.99E-01 m3/sCaudal que sale1 0.06Caudal que sale1 0.074Caudal que Pasa 2.65E-01Dametro 3.00E-01Velocidad v2 3.76E+00Dametrohf2


0.001 0.000015 988,410 8.14445971 8.144459710.01507563 0.000015 988,410 9.21043972 9.210439720.01178798 0.000015 988,410 9.12018148 9.120181480.01202245 0.000015 988,410 9.12747062 9.127470620.01200326 0.000015 988,410 9.12687968 9.126879680.01200481 0.000010 988,410 9.17098449 9.17098449

0.01188962 0.000010 988,410 9.16723202 9.167232020.01189936 0.000010 988,410 9.16755065 9.167550650.01189853 0.000010 988,410 9.16752359 9.16752359

Hf2= 1.06E+01 mHm2 3.81E+00 m

Cuadal en la Tuber 1 3.99E-01 m3/sCaudal que sale1 0.06Caudal que sale2 0.074caudal que sale 3 0.06Caudal que Pasa 2.05E-01Dametro 2.50E-01Velocidad v2 4.19E+00Dametrohf2


0.001 0.000015 918,042 8.08327624 8.083276240.01530471 0.000015 918,042 9.16199187 9.161991870.01191297 0.000015 918,042 9.06913089 9.069130890.01215818 0.000015 918,042 9.0767456 9.07674560.01213779 0.000015 918,042 9.07611867 9.076118670.01213947 0.000010 918,042 9.1176657 9.11766570.01202909 0.000010 918,042 9.11408613 9.114086130.01203854 0.000010 918,042 9.11439396 9.114393960.01203772 0.000010 918,042 9.11436748 9.11436748

Hf2= 5.20E+00 0.652000 mHm2 6.70E+00 0.690000 m


SEXTA ITERACIONDatos de IngresoH1= 2540H2= 2511.5Diferencia de cotas 28.5


Tubera I 0.6 423 4.2 concreto 0.0003

0.5 174 3.4 PVC 0.000015Tubera III 0.3 373 5.3 PVCTubera IV 0.25 121 7.5 PVCViscosidad 1.14E-006Prdida por friccionPRIMERA TUBERAL1/D1(5) 5439.8148L2/D2(5) 5568L3/D3(5) 153497.94L4/D4(5) 123904

288409.76 0.425 0.538hf= 0.0086513 m

0.5375502 0.4232505 0.18978934 0.0704597 0.0248991



Cuadal en la Tuber 1 4.01E-01 m3/sCaudal que sale 0.06Caudal que Pasa T2-6 3.41E-01Dametro 5.00E-01Velocidad v2 1.74E+00Dametro


0.001 0.000015 446,753 7.47781403 7.477814030.01788342 0.000015 446,753 8.67007418 8.670074180.01330315 0.000015 446,753 8.55211496 8.552114960.01367266 0.000015 446,753 8.56309691 8.563096910.01363761 0.000015 446,753 8.56206861 8.562068610.01364089 0.000010 446,753 8.58488083 8.584880830.01356849 0.000010 446,753 8.58269202 8.582692020.01357541 0.000010 446,753 8.5829018 8.58290180.01357475 0.000010 446,753 8.58288169 8.58288169

hf-6 7.26E-01 mHm6 5.22E-01 m

Cuadal en la Tuber 1 4.01E-01 m3/sCaudal que sale1 0.06Caudal que sale1 0.074Caudal que Pasa T3 2.67E-01Dametro 3.00E-01Velocidad v2 3.78E+00Dametrohf2


0.001 0.000015 993,658 8.14883907 8.148839070.01505943 0.000015 993,658 9.21389645 9.213896450.01177913 0.000015 993,658 9.12382511 9.123825110.01201285 0.000015 993,658 9.13109106 9.131091060.01199374 0.000015 993,658 9.13050266 9.130502660.01199529 0.000010 993,658 9.17479611 9.174796110.01187975 0.000010 993,658 9.17103104 9.17103104

0.0118895 0.000010 993,658 9.17135045 9.171350450.01188867 0.000010 993,658 9.17132335 9.17132335

Hf2= 1.07E+01 mHm2 3.85E+00 m

Cuadal en la Tuber 1 4.01E-01 m3/sCaudal que sale1 0.06Caudal que sale2 0.074caudal que sale 3 0.06Caudal que Pasa T4 2.07E-01Dametro 2.50E-01Velocidad v3 4.21E+00Dametrohf2


0.001 0.000015 924,340 8.08894911 8.088949110.01528325 0.000015 924,340 9.16649578 9.166495780.01190127 0.000015 924,340 9.07387547 9.073875470.01214547 0.000015 924,340 9.08145988 9.081459880.01212519 0.000015 924,340 9.08083632 9.080836320.01212686 0.000010 924,340 9.12261449 9.12261449

0.01201604 0.000010 924,340 9.11901915 9.119019150.01202552 0.000010 924,340 9.11932797 9.11932797

0.0120247 0.000010 924,340 9.11930144 9.11930144

Hf2= 5.27E+00 mHm2 6.79E+00 m

Perdida Total H= 28.3415 aproximadamente a 28.528.5

Error 0.55606667 %

Salidas en la Red

0.060.740.06

Vb-2 Velocidad Area Caudal Hmm/segvariable 3.14 D2/4

0.000039 0.920 0.2827 0.2600 0.1810

G(f)1/f

0.017883420.01330315

0.013672660.013637610.013640890.013568490.013575410.013574750.0135748

G(f)1/f

0.0176870.013198770.013558570.013524710.013527850.013453340.013460420.013459740.0134598

G(f)1/f

0.019706760.014256950.014718810.014672140.014676780.014620020.014625750.014625170.0146252

Salidas en la Red

0.060.740.06


0.000029 1.238 0.2827 0.3499 0.3279

G(f)1/f

0.017883420.013303150.013672660.013637610.013640890.013568490.013575410.013574750.0135748

G(f)1/f

0.015731810.012145620.01241097

0.01238830.012390210.012288020.012296960.012296180.0122962

G(f)1/f

0.016215580.012408260.01269662

0.01267130.01267349

0.01257950.012587920.012587160.0125872

Salidas en la Red

0.060.740.06

prar la formula


0.000027 1.357 0.2827 0.3836 0.3941

G(f)1/f

0.017883420.013303150.013672660.013637610.013640890.013568490.013575410.013574750.0135748

G(f)1/f

0.015266470.011892120.012135530.012115340.012116990.012005830.012015330.012014510.0120146

G(f)1/f

0.015560980.012052640.012309910.012288160.012289980.012184630.012193770.01219297

0.012193

Salidas en la Red

0.060.740.06

0.189

0.113

para la formula


0.000026 1.398 0.2827 0.3954 0.4187

G(f)1/f

0.017883420.013303150.013672660.01363761

0.013640890.013568490.013575410.013574750.0135748

G(f)1/f

0.015123230.011813960.012050660.01203122

0.01203280.011918640.011928310.011927490.0119276

G(f)

1/f

0.015368030.0119475

0.012195690.012174960.012176670.012067570.012076940.012076130.0120762

Salidas en la Red

0.060.740.06

0.189

0.113

1.2459489 para la frmula

Vb-2 Velocidad Area Caudal Hm

m/segvariable 3.14 D2/4

0.000026 1.413 0.2827 0.3995 0.4273

G(f)1/f

0.017883420.013303150.013672660.013637610.013640890.013568490.013575410.013574750.0135748

G(f)1/f

0.015075630.011787980.012022450.012003260.012004810.01188962

0.011899360.011898530.0118986

G(f)1/f

0.015304710.011912970.012158180.012137790.012139470.012029090.012038540.012037720.0120378

Salidas en la Red

0.06

0.740.06

0.189

0.113

0.0086513 1.2546 para la frmula


0.000026 1.418 0.2827 0.4009 0.4304

G(f)1/f

0.017883420.013303150.013672660.013637610.013640890.013568490.013575410.013574750.0135748

G(f)1/f

0.015059430.011779130.012012850.011993740.011995290.01187975

0.01188950.011888670.0118887

G(f)1/f

0.015283250.011901270.012145470.012125190.012126860.01201604

0.012025520.0120247

0.0120248

METODO DE LA TUBERIA EQUIVALENTEDiferencia de cotas 28.5

Dimetro Longitud Km Materialm m

Tubera I 0.6 423 4.2 concretoTubera II 0.5 174 3.4 PVCTubera III 0.3 373 5.3 PVCTubera IV 0.25 121 7.5 PVCViscosidad 1.14E-006Asumir

Dametro equivale 0.3375fe equival 0.014f(fi/fe) 1.0714286 1.0714286 0.92857143 0.92857143(de/d1)(5) 0.0563135 0.140126 1.80203247 4.48403344(fi/fe)*(de/di)(5)*Li 25.522089 26.123498 624.146818 503.813186Desnivel 28.5 fe*(Le/de)*Ve(2)/2*9.81

V(2) 11.427541Ve 3.3804646Qe 0.302423Ht 1890.3061Qe 0.302423Tubera 4Q1= 0.1659386Diametro 4 0.25Velocidad 4 3.3804646hf4 5.97587 5.97586998Hm4 4.368326 4.36832601Ht4 10.344196Tubera 3Q1= 0.1659386Q salida 0.06Q en latuberia 3 0.2259386Diametro 3 0.3Velocidad 3 3.1963692hf3 8.4167768 8.41677678Hm3 3.9054955 3.90549552Ht3 12.322272

Tubera 2Q2= 0.2259386

Q salida 0.134Q en latuberia 2 0.3599386Diametro 2 0.5Velocidad 1.8331477hf2 0.7748516 0.77485158Hm2 1.2845683 1.28456826Ht2 2.0594198

Tubera 1Q3= 0.3599386Q salida 0.194Q en latuberia 1 0.5539386Diametro 1 0.6Velocidad 1.9591523hf1 1.7929569 1.79295694Hm1 1.4672315 1.46723154Ht1 3.2601885

27.9860766

Ks Salidas en la red fi

0.0003 0.06 0.0150.000015 0.74 0.013

0.06 0.0130.013

0.3375

0.92857143

1179.60559

TUBERIAS EN PARALELO

Longitud de la tuberas= 627 mKs1 Rugosida Ks1= 0.0015 mm PVC Dametro !=Ks2 Rugosidad Ks2= 0.03 mm Asb-cem Dametro 2=Km Prdida menores= 10.6HT Diferencia de nivel= 26.4T Temperatura y otros= 20 densidad 998.2 viscosidad

Tubera IDametro Ks/d hf Va

HT mm variable variable

1 26.4 2.00E-01 7.50E-06 26.4000 -0.8129482 26.4 2.00E-01 7.50E-06 19.2340 -0.6938983 26.4 2.00E-01 7.50E-06 21.3292 -0.7307154 26.4 2.00E-01 7.50E-06 20.7226 -0.7202505 26.4 2.00E-01 7.50E-06 20.8988 -0.7233056 26.4 2.00E-01 7.50E-06 20.8477 -0.7224207 26.4 2.00E-01 7.50E-06 20.8625 -0.7226778 26.4 2.00E-01 7.50E-06 20.8582 -0.7226029 26.4 2.00E-01 7.50E-06 20.8595 -0.722624

10 26.4 2.00E-01 7.50E-06 20.8591 -0.722618Datos de QI= 0.1006salida Velocid I 3.202

hf1= 20.8591hm1= 5.5408HT= 26.3999

Tubera IIDametro Ks/d hf Va

HT mm variable variable

1 26.4 3.00E-01 1.00E-04 26.4000 -0.9956542 26.4 3.00E-01 1.00E-04 16.2327 -0.7807323 26.4 3.00E-01 1.00E-04 20.2733 -0.8725074 26.4 3.00E-01 1.00E-04 18.6744 -0.8373945 26.4 3.00E-01 1.00E-04 19.3084 -0.8514906 26.4 3.00E-01 1.00E-04 19.0572 -0.8459337 26.4 3.00E-01 1.00E-04 19.1568 -0.848140

8 26.4 3.00E-01 1.00E-04 19.1173 -0.8472669 26.4 3.00E-01 1.00E-04 19.1329 -0.847612

10 26.4 3.00E-01 1.00E-04 19.1267 -0.847475Datos de salida QII= 0.2593

Velocidad= 3.668hf2= 19.1267hm2= 7.2708HT= 26.3975

CONCLUSIONES Caudal total QT= 0.3599

0.2 m Ks1 0.00000750.3 m Ks2 0.0001

(la prdiad que se debe buscar)1.007*10(-6) 1.01E-006

Vb-1 Vb-2 Velocidad Area Caudal Hmm/seg

variable variable 3.14 D2/40.000002 0.000031 3.642 0.0314 0.1144 7.16600.000002 0.000036 3.064 0.0314 0.0962 5.07080.000002 0.000035 3.242 0.0314 0.1018 5.67740.000002 0.000035 3.191 0.0314 0.1002 5.50120.000002 0.000035 3.206 0.0314 0.1007 5.55230.000002 0.000035 3.201 0.0314 0.1006 5.53750.000002 0.000035 3.203 0.0314 0.1006 5.54180.000002 0.000035 3.202 0.0314 0.1006 5.54050.000002 0.000035 3.202 0.0314 0.1006 5.54090.000002 0.000035 3.202 0.0314 0.1006 5.5408

lts


variable variable 3.14 D2/40.000027 0.000017 4.338 0.0707 0.3066 10.16730.000027 0.000022 3.368 0.0707 0.2380 6.12670.000027 0.000019 3.781 0.0707 0.2673 7.72560.000027 0.000020 3.623 0.0707 0.2561 7.09160.000027 0.000020 3.687 0.0707 0.2606 7.34280.000027 0.000020 3.662 0.0707 0.2588 7.24320.000027 0.000020 3.671 0.0707 0.2595 7.2827

0.000027 0.000020 3.668 0.0707 0.2592 7.26710.000027 0.000020 3.669 0.0707 0.2594 7.27330.000027 0.000020 3.668 0.0707 0.2593 7.2708

lts

m3/seg

CALCULO DE POTENCIA PARA BOMBAS EN SERIEProblema- Ver grficoComo parte de un sistema de riego de una finca se utilizan dos tuberasen serie para conectar la bocatoma con el tanque de almacenamientoLos datos de muestran en la figura:

Tubera I Tubera IILongiud 184 mts Tubera II. 393Dimetro 0.2 mts 0.15Km 7.1 mts 11.2Rugosidades 0.000046 Acero 0.0000015Cuadal sale entre T-1 y T-2) 0.094 m3/segCuadal que llega la dpsito final 0.087 m3/segDatos ComplementariosT=Viscosida cinem 1.140E-006

SOLUCIONPARA LA PRIMERA TUBERAI) Hallas el caudal Q1= 0.094 0.087 0.1812.- Calculamos veloci V1= 5.76139553.- Hallamos las prdidas para ello se necesita el coeficiente de friccin4.- Se calcula Reynolds 1010771.13

f Nmero de Denomindato Ks/d Rreynoldsasumido DATO CALCULADO

0.001 0.000230 1,010,771 7.703476610.016851 0.000230 1,010,771 8.17990609

0.0149453 0.000230 1,010,771 8.167356040.0149912 0.000230 1,010,771 8.16768432

0.01499 0.000230 1,010,771 8.16767573f= 0.01499Perdidas por friccin1 23.331745 mtsPrdidas menores1 12.011983 mtsHT1 35.344 mts

PARA LA SEGUNDA TUBERAI) Hallas el caudal Q1= 0.087 0.0872.- Calculamos veloci V1= 4.9233.- Hallamos las prdidas para ello se necesita el coeficiente de friccin4.- Se calcula Reynolds 647787.025

f Nmero de Denomindato Ks/d Rreynoldsasumido DATO CALCULADO

0.001 0.000010 647,787 7.80456637

0.0164173 0.000010 647,787 8.9644660.0124437 0.000010 647,787 8.85338422

0.012758 0.000010 647,787 8.863428050.0127291 0.000010 647,787 8.862515110.0127317 0.000010 647,787 8.862598050.0127315 0.000010 647,787 8.862590520.0127315 0.000010 647,787 8.8625912

f= 0.012731Perdidas por friccin2 41.207145 mtsPrdidas menores2 13.836005 mtsHT2 55.043 mts

total de perdidas HT 90.387 mtsDiferencia de altura 31.7 mts (Z2-Z1)Altura total Requerida 122.087 mts Para el clculo de la Potencia

Potencia RequeridaCaudal Q 0.181 m3/segAltura 122.087 mDensidad 999.1 Kg/m3Gravedad 9.81 m/seg2Eficiencia 0.75Potencia Requerida 288778.4

288.78 KW solucion final

CALCULO DE POTENCIA PARA BOMBAS EN SERIE

mmmPVC

m3/seg (el total)m/s

denomina G(f)1/f

7.70347661 0.016851038.17990609 0.014945268.16735604 0.014991228.16768432 0.014990028.16767573 0.01499

m3/seg (el total)m/s

denomina G(f)1/f

7.80456637 0.01641733

8.964466 0.012443758.85338422 0.012757968.86342805 0.012729078.86251511 0.012731698.86259805 0.012731458.86259052 0.01273147

8.8625912 0.0127315

Para el clculo de la Potencia

CALCULO DE POTENCIA PARA TUBERIAS EN PARALELO

Con el fin de disminuir la vulnerabilidad del cruce subacuatico de un oleoductoal atravesar un ro, se decide colocar dos tuberas en paraleo a la existentever grficoDatos

Tubera Diametro Longitud Prdidas mI 0.45 278 7.7II 0.3 312 9.5III 0.3 312 9.5

Caudal total a bombear 0.46 m3/segPresin al inicio 875 mtsKPa

Densidad 860 Kg/m3Viscosid dinamica 0.00719 m2/seg

Calcular que pasa por cada Tubera , la altura y La Potencia

I) Como se conoce las caractersticas de la Tubera ICaudal 0.46 m3/segVelocidad 2.892290474 m/sViscosidad cinemtica 8.36047E-006Reynolds 1 155676.8308Rugosidad relativa 0.0001022222Para Hallar Hf1, se requeire de f

f Nmero dedato Ks/d Rreynoldsasumido DATO CALCULADO

0.001 0.000102 155,6770.0233852534 0.000102 155,6770.0166411739 0.000102 155,6770.0171644559 0.000102 155,6770.0171151056 0.000102 155,6770.0171196802 0.000102 155,6770.0171192555 0.000102 155,6770.0171192949 0.000102 155,6770.0171192913 0.000102 155,6770.017119292

Perdidas por friccin1 4.509235141 mtsPrdidas menores1 3.28303518 mtsHT1 7.792 mtsDiferencia de altura 96Altura total para la bomba 103.792 mtsPotencia Requerida

Caudal Q 0.46 m3/segAltura 103.792 mDensidad 860 Kg/m3Gravedad 9.81 m/seg2Eficiencia 0.85Potencia Requerida 473883.26963

473.88 KW

Suposicim inicial para la tubera existenteCaudal ini D1(5/2)

I 0.46 0.1358411296II 0.0492950302III 0.0492950302

Q1= 0.273 m3/seg

I) Como se conoce las caractersticas de la Tubera ICaudal 0.273 m3/segVelocidad 1.7164022773 m/sViscosidad cinemtica 8.36047E-006Reynolds 1 92384.934813Rugosidad relativa 0.0001022222Para Hallar Hf1, se requeire de f

f Nmero dedato Ks/d Rreynoldsasumido DATO CALCULADO

0.001 0.000102 92,3850.0268360881 0.000102 92,3850.0181302266 0.000102 92,3850.0188747321 0.000102 92,3850.0187953542 0.000102 92,3850.0188036342 0.000102 92,3850.0188027685 0.000102 92,385

0.018802859 0.000102 92,3850.0188028495 0.000102 92,3850.018802851

Perdidas por friccin1 1.7441954005 mtsPrdidas menores1 1.1561918036 mtsHT1 2.900 mts

Dametro Ks/d hfm

m variable2.9000000 3.00E-01 1.53E-04 2.90002.9000000 3.00E-01 1.53E-04 1.62572.9000000 3.00E-01 1.53E-04 2.23112.9000000 3.00E-01 1.53E-04 1.94792.9000000 3.00E-01 1.53E-04 2.08152.9000000 3.00E-01 1.53E-04 2.01872.9000000 3.00E-01 1.53E-04 2.04832.9000000 3.00E-01 1.53E-04 2.03442.9000000 3.00E-01 1.53E-04 2.04092.9000000 3.00E-01 1.53E-04 2.03782.9000000 3.00E-01 1.53E-04 2.03932.9000000 3.00E-01 1.53E-04 2.03862.9000000 3.00E-01 1.53E-04 2.03892.9000000 3.00E-01 1.53E-04 2.03882.9000000 3.00E-01 1.53E-04 2.0389

Caudal 9.43E-02 0.094 m3/seg

Caudal Total 0.273 0.094Prdidas Hf1 1.7442

Hf1 1.1562HT 2.9004

Altura Total96 2.9 98.9

Caudal Q 0.460Altura 98.900Densidad 860Gravedad 9.81Eficiencia 0.85Potencia Requerida 451546.68282

451.55

CALCULO DE POTENCIA PARA TUBERIAS EN PARALELO

Con el fin de disminuir la vulnerabilidad del cruce subacuatico de un oleoducto

Ks Material0.046 mm Acero0.046 mm Acero0.046 mm Acero

opcional

Denomin denomina G(f)1/f

6.53926534 6.539265337 0.02338525347.75189748 7.751897481 0.01664117397.63281928 7.63281928 0.01716445597.64381572 7.643815722 0.01711510567.64279439 7.642794385 0.0171196802

7.6428892 7.642889195 0.01711925557.64288039 7.642880394 0.01711929497.64288121 7.642881211 0.01711929137.64288113 7.642881135 0.0171192916

Raiz(L1)16.673332 0.00814721

17.6635217 0.00279078217.6635217 0.002790782

Denomin denomina G(f)1/f

6.10436363 6.104363626 0.02683608817.42674281 7.426742805 0.0181302266

7.2787969 7.278796903 0.01887473217.29415089 7.294150888 0.01879535427.29254475 7.292544754 0.01880363427.29271263 7.292712628 0.01880276857.29269508 7.29269508 0.0188028597.29269691 7.292696914 0.01880284957.29269672 7.292696722 0.0188028505

Va Vb-1 Vb-2 Velocidad Area Caudal Hmm/seg

variable variable variable 3.14 D2/4-0.467802 0.000041 0.000299 1.622 0.071 0.115 1.2743-0.350252 0.000041 0.000399 1.175 0.071 0.083 0.6689-0.410321 0.000041 0.000341 1.402 0.071 0.099 0.9521-0.383394 0.000041 0.000365 1.300 0.071 0.092 0.8185-0.396328 0.000041 0.000353 1.349 0.071 0.095 0.8813-0.390301 0.000041 0.000358 1.326 0.071 0.094 0.8517-0.393151 0.000041 0.000356 1.337 0.071 0.095 0.8656-0.391812 0.000041 0.000357 1.332 0.071 0.094 0.8591-0.392443 0.000041 0.000356 1.334 0.071 0.094 0.8622-0.392146 0.000041 0.000357 1.333 0.071 0.094 0.8607-0.392286 0.000041 0.000357 1.334 0.071 0.094 0.8614-0.392220 0.000041 0.000357 1.334 0.071 0.094 0.8611-0.392251 0.000041 0.000357 1.334 0.071 0.094 0.8612-0.392237 0.000041 0.000357 1.334 0.071 0.094 0.8611-0.392243 0.000041 0.000357 1.334 0.071 0.094 0.8612

por cada TuberaReal

0.094 0.461 0.460hf2 2.039 hf3 2.039hf2 0.861 hm3 0.861

2.900 2.900

TUBERIAS EQUIVALENTES , PERDIDAS MENORES.

Problema N1Para una prdida de carga de 5m/1000m y utilizando un C1=100 para todaslas tuberas Cuntas tuberas de 20 cm son equivalentes a una de 40 cm,Y a una de 60 cm.Para la tubera de 20 cmhf 5 5C= 100 5035.0060879D= 0.2 0.0003944719L= 1000 1000Cte 10.672

Multiplicando y dividiendo 0.0009305512Q20= m3/seg 0.023034

Para la tubera de 40 cmhf 5 5C= 100 5035.0060879D= 0.4 0.0115353867L= 1000 1000cte 10.672

Multiplicando y dividiendo 0.0272117421Q40= m3/seg 0.1427

Para la tubera de 60 cmhf 5 5C= 100 5035.0060879D= 0.6 0.0830991515L= 1000 1000cte 10.672

Multiplicando y dividiendo 0.1960292043Q40= m3/seg 0.41464Equivalencias(De 40 por 20) 142/23 4.77563093 6 Tuberas 20 cm equivalen a una de 40 cm(De 60 por 20) 414/23 18.0017353 18 Tuberas 20 cm equivalen a una de 60 cm(De 60 por 40) 414/142 2.90602392 2.90 Tuberas 40 cm equivalen a una de 60 cm

Qu producen la misma perdida: hf 5mts

Problema N2

Un sistema de tuberas en serie est constituido por un tramo de 1800mts de tubera de 50 cm de dimetro, otro de 1200 m de dametro de 40 cm, y 600 m de dimetro de 30 cmTodas las tuberas son nuevas de fierro fundido C=130, Hallar a partir del sistemaa) La longitud equivalente de una tubera de 40 cmb) El dimetro equivalente a la longitud si la lomgitu de tubera fuera de 3600 m.Solucin1.- Como la magnitud hidrulica comn para un sistema en serie es el caudal se tieneo se asume un caudal Q= 100 lts/seg

solucin hallamos los hfihallamos hf1Longitud 1 1800 1800D1 0.5 0.03419668C1 130 8182.93582constante 10.672 10.672Caudal supuesto 0.13 0.02290388Hf 1.572 mts o

hallamos hf2Longitud 2 1200 1200D2 0.4 0.01153539C2 130 8182.93582constante 10.672 10.672Caudal supuesto 0.13 0.02290388Hf 3.107 mts o

hallamos h3Longitud 3 600 600D3 0.3 0.00284171C3 130 8182.93582constante 10.672 10.672Caudal supuesto 0.13 0.02290388Hf 6.307 mts o

Suma total de prdidas hf1+hf2+hf3) Htt 10.987 mts

Para una tubera equivalente de 40 cm de dametro y con una prdida total de Hf= 10.987 mts se tiene:Proceso :hf 10.987 10.987C= 130 8182.9358232D= 0.4 0.0115353867Q= 0.13 0.0229038845

L= por determinarCte 10.987Despejar L de la ecuacion dada

Longitud equivalente 4121.28

Otros Mtodos de tubera equivalente y de los porcentajesPara el problema anterior hallar Q=? SiLongitud equivalente Le= 4121.28Perdidas de carga hf= 21Datos: De la frmula de Hf despejar Q=?

Longitud equivale 4121.28 mts 4121.28Prdidas 21 mts 21C= 130 8182.9358232Dimetro 0.4 0.0115353867constante 10.672 10.672

multiplic y divid 0.0450694879Q40= m3/seg 0.20952

mediante porcentajeshallamos hf1Longitud 1 1800 1800D1 0.5 0.03419668C1 130 8182.93582constante 10.672 10.672Caudal supuesto 0.13 0.02290388Hf 1.572 mts o

hallamos hf2Longitud 2 1200 1200D2 0.4 0.01153539C2 130 8182.93582constante 10.672 10.672Caudal supuesto 0.13 0.02290388Hf 3.107 mts o

hallamos h3Longitud 3 600 600D3 0.3 0.00284171C3 130 8182.93582constante 10.672 10.672

Caudal supuesto 0.13 0.02290388Hf 6.307 mts o

Suma total de prdidas hf1+hf2+hf3) Htt 10.987 mts

Problema N3Determinar , usando la Ecuacin Darcy -Wiesbach, gasto de una tubera de PVC de 4 " de dametro, y250 mts de largo, si el sistema incluye una coladera con vlvula de pie, un orifio de medida de bordescuadrados, que reduce el dametro a 2", y confusor de 2" de dametro a la slida, La prdida totalde carga en el sistema es de 8.00 metros, se puede tomar la carga medida en el orificio de 0.05 mts

solucin Htt= Prdida por fricin +perdida carga menoresHf= no se conoceHm Hallamos la suma de los coeficientes de prdidas menores

K1= 10 Para la coladera con vlvula de pieK2= 2.06 Para valvula compuerta media cerradaK3= 1 Para vvula globo totalmente abiertaK4= 5.5 confusor d/D= 0.5 es decir (2"/4")ho= 0.05 para la prdida en el orificio con borde cuadrados

suma 18.61Rugosidad absoluta Ks= 0.0000015PVCDamtero D= 0.1Longitud L= 250Viscosidad 1.140E-006 m2/segSolucinDebemos hallar Velocidad y hf

Ht= 7.95

Dametro Ks/d hf VaHT m

m variable variable

7.95 1.00E-01 1.50E-05 7.9500 -0.3154497.95 1.00E-01 1.50E-05 7.1214 -0.2985587.95 1.00E-01 1.50E-05 6.5498 -0.2863267.95 1.00E-01 1.50E-05 6.6622 -0.2887727.95 1.00E-01 1.50E-05 6.6401 -0.2882937.95 1.00E-01 1.50E-05 6.6445 -0.2883877.95 1.00E-01 1.50E-05 6.6436 -0.2883687.95 1.00E-01 1.50E-05 6.6438 -0.2883727.95 1.00E-01 1.50E-05 6.6437 -0.288371

7.95 1.00E-01 1.50E-05 6.6437 -0.288371

TUBERIAS EQUIVALENTES , PERDIDAS MENORES.

UsandoHazen-WilMono C=100 C=130

1.3*Q10023.03 18 23.4

142.68 110 143

414.64 305 396.5

6 Tuberas 20 cm equivalen a una de 40 cm18 Tuberas 20 cm equivalen a una de 60 cm2.90 Tuberas 40 cm equivalen a una de 60 cm

Un sistema de tuberas en serie est constituido por un tramo de 1800mts de tubera de 50 cm de dimetro, otro de 1200 m de dametro de 40 cm, y 600 m de dimetro de 30 cmTodas las tuberas son nuevas de fierro fundido C=130, Hallar a partir del sistema

b) El dimetro equivalente a la longitud si la lomgitu de tubera fuera de 3600 m.

1.- Como la magnitud hidrulica comn para un sistema en serie es el caudal se tiene

140

tamben con elmonogra S= Hf/L

S hf0.84m/1000m 0.93 1.674

1.67m/1000m 2.62 3.144

3.383m/1000 m 10.06 6.036

10.854

usando monogramamts Le= 4260

Otros Mtodos de tubera equivalente y de los porcentajes

206 lts/seg

Hallamos hi Ht Ordenamos los datos y calculamos el cuadal paraen % 21 cada tubera

Longitud eq 1800.00 mts 1800.00hallamos Prdidas 3.0053206 mts 3.00532064

los nuevos Damet 0.5 0.03419668hi para 21 C 130 8182.93582

0.14733*21 constante 10.672 10.67214.311 3.00532064 multiplic y divid 0.04377897

Q40= m3/seg 0.20647

Longitud eq 1200.00 mts 1200.00Prdidas 5.9395196 mts 5.93951959Damet 0.4 0.01153539C 130 8182.93582constante 10.672 10.672

28.283 5.93951959 multiplic y divid 0.04377897Q40= m3/seg 0.20647

Longitud eq 600.00 mts 600.00Prdidas 12.05516 mts 12.0551598Damet 0.3 0.00284171C 130 8182.93582

constante 10.672 10.67257.406 12.0551598 multiplic y divid 0.04377897

Q40= m3/seg 0.20647100.0

Determinar , usando la Ecuacin Darcy -Wiesbach, gasto de una tubera de PVC de 4 " de dametro, y250 mts de largo, si el sistema incluye una coladera con vlvula de pie, un orifio de medida de bordescuadrados, que reduce el dametro a 2", y confusor de 2" de dametro a la slida, La prdida totalde carga en el sistema es de 8.00 metros, se puede tomar la carga medida en el orificio de 0.05 mts

Prdida por fricin +perdida carga menores 8.00 mts

Hallamos la suma de los coeficientes de prdidas menoresPara la coladera con vlvula de pie 0.05Para valvula compuerta media cerradaPara vvula globo totalmente abiertaconfusor d/D= 0.5 es decir (2"/4")para la prdida en el orificio con borde cuadrados


variable variable 3.14 D2/4

0.000004 0.000115 1.238 0.0079 0.0097 0.82860.000004 0.000000 1.610 0.0079 0.0126 1.40020.000004 0.000000 1.544 0.0079 0.0121 1.28780.000004 0.000000 1.557 0.0079 0.0122 1.30990.000004 0.000000 1.555 0.0079 0.0122 1.30550.000004 0.000000 1.555 0.0079 0.0122 1.30640.000004 0.000000 1.555 0.0079 0.0122 1.30620.000004 0.000000 1.555 0.0079 0.0122 1.30630.000004 0.000000 1.555 0.0079 0.0122 1.3063

0.000004 0.000000 1.555 0.0079 0.0122 1.3063

METODO DE LA TEORA LINEAL

Elaboracin de Circuitossistema de Ecuaciones

PRIMERA ITERACION

1.1. Cculo de coeficientes de friccin DATOS DE IN GRESOTramo Longitud(1-2) 500(1-6) 300(2-3) 400(3-4) 200(4-5) 400(2-5) 200(5-6) 600

Tubera (1-2)Longitud= 500 Caudal 0.1 Longitud=Viscosidad= 1.1E-006 Dimetro 0.25 Viscosida=Ks 0.000100 Velocidad 2.03717851 Ks

f Nmero deDenomin denomina G(f) fdato Ks/d Rreynolds 1/f dato

asumido DATO CALCULADO asumido0.001 0.000400 446,750 7.0879478 7.087948 0.01990485 0.001

0.019905 0.000400 446,750 7.6598831 7.659883 0.01704338 0.01990490.017043 0.000400 446,750 7.6412177 7.641218 0.01712675 0.01704340.017127 0.000400 446,750 7.6418206 7.641821 0.01712404 0.01712670.017124 0.000400 446,750 7.6418011 7.641801 0.01712413 0.017124


f Nmero deDenomin denomina G(f) fdato Ks/d Rreynolds 1/f datoasumido DATO CALCULADO asumido

0.001 0.001000 1,116,874 6.933632 6.933632 0.02080072 0.0010.020801 0.001000 1,116,874 7.0877159 7.087716 0.01990616 0.0199220.019906 0.001000 1,116,874 7.0866644 7.086664 0.01991206 0.01835830.019912 0.001000 1,116,874 7.0866715 7.086672 0.01991202 0.01837930.019912 0.001000 1,116,874 7.0866715 7.086671 0.01991202 0.018379

Tramo Longitud Dimet Caudal Velocidad f(1-2) 500 0.25 0.1 2.03717851 0.0171241(1-6) 300 0.25 0.1 2.03717851 0.0171241(2-3) 400 0.15 0.1 5.65882919 0.0183791(3-4) 200 0.1 0.1 12.7323657 0.019912(4-5) 400 0.15 0.1 5.65882919 0.0183791(2-5) 200 0.1 0.1 12.7323657 0.019912(5-6) 600 0.2 0.1 3.18309142 0.017571ELABORACION DE LA MATRIZ

-1.00 -1.00 0.00 0.00 0.00 0.001.00 0.00 -1.00 0.00 0.00 -1.000.00 0.00 1.00 -1.00 0.00 0.000.00 0.00 0.00 1.00 1.00 0.000.00 0.00 0.00 0.00 -1.00 1.0072.44 -43.47 0.00 0.00 0.00 3290.52

0 0 816.24 3290.52 -799.919 -3290.52

-0.018435213 0.9508394 0.811871 0.251645 0.115 0.0004241-0.981564787 -0.950839 -0.811871 -0.251645 -0.115 -0.000424-0.007400264 -0.019734 0.8249057 0.1986 0.046 0.0001703-0.007400264 -0.019734 -0.175094 0.1986 0.046 0.00017030.007400264 0.019734 0.1750943 0.8014 -0.04634627 -0.00017-0.011034949 -0.029427 -0.013035 0.053046 0.06910952 0.0002539

0.018435213 0.0491606 0.188129 0.748355 0.88454421 -0.000424

SEGUNDO TRAMITE DATOS DE IN GRESOTramo Longitud(1-2) 500(1-6) 300(2-3) 400(3-4) 200(4-5) 400(2-5) 200(5-6) 600



0.001 0.000400 456,188 7.0991927 7.099193 0.01984185 0.0010.019842 0.000400 456,188 7.664369 7.664369 0.01702343 0.019970.017023 0.000400 456,188 7.646207 7.646207 0.0171044 0.01706410.017104 0.000400 456,188 7.6467848 7.646785 0.01710182 0.01714990.017102 0.000400 456,188 7.6467664 7.646766 0.0171019 0.0171471

CIRCUITO IITubera (3-4)

Longitud= 200 Caudal 0.0503203 Longitud=Viscosidad= 1.1E-006 Dimetro 0.1 Viscosida=Ks 0.000100 Velocidad 6.40696634 Ks


0.001 0.001000 562,015 6.7712603 6.77126 0.02181027 0.0010.02181 0.001000 562,015 7.0442786 7.044279 0.02015241 0.0208564

0.020152 0.001000 562,015 7.0407614 7.040761 0.02017255 0.01861190.020173 0.001000 562,015 7.0408066 7.040807 0.02017229 0.01865490.020172 0.001000 562,015 7.0408061 7.040806 0.02017229 0.018654

Tramo Longitud Dimet Caudal Velocidad f(1-2) 500 0.25 0.102113 2.08021682 0.0171019(1-6) 300 0.25 0.097887 1.9941402 0.0171472(2-3) 400 0.15 0.07032 3.97930643 0.0185929(3-4) 200 0.1 0.05032 6.40696634 0.0201723(4-5) 400 0.15 0.06468 3.66011297 0.018654(2-5) 200 0.1 0.051792 6.59438876 0.0201577

(5-6) 600 0.2 0.077887 2.47922578 0.017791ELABORACION DE LA MATRIZ

-1.00 -1.00 0.00 0.00 0.00 0.001.00 0.00 -1.00 0.00 0.00 -1.000.00 0.00 1.00 -1.00 0.00 0.000.00 0.00 0.00 1.00 1.00 0.000.00 0.00 0.00 0.00 -1.00 1.0073.88 -42.60 0.00 0.00 0.00 1725.27

0 0 577.12 1677.44 -525.125 -1725.266

-0.030525884 0.9165418 0.7581839 0.297905 0.154 0.0007165-0.969474116 -0.916542 -0.758184 -0.297905 -0.154 -0.000716-0.011690521 -0.031962 0.7792836 0.230655 0.059 0.0002744-0.011690521 -0.031962 -0.220716 0.230655 0.059 0.00027440.011690521 0.031962 0.2207164 0.769345 -0.05890625 -0.000274-0.018835363 -0.051496 -0.0211 0.06725 0.09490771 0.00044210.030525884 0.0834582 0.2418161 0.702095 0.84618603 -0.000716

TERCERA ITERACION DATOS DE IN GRESOTramo Longitud(1-2) 500(1-6) 300(2-3) 400(3-4) 200(4-5) 400(2-5) 200(5-6) 600



0.001 0.000400 462,585 7.1066333 7.106633 0.01980032 0.0010.0198 0.000400 462,585 7.667324 7.667324 0.01701032 0.0200155

0.01701 0.000400 462,585 7.6494913 7.649491 0.01708972 0.01707850.01709 0.000400 462,585 7.6500529 7.650053 0.01708721 0.0171662

0.017087 0.000400 462,585 7.6500352 7.650035 0.01708729 0.0171633


Longitud= 200 Caudal 0.0252994 Longitud=Viscosidad= 1.1E-006 Dimetro 0.1 Viscosida=

Ks 0.000100 Velocidad 3.22121718 Ksf Nmero deDenomin denomina G(f) f

dato Ks/d Rreynolds 1/f datoasumido DATO CALCULADO asumido

0.001 0.001000 282,563 6.5174215 6.517421 0.02354227 0.0010.023542 0.001000 282,563 6.9678171 6.967817 0.02059712 0.02173550.020597 0.001000 282,563 6.9572917 6.957292 0.02065949 0.01885940.020659 0.001000 282,563 6.9575362 6.957536 0.02065804 0.01892910.020658 0.001000 282,563 6.9575305 6.95753 0.02065807 0.0189273


-1.00 -1.00 0.00 0.00 0.00 0.001.00 0.00 -1.00 0.00 0.00 -1.000.00 0.00 1.00 -1.00 0.00 0.000.00 0.00 0.00 1.00 1.00 0.000.00 0.00 0.00 0.00 -1.00 1.0074.85 -42.02 0.00 0.00 0.00 959.63

0 0 457.02 863.67 -388.829 -959.6317

-0.045857163 0.8724605 0.6931521 0.354293 0.202 0.0010913-0.954142837 -0.872461 -0.693152 -0.354293 -0.202 -0.001091-0.016486887 -0.045854 0.7184586 0.273053 0.073 0.0003923-0.016486887 -0.045854 -0.281541 0.273053 0.073 0.00039230.016486887 0.0458539 0.2815414 0.726947 -0.07252985 -0.000392-0.029370276 -0.081686 -0.025306 0.08124 0.12920703 0.00069890.045857163 0.1275395 0.3068479 0.645707 0.79826312 -0.001091

CUARTA ITERACION DATOS DE IN GRESOTramo Longitud(1-2) 500(1-6) 300(2-3) 400(3-4) 200(4-5) 400(2-5) 200(5-6) 600



0.001 0.000400 467,905 7.1127124 7.112712 0.01976649 0.0010.019766 0.000400 467,905 7.6697304 7.66973 0.01699964 0.0200542

0.017 0.000400 467,905 7.6521646 7.652165 0.01707778 0.01709080.017078 0.000400 467,905 7.6527132 7.652713 0.01707533 0.017180.017075 0.000400 467,905 7.6526961 7.652696 0.01707541 0.017177




0.001 0.001000 139,338 6.1515291 6.151529 0.02642615 0.0010.026426 0.001000 139,338 6.8379622 6.837962 0.02138684 0.0223850.021387 0.001000 139,338 6.8102261 6.810226 0.0215614 0.01904710.021561 0.001000 139,338 6.8113298 6.81133 0.02155441 0.01914010.021554 0.001000 139,338 6.8112859 6.811286 0.02155469 0.0191372


-1.00 -1.00 0.00 0.00 0.00 0.001.00 0.00 -1.00 0.00 0.00 -1.000.00 0.00 1.00 -1.00 0.00 0.000.00 0.00 0.00 1.00 1.00 0.000.00 0.00 0.00 0.00 -1.00 1.0075.66 -41.54 0.00 0.00 0.00 601.25

0 0 394.66 444.38 -322.959 -601.2509

-0.06089314 0.8281895 0.6308982 0.408749 0.247 0.001466-0.93910686 -0.828189 -0.630898 -0.408749 -0.247 -0.001466

-0.020763984 -0.058586 0.6503161 0.322541 0.084 0.0004999-0.020763984 -0.058586 -0.349684 0.322541 0.084 0.00049990.020763984 0.0585858 0.3496839 0.677459 -0.08432693 -0.0005-0.040129157 -0.113225 -0.019418 0.086208 0.16297299 0.00096610.06089314 0.1718105 0.3691018 0.591251 0.75270008 -0.001466

QUINTA ITERACION DATOS DE IN GRESOTramo Longitud(1-2) 500(1-6) 300(2-3) 400(3-4) 200(4-5) 400(2-5) 200(5-6) 600



0.001 0.000400 472,489 7.1178743 7.117874 0.01973783 0.0010.019738 0.000400 472,489 7.6717681 7.671768 0.01699061 0.02008810.016991 0.000400 472,489 7.6544275 7.654427 0.01706768 0.01710170.017068 0.000400 472,489 7.6549651 7.654965 0.01706529 0.01719220.017065 0.000400 472,489 7.6549485 7.654948 0.01706536 0.0171891




0.001 0.001000 63,282 5.6337213 5.633721 0.03150716 0.0010.031507 0.001000 63,282 6.6130321 6.613032 0.02286645 0.02276110.022866 0.001000 63,282 6.5472522 6.547252 0.02332823 0.01915750.023328 0.001000 63,282 6.5515179 6.551518 0.02329787 0.01926520.023298 0.001000 63,282 6.5512406 6.551241 0.02329984 0.0192616

Tramo Longitud Dimet Caudal Velocidad f

(1-2) 500 0.25 0.105761 2.15454771 0.0170654(1-6) 300 0.25 0.094239 1.9198093 0.0171892(2-3) 400 0.15 0.043166 2.44269119 0.0190186(3-4) 200 0.1 0.005666 0.72141804 0.0232998(4-5) 400 0.15 0.034959 1.97826912 0.0192617(2-5) 200 0.1 0.012595 1.60368519 0.021539(5-6) 600 0.2 0.056739 1.80604276 0.0181406ELABORACION DE LA MATRIZ

-1.00 -1.00 0.00 0.00 0.00 0.001.00 0.00 -1.00 0.00 0.00 -1.000.00 0.00 1.00 -1.00 0.00 0.000.00 0.00 0.00 1.00 1.00 0.000.00 0.00 0.00 0.00 -1.00 1.0076.35 -41.12 0.00 0.00 0.00 448.32

0 0 360.35 218.16 -293.074 -448.3164

-0.071761379 0.7949794 0.5813636 0.452037 0.278 0.0017453-0.928238621 -0.794979 -0.581364 -0.452037 -0.278 -0.001745-0.024374366 -0.069637 0.5847938 0.37558 0.095 0.0005928-0.024374366 -0.069637 -0.415206 0.37558 0.095 0.00059280.024374366 0.069637 0.4152062 0.62442 -0.09452786 -0.000593-0.047387013 -0.135384 -0.00343 0.076457 0.18377475 0.00115250.071761379 0.2050206 0.4186364 0.547963 0.72169739 -0.001745

SEXTA ITERACION DATOS DE IN GRESOTramo Longitud(1-2) 500(1-6) 300(2-3) 400(3-4) 200(4-5) 400(2-5) 200(5-6) 600



0.001 0.000400 475,737 7.1214908 7.121491 0.01971779 0.0010.019718 0.000400 475,737 7.6731927 7.673193 0.01698431 0.02011250.016984 0.000400 475,737 7.6560089 7.656009 0.01706063 0.01710940.017061 0.000400 475,737 7.6565391 7.656539 0.01705827 0.0172009

0.017058 0.000400 475,737 7.6565227 7.656523 0.01705834 0.0171978




0.001 0.001000 21,543 4.8057635 4.805763 0.04329874 0.0010.043299 0.001000 21,543 6.1616289 6.161629 0.02633958 0.0229365

0.02634 0.001000 21,543 6.0103264 6.010326 0.02768241 0.01920940.027682 0.001000 21,543 6.0259615 6.025962 0.02753894 0.01932430.027539 0.001000 21,543 6.0243327 6.024333 0.02755384 0.0193203


-1.00 -1.00 0.00 0.00 0.00 0.001.00 0.00 -1.00 0.00 0.00 -1.000.00 0.00 1.00 -1.00 0.00 0.000.00 0.00 0.00 1.00 1.00 0.000.00 0.00 0.00 0.00 -1.00 1.0076.85 -40.82 0.00 0.00 0.00 389.50

0 0 340.56 87.83 -280.720 -389.4999

-0.077997849 0.7751667 0.5444589 0.484962 0.295 0.0019107-0.922002151 -0.775167 -0.544459 -0.484962 -0.295 -0.001911-0.027653302 -0.079712 0.5284989 0.427462 0.105 0.0006774-0.027653302 -0.079712 -0.471501 0.427462 0.105 0.00067740.027653302 0.0797122 0.4715011 0.572538 -0.10451582 -0.000677-0.050344547 -0.145121 0.01596 0.057501 0.19027751 0.00123330.077997849 0.2248333 0.4555411 0.515038 0.70520667 -0.001911

SETIMA ITERACION DATOS DE IN GRESOTramo Longitud(1-2) 500

(1-6) 300(2-3) 400(3-4) 200(4-5) 400(2-5) 200(5-6) 600



0.001 0.000400 477,507 7.1234459 7.123446 0.01970696 0.0010.019707 0.000400 477,507 7.6739618 7.673962 0.0169809 0.02012590.016981 0.000400 477,507 7.6568625 7.656863 0.01705683 0.01711370.017057 0.000400 477,507 7.6573886 7.657389 0.01705449 0.01720570.017054 0.000400 477,507 7.6573724 7.657372 0.01705456 0.0172026


Longitud= 200 Caudal -0.000112 Longitud=Viscosidad= 1.1E-006 Dimetro 0.1 Viscosida=Ks 0.000100 Velocidad 0.01425784 Ks


0.001 0.001000 1,251 2.3912589 2.391259 0.17488267 0.0010.174883 0.001000 1,251 4.5901076 4.590108 0.0474629 0.02300870.047463 0.001000 1,251 4.0461872 4.046187 0.06108127 0.01923080.061081 0.001000 1,251 4.1524193 4.152419 0.05799594 0.01934870.057996 0.001000 1,251 4.1306249 4.130625 0.05860956 0.0193446

Tramo Longitud Dimet Caudal Velocidad f(1-2) 500 0.25 0.106885 2.17742975 0.0170546(1-6) 300 0.25 0.093115 1.89692726 0.0172027(2-3) 400 0.15 0.039263 2.22182718 0.0191229(3-4) 200 0.1 -0.000112 0.01425784 0.0586096(4-5) 400 0.15 0.032768 1.85429822 0.0193447(2-5) 200 0.1 0.010122 1.28871454 0.021928(5-6) 600 0.2 0.05374 1.7106066 0.0182095ELABORACION DE LA MATRIZ

-1.00 -1.00 0.00 0.00 0.00 0.001.00 0.00 -1.00 0.00 0.00 -1.00

0.00 0.00 1.00 -1.00 0.00 0.000.00 0.00 0.00 1.00 1.00 0.000.00 0.00 0.00 0.00 -1.00 1.0077.12 -40.66 0.00 0.00 0.00 366.77

0 0 329.30 -10.85 -275.891 -366.7716

-0.081942741 0.762641 0.5093832 0.517725 0.306 0.0020154-0.918057259 -0.762641 -0.509383 -0.517725 -0.306 -0.002015-0.031270145 -0.090578 0.4701538 0.484622 0.117 0.0007691-0.031270145 -0.090578 -0.529846 0.484622 0.117 0.00076910.031270145 0.0905785 0.5298462 0.515378 -0.11659787 -0.000769-0.050672596 -0.146781 0.0392294 0.033103 0.18894433 0.00124630.081942741 0.237359 0.4906168 0.482275 0.6944578 -0.002015

OCTVA ITERACION DATOS DE IN GRESOTramo Longitud(1-2) 500(1-6) 300(2-3) 400(3-4) 200(4-5) 400(2-5) 200(5-6) 600



0.001 0.000400 478,257 7.1242716 7.124272 0.0197024 0.0010.019702 0.000400 478,257 7.6742864 7.674286 0.01697946 0.02013160.016979 0.000400 478,257 7.6572228 7.657223 0.01705522 0.01711560.017055 0.000400 478,257 7.6577472 7.657747 0.01705289 0.01720780.017053 0.000400 478,257 7.657731 7.657731 0.01705296 0.0172046




0.001 0.001000 13,681 4.4333581 4.433358 0.05087851 0.001

0.050879 0.001000 13,681 5.9302435 5.930244 0.02843511 0.02303440.028435 0.001000 13,681 5.734044 5.734044 0.03041431 0.01923850.030414 0.001000 13,681 5.7573732 5.757373 0.03016833 0.01935750.030168 0.001000 13,681 5.7545661 5.754566 0.03019777 0.0193532


-1.00 -1.00 0.00 0.00 0.00 0.001.00 0.00 -1.00 0.00 0.00 -1.000.00 0.00 1.00 -1.00 0.00 0.000.00 0.00 0.00 1.00 1.00 0.000.00 0.00 0.00 0.00 -1.00 1.0077.23 -40.59 0.00 0.00 0.00 357.46

0 0 322.93 -61.13 -274.203 -357.458

-0.084105819 0.7558702 0.4881634 0.538838 0.312 0.002072-0.915894181 -0.75587 -0.488163 -0.538838 -0.312 -0.002072-0.033649111 -0.097672 0.4337851 0.522477 0.125 0.000829-0.033649111 -0.097672 -0.566215 0.522477 0.125 0.0008290.033649111 0.0976716 0.5662149 0.477523 -0.12463641 -0.000829-0.050456709 -0.146458 0.0543782 0.016361 0.1868918 0.00124310.084105819 0.2441298 0.5118366 0.461162 0.68847179 -0.002072

NOVENA ITERACION DATOS DE IN GRESOTramo Longitud(1-2) 500(1-6) 300(2-3) 400(3-4) 200(4-5) 400(2-5) 200(5-6) 600


f Nmero deDenomin denomina G(f) f

dato Ks/d Rreynolds 1/f datoasumido DATO CALCULADO asumido

0.001 0.000400 478,610 7.1246607 7.124661 0.01970025 0.0010.0197 0.000400 478,610 7.6744393 7.674439 0.01697879 0.0201343

0.016979 0.000400 478,610 7.6573925 7.657392 0.01705447 0.01711640.017054 0.000400 478,610 7.657916 7.657916 0.01705214 0.01720880.017052 0.000400 478,610 7.6578999 7.6579 0.01705221 0.0172056




0.001 0.001000 20,051 4.7475741 4.747574 0.04436664 0.0010.044367 0.001000 20,051 6.1264057 6.126406 0.02664333 0.02304570.026643 0.001000 20,051 5.9683051 5.968305 0.02807359 0.01924180.028074 0.001000 20,051 5.9850394 5.985039 0.02791682 0.01936130.027917 0.001000 20,051 5.9832528 5.983253 0.0279335 0.019357


-1.00 -1.00 0.00 0.00 0.00 0.001.00 0.00 -1.00 0.00 0.00 -1.000.00 0.00 1.00 -1.00 0.00 0.000.00 0.00 0.00 1.00 1.00 0.000.00 0.00 0.00 0.00 -1.00 1.0077.28 -40.56 0.00 0.00 0.00 353.10

0 0 319.64 -82.87 -273.467 -353.1011

-0.085160746 0.7525662 0.4780682 0.549238 0.314 0.0020997-0.914839254 -0.752566 -0.478068 -0.549238 -0.314 -0.0021-0.03483047 -0.1012 0.4162934 0.541393 0.129 0.0008588-0.03483047 -0.1012 -0.583707 0.541393 0.129 0.00085880.03483047 0.1011996 0.5837066 0.458607 -0.12858493 -0.000859

-0.050330276 -0.146234 0.0617748 0.007844 0.18580613 0.00124090.085160746 0.2474338 0.5219318 0.450762 0.68560894 -0.0021

METODO DE LA

Tramo Longitud Dimet Caudal Velocidad f(1-2) 500 0.25 0.1071 2.1824637 0.0170522(1-6) 300 0.25 0.0929 1.89189332 0.0172057(2-3) 400 0.15 0.0380 2.15309609 0.0191592(3-4) 200 0.1 -0.0018 0.22858575 0.0279335(4-5) 400 0.15 0.0325 1.83682058 0.0193572(2-5) 200 0.1 0.0097 1.23608979 0.0220094(5-6) 600 0.2 0.0530 1.68782032 0.0182269

HARDY CROSSCIRCUITO TUBERA LONGIT DIAMETRO CAUDAL

I (1-2) 500 0.25 0.10733I (2-5) 200 0.1 0.00956I (5-6) 600 0.2 -0.05267I (6-1) 300 0.25 -0.09267

CIRCUITO TUBERA LONGIT DIAMETRO CAUDAL

II (2-3) Dimet Caudal 0.03777II (3-4) 0.25 0.107132 -0.00223II (4-5) 0.25 0.092868 -0.03223II (2-5) 0.15 0.038048 -0.00956

otro problema

PRIMERA ITERACION

1.1. Cculo de coeficientes de friccin DATOS DE IN GRESOTramo Longitud(1-2) 500(1-6) 300(2-3) 400(3-4) 200(4-5) 400(2-5) 200

(5-6) 600Tubera (1-2)



0.001 0.000400 670,125 7.2896584 7.289658 0.01881853 0.0010.018819 0.000400 670,125 7.7366854 7.736685 0.01670668 0.01881850.016707 0.000400 670,125 7.7260111 7.726011 0.01675287 0.01670670.016753 0.000400 670,125 7.7262645 7.726264 0.01675178 0.01675290.016752 0.000400 670,125 7.7262584 7.726258 0.0167518 0.0167518



0.001 0.001000 1,675,311 6.9961066 6.996107 0.02043088 0.0010.020431 0.001000 1,675,311 7.1033542 7.103354 0.0198186 0.01929120.019819 0.001000 1,675,311 7.1028572 7.102857 0.01982138 0.01819310.019821 0.001000 1,675,311 7.1028595 7.102859 0.01982136 0.01820360.019821 0.001000 1,675,311 7.1028595 7.102859 0.01982136 0.0182035


-1.00 -1.00 0.00 0.00 0.00 0.001.00 0.00 -1.00 0.00 0.00 -1.000.00 0.00 1.00 -1.00 0.00 0.000.00 0.00 0.00 1.00 1.00 0.000.00 0.00 0.00 0.00 -1.00 1.00

106.30 -66.16 0.00 0.00 0.00 5006.260 0 1225.14 5006.26 -1206.777 -5006.263

-0.018519135 0.9517258 0.8137691 0.250039 0.114 0.0002799-0.981480865 -0.951726 -0.813769 -0.250039 -0.114 -0.00028-0.007450046 -0.01942 0.8266327 0.197561 0.046 0.0001126-0.007450046 -0.01942 -0.173367 0.197561 0.046 0.00011260.007450046 0.0194202 0.1733673 0.802439 -0.04592137 -0.000113-0.011069089 -0.028854 -0.012864 0.052478 0.0682288 0.00016730.018519135 0.0482742 0.1862309 0.749961 0.88584983 -0.00028

SEGUNDO TRAMITE DATOS DE IN GRESOTramo Longitud(1-2) 500(1-6) 300(2-3) 400(3-4) 200(4-5) 400(2-5) 200(5-6) 600



0.001 0.000400 576,279 7.2186881 7.218688 0.01919037 0.0010.01919 0.000400 576,279 7.7105447 7.710545 0.01682015 0.01802020.01682 0.000400 576,279 7.6973119 7.697312 0.01687803 0.01647

0.016878 0.000400 576,279 7.6976653 7.697665 0.01687648 0.01649510.016876 0.000400 576,279 7.6976558 7.697656 0.01687652 0.0164947




0.001 0.001000 849,855 6.8785937 6.878594 0.02113492 0.0010.021135 0.001000 849,855 7.0734512 7.073451 0.01998652 0.02014530.019987 0.001000 849,855 7.0717327 7.071733 0.01999624 0.01841790.019996 0.001000 849,855 7.0717478 7.071748 0.01999615 0.01844360.019996 0.001000 849,855 7.0717477 7.071748 0.01999615 0.0184432


-1.00 -1.00 0.00 0.00 0.00 0.001.00 0.00 -1.00 0.00 0.00 -1.000.00 0.00 1.00 -1.00 0.00 0.000.00 0.00 0.00 1.00 1.00 0.000.00 0.00 0.00 0.00 -1.00 1.0092.10 -97.70 0.00 0.00 0.00 2598.22

0 0 784.61 2538.33 -720.123 -2598.223

-0.047680405 0.9073727 0.7575645 0.272912 0.135 0.000488-0.952319595 -0.907373 -0.757564 -0.272912 -0.135 -0.000488-0.018653661 -0.036238 0.7870125 0.2152 0.053 0.0001909-0.018653661 -0.036238 -0.212987 0.2152 0.053 0.00019090.018653661 0.0362379 0.2129875 0.7848 -0.05297783 -0.000191-0.029026744 -0.056389 -0.029448 0.057711 0.08243819 0.00029710.047680405 0.0926273 0.2424355 0.727088 0.86458398 -0.000488

TERCERA ITERACION DATOS DE IN GRESOTramo Longitud(1-2) 500(1-6) 300(2-3) 400(3-4) 200(4-5) 400(2-5) 200(5-6) 600



0.001 0.000400 547,404 7.1933905 7.193391 0.01932559 0.0010.019326 0.000400 547,404 7.7009964 7.700996 0.01686189 0.01779290.016862 0.000400 547,404 7.6867847 7.686785 0.01692429 0.0164044

0.016924 0.000400 547,404 7.6871794 7.687179 0.01692256 0.01642460.016923 0.000400 547,404 7.6871685 7.687168 0.0169226 0.0164243




0.001 0.001000 451,805 6.7014272 6.701427 0.02226719 0.0010.022267 0.001000 451,805 7.0243098 7.02431 0.02026715 0.02118440.020267 0.001000 451,805 7.0192577 7.019258 0.02029634 0.01870330.020296 0.001000 451,805 7.0193365 7.019337 0.02029588 0.01875560.020296 0.001000 451,805 7.0193353 7.019335 0.02029589 0.0187544


-1.00 -1.00 0.00 0.00 0.00 0.001.00 0.00 -1.00 0.00 0.00 -1.000.00 0.00 1.00 -1.00 0.00 0.000.00 0.00 0.00 1.00 1.00 0.000.00 0.00 0.00 0.00 -1.00 1.0087.72 -111.99 0.00 0.00 0.00 1499.05

0 0 578.18 1363.52 -468.308 -1499.054

-0.084472121 0.8493649 0.6821317 0.287745 0.152 0.0007542-0.915527879 -0.849365 -0.682132 -0.287745 -0.152 -0.000754-0.032393466 -0.057766 0.7301959 0.230145 0.058 0.0002892-0.032393466 -0.057766 -0.269804 0.230145 0.058 0.00028920.032393466 0.0577657 0.2698041 0.769855 -0.05840099 -0.000289-0.052078655 -0.092869 -0.048064 0.0576 0.0938907 0.0004650.084472121 0.1506351 0.3178683 0.712255 0.84770831 -0.000754

CUARTA ITERACION DATOS DE IN GRESOTramo Longitud

(1-2) 500(1-6) 300(2-3) 400(3-4) 200(4-5) 400(2-5) 200(5-6) 600



0.001 0.000400 553,450 7.1988436 7.198844 0.01929632 0.0010.019296 0.000400 553,450 7.7030649 7.703065 0.01685283 0.01772370.016853 0.000400 553,450 7.6890671 7.689067 0.01691425 0.01638470.016914 0.000400 553,450 7.6894527 7.689453 0.01691255 0.01640350.016913 0.000400 553,450 7.6894421 7.689442 0.0169126 0.0164032




0.001 0.001000 266,979 6.4919598 6.49196 0.0237273 0.0010.023727 0.001000 266,979 6.959546 6.959546 0.02064611 0.022290.020646 0.001000 266,979 6.9480967 6.948097 0.02071421 0.01901940.020714 0.001000 266,979 6.9483752 6.948375 0.02071255 0.01910880.020713 0.001000 266,979 6.9483685 6.948368 0.02071259 0.0191061


-1.00 -1.00 0.00 0.00 0.00 0.00

1.00 0.00 -1.00 0.00 0.00 -1.000.00 0.00 1.00 -1.00 0.00 0.000.00 0.00 0.00 1.00 1.00 0.000.00 0.00 0.00 0.00 -1.00 1.0088.64 -117.11 0.00 0.00 0.00 1060.81

0 0 485.79 820.56 -332.640 -1060.814

-0.116902655 0.7946168 0.6040753 0.282228 0.152 0.0009982-0.883097345 -0.794617 -0.604075 -0.282228 -0.152 -0.000998-0.045933775 -0.0807 0.6644967 0.234103 0.060 0.0003922-0.045933775 -0.0807 -0.335503 0.234103 0.060 0.00039220.045933775 0.0806998 0.3355033 0.765897 -0.05962849 -0.000392-0.07096888 -0.124683 -0.060421 0.048125 0.09212757 0.0006060.116902655 0.2053832 0.3959247 0.717772 0.84824394 -0.000998

QUINTA ITERACION DATOS DE IN GRESOTramo Longitud(1-2) 500(1-6) 300(2-3) 400(3-4) 200(4-5) 400(2-5) 200(5-6) 600



0.001 0.000400 570,732 7.2139713 7.213971 0.01921548 0.0010.019215 0.000400 570,732 7.7087736 7.708774 0.01682788 0.01770960.016828 0.000400 570,732 7.6953609 7.695361 0.01688659 0.01638070.016887 0.000400 570,732 7.6957218 7.695722 0.01688501 0.01639920.016885 0.000400 570,732 7.6957121 7.695712 0.01688505 0.0163989




0.001 0.001000 183,321 6.3057878 6.305788 0.02514903 0.0010.025149 0.001000 183,321 6.8956177 6.895618 0.0210307 0.02329990.021031 0.001000 183,321 6.8761668 6.876167 0.02114985 0.0193177

0.02115 0.001000 183,321 6.8768013 6.876801 0.02114594 0.0194480.021146 0.001000 183,321 6.8767806 6.876781 0.02114607 0.0194432


-1.00 -1.00 0.00 0.00 0.00 0.001.00 0.00 -1.00 0.00 0.00 -1.000.00 0.00 1.00 -1.00 0.00 0.000.00 0.00 0.00 1.00 1.00 0.000.00 0.00 0.00 0.00 -1.00 1.0091.26 -118.20 0.00 0.00 0.00 920.89

0 0 445.96 574.68 -258.533 -920.8905

-0.13689948 0.7574125 0.5412224 0.262632 0.137 0.0011582-0.86310052 -0.757412 -0.541222 -0.262632 -0.137 -0.001158

-0.057302494 -0.101541 0.6052641 0.227442 0.057 0.0004848-0.057302494 -0.101541 -0.394736 0.227442 0.057 0.00048480.057302494 0.1015407 0.3947359 0.772558 -0.05747114 -0.000485-0.079596986 -0.141047 -0.064042 0.03519 0.07983125 0.00067340.13689948 0.2425875 0.4587776 0.737368 0.8626976 -0.001158

SEXTA ITERACION DATOS DE IN GRESOTramo Longitud(1-2) 500(1-6) 300(2-3) 400(3-4) 200(4-5) 400(2-5) 200(5-6) 600



0.001 0.000400 584,357 7.2254407 7.225441 0.01915452 0.0010.019155 0.000400 584,357 7.7130729 7.713073 0.01680913 0.01770920.016809 0.000400 584,357 7.7000954 7.700095 0.01686583 0.01638050.016866 0.000400 584,357 7.7004383 7.700438 0.01686433 0.0163990.016864 0.000400 584,357 7.7004292 7.700429 0.01686437 0.0163988




0.001 0.001000 145,195 6.1756241 6.175624 0.02622034 0.0010.02622 0.001000 145,195 6.8472509 6.847251 0.02132885 0.024076

0.021329 0.001000 145,195 6.8209066 6.820907 0.02149393 0.01955220.021494 0.001000 145,195 6.8219251 6.821925 0.02148751 0.01971790.021488 0.001000 145,195 6.8218857 6.821886 0.02148776 0.0197109


-1.00 -1.00 0.00 0.00 0.00 0.001.00 0.00 -1.00 0.00 0.00 -1.000.00 0.00 1.00 -1.00 0.00 0.000.00 0.00 0.00 1.00 1.00 0.000.00 0.00 0.00 0.00 -1.00 1.0093.32 -118.24 0.00 0.00 0.00 876.64

0 0 428.71 462.32 -218.755 -876.641

-0.147781572 0.7355831 0.4991159 0.24411 0.123 0.0012498-0.852218428 -0.735583 -0.499116 -0.24411 -0.123 -0.00125-0.065218236 -0.116691 0.5631321 0.217854 0.054 0.0005516-0.065218236 -0.116691 -0.436868 0.217854 0.054 0.0005516

0.065218236 0.1166912 0.4368679 0.782146 -0.05448044 -0.000552-0.082563335 -0.147726 -0.064016 0.026256 0.06896977 0.00069830.147781572 0.2644169 0.5008841 0.75589 0.87654979 -0.00125

SETIMA ITERACION DATOS DE IN GRESOTramo Longitud(1-2) 500(1-6) 300(2-3) 400(3-4) 200(4-5) 400(2-5) 200(5-6) 600



0.001 0.000400 592,035 7.2317358 7.231736 0.01912119 0.0010.019121 0.000400 592,035 7.715422 7.715422 0.01679889 0.01771010.016799 0.000400 592,035 7.7026803 7.70268 0.01685451 0.01638080.016855 0.000400 592,035 7.7030136 7.703014 0.01685306 0.01639930.016853 0.000400 592,035 7.7030049 7.703005 0.01685309 0.016399




0.001 0.001000 127,219 6.0971505 6.09715 0.02689962 0.0010.0269 0.001000 127,219 6.8166123 6.816612 0.02152102 0.0245829

0.021521 0.001000 127,219 6.7856042 6.785604 0.02171816 0.01970750.021718 0.001000 127,219 6.786918 6.786918 0.02170975 0.0198979

0.02171 0.001000 127,219 6.7868623 6.786862 0.0217101 0.0198893

Tramo Longitud Dimet Caudal Velocidad f(1-2) 500 0.25 0.13252 2.69967792 0.0168531(1-6) 300 0.25 0.265917 5.41720519 0.016399(2-3) 400 0.15 0.050766 2.87274065 0.0188577(3-4) 200 0.1 0.011391 1.45029748 0.0217101

(4-5) 400 0.15 0.022828 1.29180396 0.0198897(2-5) 200 0.1 0.025036 3.18768189 0.0206679(5-6) 600 0.2 0.029667 0.94432964 0.0191665ELABORACION DE LA MATRIZ

-1.00 -1.00 0.00 0.00 0.00 0.001.00 0.00 -1.00 0.00 0.00 -1.000.00 0.00 1.00 -1.00 0.00 0.000.00 0.00 0.00 1.00 1.00 0.000.00 0.00 0.00 0.00 -1.00 1.0094.48 -118.17 0.00 0.00 0.00 857.68

0 0 420.86 409.19 -198.041 -857.6801

-0.153751362 0.7233148 0.4742587 0.23211 0.115 0.0013011-0.846248638 -0.723315 -0.474259 -0.23211 -0.115 -0.001301-0.069928389 -0.125841 0.5377068 0.210585 0.052 0.0005918-0.069928389 -0.125841 -0.462293 0.210585 0.052 0.00059180.069928389 0.1258405 0.4622932 0.789415 -0.05226494 -0.000592-0.083822973 -0.150845 -0.063448 0.021525 0.06264984 0.00070940.153751362 0.2766852 0.5257413 0.76789 0.88508522 -0.001301

OCTVA ITERACION DATOS DE IN GRESOTramo Longitud(1-2) 500(1-6) 300(2-3) 400(3-4) 200(4-5) 400(2-5) 200(5-6) 600



0.001 0.000400 595,966 7.2349137 7.234914 0.01910439 0.0010.019104 0.000400 595,966 7.716605 7.716605 0.01679374 0.01771070.016794 0.000400 595,966 7.7039816 7.703982 0.01684882 0.0163810.016849 0.000400 595,966 7.7043101 7.70431 0.01684738 0.01639950.016847 0.000400 595,966 7.7043015 7.704302 0.01684742 0.0163992




0.001 0.001000 118,418 6.0532385 6.053238 0.02729131 0.0010.027291 0.001000 118,418 6.7989801 6.79898 0.02163279 0.02487590.021633 0.001000 118,418 6.765199 6.765199 0.02184937 0.0197980.021849 0.001000 118,418 6.7667011 6.766701 0.02183967 0.0200033

0.02184 0.001000 118,418 6.7666343 6.766634 0.0218401 0.0199936


-1.00 -1.00 0.00 0.00 0.00 0.001.00 0.00 -1.00 0.00 0.00 -1.000.00 0.00 1.00 -1.00 0.00 0.000.00 0.00 0.00 1.00 1.00 0.000.00 0.00 0.00 0.00 -1.00 1.0095.08 -118.12 0.00 0.00 0.00 848.33

0 0 417.08 383.13 -187.531 -848.3291

-0.156954218 0.7167116 0.460657 0.225443 0.110 0.0013287-0.843045782 -0.716712 -0.460657 -0.225443 -0.110 -0.001329-0.072518563 -0.13089 0.5236464 0.2063 0.051 0.0006139-0.072518563 -0.13089 -0.476354 0.2063 0.051 0.00061390.072518563 0.1308896 0.4763536 0.7937 -0.05096856 -0.000614-0.084435655 -0.152399 -0.062989 0.019143 0.05934431 0.00071480.156954218 0.2832884 0.539343 0.774557 0.88968713 -0.001329

NOVENA ITERACION DATOS DE IN GRESOTramo Longitud(1-2) 500(1-6) 300(2-3) 400(3-4) 200(4-5) 400

(2-5) 200(5-6) 600



0.001 0.000400 597,938 7.2364964 7.236496 0.01909604 0.0010.019096 0.000400 597,938 7.7171935 7.717193 0.01679118 0.0177110.016791 0.000400 597,938 7.7046287 7.704629 0.01684599 0.0163810.016846 0.000400 597,938 7.7049548 7.704955 0.01684457 0.01639960.016845 0.000400 597,938 7.7049464 7.704946 0.0168446 0.0163993




0.001 0.001000 114,036 6.0297726 6.029773 0.02750414 0.0010.027504 0.001000 114,036 6.7894143 6.789414 0.02169379 0.02503370.021694 0.001000 114,036 6.7541039 6.754104 0.02192121 0.01984690.021921 0.001000 114,036 6.7557138 6.755714 0.02191076 0.02006030.021911 0.001000 114,036 6.7556404 6.75564 0.02191124 0.0200501


-1.00 -1.00 0.00 0.00 0.00 0.001.00 0.00 -1.00 0.00 0.00 -1.000.00 0.00 1.00 -1.00 0.00 0.000.00 0.00 0.00 1.00 1.00 0.000.00 0.00 0.00 0.00 -1.00 1.0095.38 -118.10 0.00 0.00 0.00 843.65

0 0 415.19 370.14 -182.257 -843.6461

-0.158623039 0.7132731 0.4535215 0.22196 0.108 0.0013431-0.841376961 -0.713273 -0.453522 -0.22196 -0.108 -0.001343-0.073884288 -0.133553 0.5162252 0.204011 0.050 0.0006256-0.073884288 -0.133553 -0.483775 0.204011 0.050 0.00062560.073884288 0.1335532 0.4837748 0.795989 -0.05027557 -0.000626-0.084738751 -0.153174 -0.062704 0.017948 0.05766164 0.00071750.158623039 0.2867269 0.5464785 0.77804 0.8920628 -0.001343

METODO DE LA

Tramo Longitud Dimet Caudal Velocidad f(1-2) 500 0.25 0.1338 2.72659865 0.0168446(1-6) 300 0.25 0.2658 5.41415765 0.0163993(2-3) 400 0.15 0.0501 2.83247422 0.0188708(3-4) 200 0.1 0.0102 1.30001504 0.0219112(4-5) 400 0.15 0.0208 1.17954726 0.0200506(2-5) 200 0.1 0.0246 3.13320034 0.0206844(5-6) 600 0.2 0.0267 0.85004341 0.0193795

Dimetro Caudal0.25 0.10.25 0.10.15 0.1

0.1 0.10.15 0.1

0.1 0.10.2 0.1

Tubera (1-6)300 Caudal 0.1 Longitud=

Viscosida= 1.14E-006 Dimetro 0.25 Viscosida=0.000100 Velocidad 2.03717851 Ks

Nmero de Denomin denomina G(f) fKs/d Rreynolds 1/f dato Ks/d

DATO CALCULADO asumido DATO0.000400 446,750 7.0879478 7.0879478 0.01990485 0.001 0.0006670.000400 446,750 7.6598831 7.6598831 0.01704338 0.019922 0.0006670.000400 446,750 7.6412177 7.6412177 0.01712675 0.0183583 0.0006

Problemas Primera Unidad Fluidos II

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