diseno de un canal cerrado[1]

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


Viscosida=1.15E-06Dimetro0.15


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


Viscosida=0.00000115Dimetro0.15


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


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




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




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




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)


Viscosidad=1.15E-06Dimetro0.2


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)




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)




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)




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)




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)




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)




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


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:


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


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

diseno de un canal cerrado[1]

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