Hoja1 EJEMPLO DE APLICACIN DEL MTODO DE HARDY-CROSSDetermine en el sistema de tuberas mostrado:a) Los caudales en cada tubera.b) La CPA cuando Zc= 100 m. y Pc/=15 m. c) El nivel del reservorio (Z0) para Zc= 100 m. y Pc/=15 m.

TuberaLongitud(Km)Dimetro(Plg)C(p^0.5/s)10.25813520.31214030.21214040.25813550.312140

Iteracin 1Iteracin 2Iteracin 3Iteracin 4Iteracin 5Iteracin 6Circuito TuberaLongitudL (Km)DimetroD (plg)Coef. H & W(p^0.5/s)CoeficienteRCaudalQ (l/s)Prdidah (m)h/QCaudalQ (l/s)Prdidah (m)h/QCaudalQ (l/s)Prdidah (m)h/QCaudalQ (l/s)Prdidah (m)h/QCaudalQ (l/s)Prdidah (m)h/QCaudalQ (l/s)Prdidah (m)h/QI10.2581350.00197550231.1920.420298.0274.4160.250254.0155.3700.218253.1055.0040.217252.7254.8510.217252.7154.8480.21720.30121400.00031-315-12.8400.041-566.98-38.0890.067-610.99-43.7390.072-611.90-43.8590.072-612.28-43.9100.072-612.29-43.9110.07230.20121400.00020850.7590.009-310.57-8.3390.027-362.37-11.0930.031-359.30-10.9200.030-359.61-10.9370.030-359.58-10.9350.030219.1110.47027.9890.3440.5380.3200.2250.3190.0040.3190.0020.319Q1=-251.98Q1=-44.01Q1=-0.91Q1=-0.38Q1=-0.01Q1=-0.00II30.20121400.00020-85-0.7590.009310.578.3390.027362.3711.0930.031359.3010.9200.030359.6110.9370.030359.5810.9350.03040.2581350.00197-400-128.2670.321-256.41-56.3410.220-248.62-53.2160.214-252.60-54.8020.217-252.67-54.8310.217-252.71-54.8460.21750.30121400.0003146526.3930.057608.5943.4210.071616.3844.4550.072612.4043.9260.072612.3343.9160.072612.2943.9110.072-102.6320.386-4.5810.3182.3320.3170.0430.3190.0210.3190.0000.319Q2=143.59Q2=7.79Q2=-3.98Q2=-0.07Q2=-0.04Q2=-0.00

Zo21543+ II+ I865 l/s55031540085465

PROB4PROBLEMA 4: En la Fig. 3 El sistema de tuberas se encuentra en un plano horizontal. Empleando el mtodode Hardy-Cross (u otro alternativo) determinar los caudales y prdidas de carga en el sistema.

2TuberaLongitud (Km)Dimetro (Plg)C (Pie^0.5/s)10.52814020.62614030.51614040.63814050.70614061.60614070.728140Utilizando el Mtodo de Hardy-CrossCoeficiente: R = (1.72*10^6*L)/(C^1.85*D^4.87)Factor de aceleracin de convergencia: n=1.85Iteracin #1Iteracin #2Iteracin #3Iteracin #4Iteracin #5Iteracin #6CircuitoTuberaLongitudL (Km)DimetroD (Plg)Coef. de H & WC (pies^0.5/s)CoeficienteRCaudalQ (l/s)Prdidah (m)h/QCaudalQ (l/s)Prdidah (m)h/QCaudalQ (l/s)Prdidah (m)h/QCaudalQ (l/s)Prdidah (m)h/QCaudalQ (l/s)Prdidah (m)h/QCaudalQ (l/s)Prdidah (m)h/QI10.5281400.00383-85-14.2090.167-86.956-14.8200.170-87.903-15.1200.172-88.103-15.1840.172-88.141-15.1960.172-88.147-15.1980.17220.6261400.01853-33-11.9460.362-34.956-13.2890.380-35.903-13.9630.389-36.103-14.1070.391-36.141-14.1340.391-36.147-14.1390.39130.5161400.015254819.6540.40946.04418.1990.39545.09717.5120.38844.89717.3690.38744.85917.3420.38744.85317.3370.38740.6381400.004646510.4800.16169.51311.8660.17169.89211.9860.17169.93712.0000.17269.94412.0030.17269.94512.0030.1723.9791.1001.9561.1170.4161.1210.0781.1220.0141.1220.0031.122Q1=-1.956Q1=-0.947Q1=-0.201Q1=-0.038Q1=-0.007Q1=-0.001II40.6381400.00464-65-10.4800.161-69.513-11.8660.171-69.892-11.9860.171-69.937-12.0000.172-69.944-12.0030.172-69.945-12.0030.17250.7061400.0209391.2190.1352.5310.1170.0461.2050.0300.0250.9600.0190.0200.9150.0180.0190.9070.0170.01961.6061400.047832417.1040.71317.5319.5670.54616.2058.2720.51015.9608.0410.50415.9158.0000.50315.9077.9920.50270.7281400.00530445.8190.13237.5314.3360.11636.2054.0570.11235.9604.0060.11135.9153.9970.11135.9073.9950.11113.6621.1422.1530.8780.3720.8180.0660.8070.0120.8050.0020.805Q2=-6.469Q2=-1.326Q2=-0.246Q2=-0.044Q2=-0.008Q2=-0.001Luego de 6 iteraciones, obtenemos un error de prdida Q < 0.001con lo cual concluye el proceso iterativo.Obteniendo los siguientes caudales y prdidas finales:Resultados FinalesCircuitoTuberaCaudalQ (l/s)Prdidah (m)I1-88.147-15.1982-36.147-14.139344.85317.337469.94512.0030.003Q1=-0.001II4-69.945-12.00350.9070.017615.9077.992735.9073.9950.002Q2=-0.001

1273546+ I+ I I2015265281194 l/s85 l/s48944332465

Hoja2EJEMPLO DE APLICACIN DEL MTODO DE HARDY-CROSS Caso de seudo-circuito / seudo-tuberaEn el sistema de los 3 reservorios, determine los caudales que transportan las tuberas, y lacota piezomtrica en el punto DTuberaLongitud (Km)Dimetro (Plg)C (Pie^0.5/s)1410120268120356120Q1= -[h+(ZA-ZB)]/[1.85*(h/Q)]Q2= -[h+(ZB-ZC)]/[1.85*(h/Q)]

Iteracin #1Iteracin #2Iteracin #3Iteracin #4Iteracin #5Iteracin #6Iteracin #7Iteracin #8Iteracin #9CircuitoTuberaLongitudL (Km)DimetroD (Plg)Coef. de H & WC (pies^0.5/s)CoeficienteRCaudalQ (l/s)Prdidah (m)h/QCaudalQ (l/s)Prdidah (m)h/QCaudalQ (l/s)Prdidah (m)h/QCaudalQ (l/s)Prdidah (m)h/QCaudalQ (l/s)Prdidah (m)h/QCaudalQ (l/s)Prdidah (m)h/QCaudalQ (l/s)Prdidah (m)h/QCaudalQ (l/s)Prdidah (m)h/QCaudalQ (l/s)Prdidah (m)h/Q114101200.0132160944-40-12.1590.304-46.072-15.7930.343-37.267-10.6670.286-30.111-7.1900.239-26.467-5.6640.214-24.719-4.9910.202-23.960-4.7120.197-23.644-4.5970.194-23.518-4.5520.1942681200.05876870972014.9990.750-14.121-7.8780.558-16.561-10.5800.639-13.224-6.9770.528-11.704-5.5660.476-10.952-4.9230.449-10.632-4.6600.438-10.496-4.5500.434-10.442-4.5070.43249.0009.0009.0009.0009.0009.0009.0009.0009.00011.8391.054-14.6710.901-12.2470.925-5.1670.766-2.2300.690-0.9140.651-0.3710.635-0.1470.628-0.0590.625

Q1=-6.072Q1=8.805Q1=7.156Q1=3.644Q1=1.748Q1=0.758Q1=0.316Q1=0.127Q1=0.051

22681200.058769-20.000-14.9990.75014.1217.8780.55816.56110.5800.63913.2246.9770.52811.7045.5660.47610.9524.9230.44910.6324.6600.43810.4964.5500.43410.4424.5070.4323561200.198800-57.500-357.9336.225-29.451-103.8123.525-18.206-42.6402.342-14.387-27.5851.917-12.263-20.5271.674-11.267-17.5491.558-10.829-16.3081.506-10.649-15.8091.485-10.576-15.6091.476511.00011.00011.00011.00011.00011.00011.00011.00011.000-361.9326.975-84.9344.083-21.0602.981-9.6082.445-3.9612.149-1.6262.007-0.6481.944-0.2591.918-0.1021.908Q2=28.049Q2=11.245Q2=3.819Q2=2.124Q2=0.996Q2=0.438Q2=0.180Q2=0.073Q2=0.029

12391 m80 m

100 m2.5 l/s

45+ 1+ 24057.520

PROB3PROBLEMA 3: Cules son los gastos que fluyen por las tuberas del sistema mostrado en la Fig. 2? El nivel de agua en A se encuentra en la cota 91.40 m, B en la 85.30 m, C en la 70 m, y D en la 51.20 m

SOLUCIN:Utilizando el Mtodo de Hardy-CrossCoeficiente: R = (1.72*10^6*L)/(C^1.85*D^4.87)Factor de aceleracin de convergencia: n=1.85

TuberaLongitud(Km)Dimetro(Plg)C(p^0.5/s)11.221610020.61814031.51013046.11290

Iteracin #1Iteracin #2Iteracin #3Iteracin #4Iteracin #5Iteracin #6Iteracin #7CircuitoTuberaLongitudL (Km)DimetroD (Plg)Coef. de H & WC (pies^0.5/s)CoeficienteRCaudalQ (l/s)Prdidah (m)h/QCaudalQ (l/s)Prdidah (m)h/QCaudalQ (l/s)Prdidah (m)h/QCaudalQ (l/s)Prdidah (m)h/QCaudalQ (l/s)Prdidah (m)h/QCaudalQ (l/s)Prdidah (m)h/QCaudalQ (l/s)Prdidah (m)h/Q11 (*)1.22161000.000573-100-2.8700.029-138.400-5.2350.038-145.098-5.7130.039-148.965-5.9980.040-149.942-6.0710.040-150.237-6.0930.041-150.308-6.0990.0412(**)0.6181400.004492201.1470.0578.5630.2390.0285.3590.1000.0191.8610.0140.0080.8940.0040.0040.5460.0010.0030.4530.0010.00266.16.16.16.16.16.16.14.3770.0861.1040.0660.4870.0580.1160.0480.0320.0450.0080.0430.0020.043

Q1=-27.503Q1=-9.079Q1=-4.530Q1=-1.308Q1=-0.392Q1=-0.100Q1=-0.028

22(**)0.6181400.004492-20-1.1470.057-8.563-0.2390.028-5.359-0.1000.019-1.861-0.0140.008-0.894-0.0040.004-0.546-0.0010.003-0.453-0.0010.00231.5101300.004274-60-8.3250.139-76.066-12.9130.170-81.942-14.8190.181-82.974-15.1660.183-83.315-15.2810.183-83.358-15.2960.183-83.365-15.2980.184715.30015.30015.30015.30015.30015.30015.3005.8280.1962.1480.1980.3810.2000.1200.1900.0150.1880.0030.1860.0000.186

Q2=-16.066Q2=-5.875Q2=-1.032Q2=-0.341Q2=-0.044Q2=-0.007Q2=-0.001

31(*)1.22161000.0005731002.8700.029138.4005.2350.038145.0985.7130.039148.9655.9980.040149.9426.0710.040150.2376.0930.041150.3086.0990.04146.112900.0141226027.5090.45870.89737.4590.52868.51635.1650.51367.85234.5370.50967.52234.2270.50767.42534.1360.50667.39634.1090.5065-40.200-40.200-40.200-40.200-40.200-40.200-40.200-9.8210.4872.4940.5660.6780.5530.3360.5490.0980.5470.0290.5470.0080.547Q3=10.897Q3=-2.381Q3=-0.663Q3=-0.330Q3=-0.097Q3=-0.029Q3=-0.007Luego de 7 iteraciones, obtenemos un error de prdida Q < 0.001con lo cual concluye el proceso iterativo.Obteniendo los siguientes caudales finales:Resultados FinalesCircuitoTuberaCaudalQ (l/s)11 (*)-150.3082(**)0.4536

22(**)-0.4533-83.3657

31(*)150.308467.3965

132465770.0 m.85.30 m.51.20 m.91.40 m.+ 1+ 2+ 3100206060