diseno de un canal cerrado[1]
DESCRIPTION
mTRANSCRIPT
DISEO DE TUBERASMtodo Teora lineal1. Datos iniciales:
2. Datos de entrada DATOS DE ENTRADA
TramoLongitudDimetroCaudal
(1-2)3000.20.1
(1-6)4000.150.1
(2-3)4000.10.1
(3-4)2000.250.1
(4-5)3000.10.1
(2-5)3000.150.1
(5-6)5000.20.1
3. Iteraciones.Calculo del coeficiente de friccin:
TRAMO 2-5
Longitud=300Caudal0.135425712
Viscosidad=0.00000115Dimetro0.2
Rugosidad Ks PVC0.000100Velocidad4.310724231
fKs/dRef
0.0010.000500749,6917.2359317.235931230.019099022
0.01910.000500749,6917.5952347.595233940.017334754
0.017330.000500749,6917.5887027.58870190.017364609
0.017360.000500749,6917.588827.588820210.017364068
0.017360.000500749,6917.5888187.588818070.017364078
Tramo 1-6
Longitud=400Caudal0.06457429
Viscosida=1.15E-06Dimetro0.15
Rugosidad Ks PVC0.000100Velocidad3.65414863
fKs/dReffKs/d
0.0010.000667476,6286.9200656.9200650.02088236
0.020882360.000667476,6287.3285937.3285930.0186191
0.01861910.000667476,6287.320017.320010.0186628
0.01866280.000667476,6287.3201897.3201890.01866188
0.018661880.000667476,6287.3201857.3201850.0186619
Tramo 2-3
Longitud=400Caudal0.03450257
Viscosida=0.00000115Dimetro0.15
Rugosidad Ks PVC0.000100Velocidad1.95244166
fKs/dReffKs/d
0.0010.000667254,6666.616325166.616325160.02284369
0.0228440.000667254,6667.220283057.220283050.0191819
0.0191820.000667254,6667.199464547.199464540.01929299
0.0192930.000667254,6667.200173917.200173910.01928919
0.0192890.000667254,6667.200149737.200149730.01928932
Tramo 3-4
Longitud=200Caudal-0.00534118
Viscosidad=0.00000115Dimetro0.25
Rugosidad Ks PVC0.000100Velocidad0.108809313
fKs/dReffKs/d
0.0010.00040023,6544.9209274.920926540.041295834
0.04130.00040023,6546.4009356.400934810.024406932
0.024410.00040023,6546.2076916.207691210.025950145
0.025950.00040023,6546.2306136.230612990.02575956
0.025760.00040023,6546.2278626.227862270.02578232
Tramo 4-5
Longitud=300Caudal0.03600524
Viscosida=1.15E-06Dimetro0.1
Rugosidad Ks PVC0.000100Velocidad4.58431878
fKs/dReffKs/d
0.0010.001000398,6366.6569476.6569470.02256575
0.022565750.001000398,6367.0111757.0111750.02034316
0.020343160.001000398,6367.0049917.0049910.02037909
0.020379090.001000398,6367.0050997.0050990.02037847
0.020378470.001000398,6367.0050977.0050970.02037848
Tramo 2-5
Longitud=300Caudal0.04154814
Viscosida=0.00000115Dimetro0.15
Rugosidad Ks PVC0.000100Velocidad2.35113825
fKs/dReffKs/d
0.0010.000667306,6706.715065536.715065530.02217683
0.0221770.000667306,6707.257343667.257343660.01898649
0.0189860.000667306,6707.241101517.241101510.01907176
0.0190720.000667306,6707.24158367.24158360.01906922
0.0190690.000667306,6707.241569297.241569290.01906929
Tramo 5-6
Longitud=500Caudal0.02473054
Viscosida=0.00000115Dimetro0.2
Rugosidad Ks PVC0.000100Velocidad0.78719562
fKs/dReffKs/d
0.0010.000500136,9046.291498046.291498040.0252634
0.02526340.000500136,9047.202440357.202440350.01927705
0.019277050.000500136,9047.146375257.146375250.01958071
0.019580710.000500136,9047.149723297.149723290.01956237
0.019562370.000500136,9047.149522997.149522990.01956347
TramoLongitudDimetCaudalVelocidadfhfiKmiHFI+km
1-23000.20.13.1830914180.0175779413.616280136.1628
1-64000.150.15.6588291880.0183835980.011640800.1164
2-34000.10.112.732365670.01838359607.5884106158.51
3-42000.250.12.0371785080.017133522.899318028.99318
4-53000.10.112.732365670.01991439493.636704936.367
2-53000.150.15.6588291880.0183835960.008730600.0873
5-65000.20.13.1830914180.0175779422.693790226.9379
Elaboramos la matriz-1.00-1.000.000.000.000.000.00Q1-2-0.2
1.000.00-1.000.000.00-1.000.00Q1-60.06
0.000.001.00-1.000.000.000.00Q2-30.04
0.000.000.001.001.000.000.00Q340.03
0.000.000.000.00-1.001.001.00Q540.03
136.16-800.120.000.000.00600.09-226.94Q250.00
006158.5128.99-4936.367-600.08730Q650.00
-0.461803890.4596069230.277670.276813710.1310.000577172.95E-05Q1-20.143278
-0.53819611-0.45960692-0.27767-0.2768137-0.131-0.0005772-3E-05Q1-60.056722
-0.02363729-0.027659860.4377350.435218170.0072.9542E-058.68E-05Q2-30.033835
-0.02363729-0.02765986-0.562270.435218170.0072.9542E-058.68E-05Q34-0.00617
0.023637290.0276598590.5622650.56478183-0.00670427-2.954E-05-8.7E-05Q540.036165
-0.4381666-0.51273322-0.16006-0.15840450.1242777020.00054763-5.7E-05Q250.049443
0.461803890.5403930770.722330.723186290.869018025-0.0005772-3E-05Q650.016722
Siendo nuestros nuevos caudales para la prxima iteracin:Nuevos
Q1-20.12163894
Q1-60.07836106
Q2-30.06691747
Q340.04691747
Q540.06808253
Q250.07472147
Q650.05836106
Este proceso lo repetiremos durante 9 iteraciones obteniendo finalmente los siguientes resultados:Q1-20.13546767
Q1-60.06453233
Q2-30.03437682
Q34-0.00554506
Q540.03587709
Q250.04140335
Q650.02461046
METODO DE HARDY CROSSCalculo del coeficiente de friccin:
Primera iteracinTubera (1-2)
Longitud=300Caudal0.12
Viscosidad=1.15E-06Dimetro0.2
Rugosidad Ks PVC0.000100Velocidad3.819709702
fKs/dReffKs/d
0.0010.000500664,2977.188227.1882170.019353419
0.019350.000500664,2977.579397.5793880.017407312
0.017410.000500664,2977.571517.5715140.017443538
0.017440.000500664,2977.571677.5716720.017442811
0.017440.000500664,2977.571677.5716680.017442825
Tubera (2-5)
Longitud=300Caudal0.01
Viscosida=1.15E-06Dimetro0.15
Rugosidad Ks PVC0.000100Velocidad0.56588
fKs/dReffKs/d
0.0010.00066773,8115.80235.8023390.0297
0.0297030.00066773,8116.84626.8461810.02134
0.0213360.00066773,8116.76816.768120.02183
0.0218310.00066773,8116.77376.7737210.02179
0.0217940.00066773,8116.77336.7733180.0218
Tubera (5-6)
Longitud=500Caudal-0.04
Viscosida=1.15E-06Dimetro0.2
Rugosidad Ks PVC0.000100Velocidad1.2732366
fKs/dReffKs/d
0.0010.000500221,4326.613276.61327020.0228648
0.0228650.000500221,4327.3551547.35515430.0184849
0.0184850.000500221,4327.3210667.32106570.0186574
0.0186570.000500221,4327.3226037.3226030.0186496
0.018650.000500221,4327.3225347.32253360.0186499
Tubera (1-6)
Longitud=400Caudal-0.08
Viscosida=1.15E-06Dimetro0.15
Rugosidad Ks PVC0.000100Velocidad4.527063
fKs/dReffKs/d
0.0010.000667590,4877.00457.00450.020382
0.02038210.000667590,4877.35587.35580.018482
0.01848190.000667590,4877.34967.34960.018513
0.01851280.000667590,4877.34977.34970.018512
0.01851230.000667590,4877.34977.34970.018512
Tubera (2-3)
Longitud=400Caudal0.05
Viscosida=1.15E-06Dimetro0.1
Rugosidad Ks PVC0.000100Velocidad6.366182837
fKs/dReffKs/d
0.0010.001000553,5816.766736.7667310.021839476
0.021840.001000553,5817.043017.0430070.020159684
0.020160.001000553,5817.03947.0393990.020180354
0.020180.001000553,5817.039457.0394460.020180085
0.020180.001000553,5817.039457.0394460.020180088
Tubera (3-4)
Longitud=200Caudal0.01
Viscosida=1.15E-06Dimetro0.25
Rugosidad Ks PVC0.000100Velocidad0.20372
fKs/dReDenomindenominaG(f)
0.0010.00040044,2865.44235.4423220.03376
0.0337620.00040044,2866.76066.7606460.02188
0.0218790.00040044,2866.61736.6173460.02284
0.0228370.00040044,2866.63186.6318260.02274
0.0227370.00040044,2866.63046.630352Correcin
Tubera (4-5)
Longitud=300Caudal-0.02
Viscosida=1.15E-06Dimetro0.1
Rugosidad Ks PVC0.000100Velocidad2.5464731
fKs/dReDenomindenominaG(f)
0.0010.001000221,4326.4030816.40308070.0243906
0.0243910.001000221,4326.9297896.92978910.0208238
0.0208240.001000221,4326.9147946.91479370.0209142
0.0209140.001000221,4326.9152176.91521710.0209117
0.0209120.001000221,4326.9152056.91520510.0209117
UNIVERSIDAD NACIONAL DE CAJAMARCA FACULTAD DE INGENIERAEscuela Acadmico Profesional de Ingeniera Civil
METODOS NUMERICOS
CIRCUITOTUBERALONGITDIAMETROCAUDALVELOCIDADfhfiKmiHFI+kmCorrecinNuevo
supuestoCaudal
I(1-2)3000.20.1203.819710.0174419.4567280162.13940.018090.138
I(2-5)3000.150.0100.5658830.02180.7115104071.151040.018090.0162930.044
I(5-6)5000.2-0.0401.2732370.01865-3.852445096.311130.01809-0.022
I(6-1)4000.15-0.0804.5270630.01851-51.566020644.57520.01809-0.062
sumas-35.25022974.1768
Correcin Q=
0.0180923
CIRCUITOTUBERALONGITDIAMETROCAUDALVELOCIDADfhfiKmiHFI+kmCorrecinNuevo
supuestoCaudal
II(2-3)4000.10.0506.3661830.02016166.57236103352.104-0.016290.034
II(3-4)2000.250.0100.2037180.021880.037023103.70231-0.01629-0.006
II(4-5)3000.1-0.0202.5464730.02082-20.6471601032.358-0.01629-0.036
II(2-5)3000.15-0.0100.5658830.02134-0.696446069.6446-0.01629-0.01809-0.044
sumas145.265774457.809
Correcin Q=
-0.016293
Podemos apreciar el valor de los nuevos caudales, que para 9 iteraciones es el siguiente:
CIRCUITOTUBERALONGITDIAMETROCAUDALVELOCIDADfhfiKmiHFI+kmCorrecinNuevo
Caudal
I(1-2)3000.20.1354.3103760.0188326.7460330197.5119-8.7E-090.13541
I(2-5)3000.150.0422.3566450.0205811.6520760279.7922-8.7E-092.28E-090.04165
I(5-6)5000.2-0.0250.782570.02064-1.610823065.51998-8.7E-09-0.02459
I(6-1)4000.15-0.0653.6547670.02026-36.787270569.5927-8.7E-09-0.06459
sumas1.943E-051112.417
Correcin Q=
-8.73E-09
CIRCUITOTUBERALONGITDIAMETROCAUDALVELOCIDADfhfiKmiHFI+kmCorrecinNuevo
Caudal
II(2-3)4000.10.0344.2996340.022384.048526102498.324-2.3E-090.03377
II(3-4)2000.25-0.0060.126930.02430.01596330-2.56204-2.3E-09-0.00623
II(4-5)3000.1-0.0364.6130220.02226-72.4426701999.485-2.3E-09-0.03623
II(2-5)3000.15-0.041652.3566450.02053-11.621790279.0651-2.3E-098.73E-09-0.04165
sumas2.173E-054774.312
Correcin Q=
-2.28E-09
Que como podemos notar en ambos mtodos los resultados coinciden por lo que podemos decir que no hubo errores al realizar el diseo de tuberas.MODELADOS MATEMATICOS.
1) Analizaremos las propiedades fisicas del agua tales como la viscosidad y la densidadPARA LA VISCOSIDAD (MODELO LINEAL)
Modelo polinmico
Modelo exponencial
Siendo el mejor modelo el polinomico puesto que (r cuadrado=0.9997) ms prximo a uno