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Nudo Cota Demanda(l/s)
1 100.00 02 95.00 603 95.00 404 95.00 305 95.00 306 95.00 40
NT 7 = Numero de TuberiasNN 6 = Numero de NudosNS 1 = Numero de Nudos con Cota Piezometrica Conocida
1T 14.971 = Temperatura
Solución :Primer Paso :
Matriz de Conectividad de Dimensión 0
1 2 3 41 -1 1 0 02 0 -1 1 03 0 0 1 -1
At 4 0 0 0 15 0 -1 0 06 0 0 0 07 -1 0 0 0
Segundo Paso :Matriz de Nudo sin Datos Dimensión A12 = NT
2 3 4 51 1 0 0 02 -1 1 0 03 0 1 -1 0
A12 4 0 0 1 -15 -1 0 0 16 0 0 0 17 0 0 0 0
Tercer Paso :Matriz de Nudos sin Datos de Dimensión NN
1 2 3 42 1 -1 0 0
A21 3 0 1 1 04 0 0 -1 15 0 0 0 -16 0 0 0 0
Cuarto Paso :Matriz Topologica de Cota Piezometrica Conocida
11 -12 03 0
A10 4 05 06 07 -1
Sesto Paso :=
1 2 3 41 1 0 0 02 0 1 0 03 0 0 1 0
I= 4 0 0 0 15 0 0 0 06 0 0 0 07 0 0 0 0
Septimo Paso :
Conciderando: DARCY W; m=2N=m x I = 2 x I
1 2 3 41 2 0 0 0
Obtencion de la Matriz Identidad (NT x NT)
Difinición Matriz Diagonal (N) de Dimensión (NT x NT)*2
2 0 2 0 03 0 0 2 0
Ndw 4 0 0 0 25 0 0 0 06 0 0 0 07 0 0 0 0
Octavo Paso PROCESO DE ITERACIÓN: PRIMERA ITERACIÓN
Calculo de la Viscocidad Cinematica
Ѵ = m =r
Ѵ = 1.1409 x
Ks = 0.00006
Tuberia Q L D V
(i) (j) (m) (m) (m/s)1 2 0.100 500.00 0.25 2.037182 3 0.100 400.00 0.15 5.658844 3 0.100 200.00 0.10 12.732405 4 0.100 400.00 0.15 5.658842 5 0.100 200.00 0.10 12.732406 5 0.100 600.00 0.20 3.183101 6 0.100 300.00 0.25 2.03718
Calculo de la Matriz A11
1 2 3 4 5 6 71 67.3852 0 0 0 0 0 02 0 888.5422 0 0 0 0 0
A11 3 0 0 2940.589 0 0 0 04 0 0 0 725.3287 0 0 05 0 0 0 0 2940.589 0 06 0 0 0 0 0 250.17612004 07 0 0 0 0 0 0 40.43112
Finalmente:
=
(1.14 - 0.031 (T-15) + 0.00068 (T - 15)2)
10-6 m2/s
(m3/s)
A11 = αij x Qij(nj-1)+βi+(gi/Qi)
H(next) [(A21 x Ndw-1 x A11
-1 x A12)] [A21 x Ndw-1 x (Qa x A11
-1 x A10 x Hn) + q - A21 x Qa]
Calculo de Matrices por Partes para el calculo del (H next)
1 2 3 4 5 6 71 0.5 0 0 0 0 0 02 0 0.5 0 0 0 0 03 0 0 0.5 0 0 0 0
4 0 0 0 0.5 0 0 05 0 0 0 0 0.5 0 06 0 0 0 0 0 0.5 07 0 0 0 0 0 0 0.5
1 2 3 4 5 6 71 67.3852 0 0 0 0 0 02 0 888.5422 0 0 0 0 0
A11 ' 3 0 0 2940.589 0 0 0 04 0 0 0 725.3287 0 0 05 0 0 0 0 2940.589 0 06 0 0 0 0 0 250.17612004 07 0 0 0 0 0 0 40.43112
1 2 3 4 5 6 71 134.7704 0 0 0 0 0 02 0 1777.084 0 0 0 0 03 0 0 5881.177 0 0 0 0
4 0 0 0 1450.657 0 0 05 0 0 0 0 5881.177 0 06 0 0 0 0 0 500.35224008 07 0 0 0 0 0 0 80.86225
1 2 3 4 5 6 71 0.0074 0 0 0 0 0 02 0 0.0006 0 0 0 0 03 0 0 0.0002 0 0 0 0
4 0 0 0 0.0007 0 0 05 0 0 0 0 0.0002 0 06 0 0 0 0 0 0.0020 07 0 0 0 0 0 0 0.0124
[A21] [([N] x [A11]')-1]
Ndw-1
[N] x [A11']
[N] x [A11']
([N] x [A11])-1
([N] x [A11])-1
1 2 3 4 5 6 71 0.00742 -0.00056 0 0 -0.00017 0 02 0 0.000563 0.00017 0 0 0 03 0 0 -0.00017 0.000689 0 0 04 0 0 0 -0.00069 0.00017 0.001998592 05 0 0 0 0 0 -0.001998592 0.012367
[A21] [([N] x [A11])-1][A12]1 2 3 4 5 6 7
1 0.008153 -0.00056 0 -0.00017 02 -0.00056 0.000733 -0.00017 0 03 0 -0.00017 0.000859 -0.00069 04 -0.00017 0 -0.00069 0.002858 -0.0025 0 0 0 -0.002 0.014365
.-([A12])([N][A11]')-1[A12])-11 2 3 4 5 6 7
1 -130.536 -108.632 -36.1407 -18.2599 -2.540432 -108.632 -1539.82 -395.086 -112.725 -15.6833 -36.1407 -395.086 -1583 -425.353 -59.17784 -18.2599 -112.725 -425.353 -502.466 -69.90635 -2.54043 -15.683 -59.1778 -69.9063 -79.338
[A11][Q] [A10][Ho]1 1
1 6.73852 1 -100 12 88.85422 2 0 23 294.0589 3 0 34 72.53287 4 0 45 294.0589 5 0 56 25.01761 6 0 67 4.043112 7 -100 7
[A21][Q]
1 11 -0.792 1 -0.1 12 0.100 2 0.2 23 0.000 3 0 34 0.050 4 0.1 45 -1.237 5 0 5
Hi+1=-([A12])([N][A11]')-1[A12])-1(([A21][N][A11'])-1([A11][Q]+[A10][Ho])-[A21][Q]-[q])
[A21] [([N] x [A11])-1]
([A21][N][A11'])-1([A11][Q]+[A10][Ho])
([A21][N][A11'])-1([A11][Q]+[A10][Ho])-[A21][Q]-[q]
H2 91.33828H3 170.2142H4 = 78.37967H5 99.2474H6 97.11081
Cálculo de Qi+1Para el cálculo de Qi+1 se utilizará la Ecuación
de la resolución sistemática de esta ecuación resultan las siguientes matrices:
[A12][Hi+1] [A12][Hi+1]+[A10][Ho]91.33828 -8.6617278.87591 78.8759191.83452 91.83452-20.8677 -20.86777.909113 7.909113
2.13659 2.1365997.11081 -2.88919
([N] x [A11])-1[A11]
0.5 0 0 0 0 0 00 0.5 0 0 0 0 00 0 0.5 0 0 0 00 0 0 0.5 0 0 00 0 0 0 0.5 0 00 0 0 0 0 0.5 00 0 0 0 0 0 0.5
[I]-(([N] x [A11])-1[A11])0.5 0 0 0 0 0 0
0 0.5 0 0 0 0 00 0 0.5 0 0 0 00 0 0 0.5 0 0 00 0 0 0 0.5 0 00 0 0 0 0 0.5 00 0 0 0 0 0 0.5
Luego
Tuberia No Q(m3/s)1 2 0.11432 3 0.00564 3 0.03445 4 0.06442 5 0.04876 5 0.04571 6 0.0857
Nudo Nudo Longitud Diametro Rugosidad Velocidad KInicial Final (m) (mm) Ks(m) V(m/s) Local
1 1 2 500 250 0.00006 2.037183272 02 2 3 400 150 0.00006 5.658842421 16.321354513 4 3 200 100 0.00006 12.73239545 04 5 4 400 150 0.00006 5.658842421 05 2 5 200 100 0.00006 12.73239545 06 6 5 600 200 0.00006 3.183098862 07 1 6 300 250 0.00006 2.037183272 0
x NT = 7 x 6
Numero de Nudos
5 60 00 00 0
-1 01 01 -10 1
x NN = 7 x 5Numero de Nudos
600000
-11
x NT = 5 x 7
5 6 7-1 0 00 0 00 0 01 1 00 -1 1
Q(m3/s) H(m) q(m3/s)1 0.1 2 95 2 0.062 0.1 3 95 3 0.043 0.1 4 95 4 0.034 0.1 5 95 5 0.035 0.1 6 95 6 0.046 0.17 0.1 Quinto Paso :
Vector de Cota Piezometrica Fija
Ho = 1 100
7 X 7
5 6 70 0 00 0 00 0 00 0 01 0 00 1 00 0 1
5 6 70 0 0
0 0 00 0 00 0 02 0 00 2 00 0 2
x
V Re f hf hf+hm B=hl α = hf
(m/s) (m) (m) (m) (m)2.03718 446398.46525 0.01593 6.739 6.739 0.000 673.8525.65884 743997.44209 0.01667 72.533 88.854 16.321 8885.422
12.73240 1115996.16313 0.01780 294.059 294.059 0.000 29405.8875.65884 743997.44209 0.01667 72.533 72.533 0.000 7253.287
12.73240 1115996.16313 0.01780 294.059 294.059 0.000 29405.8873.18310 557998.08157 0.01615 25.018 25.018 0.000 2501.7612.03718 446398.46525 0.01593 4.043 4.043 0.000 404.311
10-6 m2/s
[A21 x Ndw-1 x (Qa x A11
-1 x A10 x Hn) + q - A21 x Qa]
([A11][Q]+[A10][Ho])1
-93.26188.854294.0672.533294.0625.018
-95.957
1-0.63-0.060.03-0.02-1.20
Hi+1=-([A12])([N][A11]')-1[A12])-1(([A21][N][A11'])-1([A11][Q]+[A10][Ho])-[A21][Q]-[q])
([A21][N][A11'])-1([A11][Q]+[A10][Ho])-[A21][Q]-[q]
([N] x [A11])-1([A12][Hi+1]+[A10][Ho])-0.06430.04440.0156
-0.01440.00130.0043
-0.0357
([I]-(([N] x [A11])-1)[A11])[Q]0.050.050.050.050.050.050.05
α = hf
(m) (m)673.852 0
8885.422 029405.887 07253.287 0
29405.887 02501.761 0404.311 0
g = hBomba
Re D K f X0 0.001### 0.005701943 0.010460428446398.4653 0.25 0.00006 0.015929 X1 0.002542613### 0.010460428 0.014589634743997.4421 0.15 0.00006 0.016666 F(X) 24.39219263### 5.530051343 1.9333874161115996.163 0.10 0.00006 0.017795 F'(X) -15812.2569### -1162.1454 -468.222523743997.4421 0.15 0.00006 0.016666 ERROR 6067038073### 4549034788 28302330131115996.163 0.10 0.00006 0.017795 X0 0.001### 0.005687625 0.010510936557998.0816 0.20 0.00006 0.016149 X1 0.002535874### 0.010510936 0.014922292446398.4653 0.25 0.00006 0.015929 F(X) 24.28563705### 5.626553556 2.050653931
F'(X) -15812.257### -1166.53331 -464.85792ERROR 6056586670### 4588850571 2956218917X0 0.001### 0.00573291 0.010739438X1 0.002540382### 0.010739438 0.015574788F(X) 24.35692246### 5.771269518 2.176529776F'(X) -15812.257### -1152.74892 -450.128653ERROR 6063584760### 4661815505 3104601060X0 0.001### 0.005687625 0.010510936X1 0.002535874### 0.010510936 0.014922292F(X) 24.28563705### 5.626553556 2.050653931F'(X) -15812.257### -1166.53331 -464.85792ERROR 6056586670### 4588850571 2956218917X0 0.001### 0.00573291 0.010739438X1 0.002540382### 0.010739438 0.015574788F(X) 24.35692246### 5.771269518 2.176529776F'(X) -15812.257### -1152.74892 -450.128653ERROR 6063584760### 4661815505 3104601060X0 0.001### 0.005685652 0.010447283X1 0.002538035### 0.010447283 0.014660663F(X) 24.31981018### 5.557490552 1.976517217F'(X) -15812.257### -1167.14009 -469.104856ERROR 6059944556### 4557769931 2873935773X0 0.001### 0.005701943 0.010460428X1 0.002542613### 0.010460428 0.014589634F(X) 24.39219263### 5.530051343 1.933387416F'(X) -15812.2569### -1162.1454 -468.222523ERROR 6067038073### 4549034788 2830233013
0.014589634 0.015895086 0.015930594 0.015929193 0.01592925 0.015929248 0.0159292480.015895086 0.015930594 0.015929193 0.01592925 0.015929248 0.015929248 0.0159292480.371528304 0.00889025 -0.00034968 1.43857E-05 -5.90801E-07 2.42651E-08 -9.96602E-10-284.597439 -250.371595 -249.537872 -249.570686 -249.569336 -249.569391 -249.569389
821292839 22289326.6 879705.2731 36186.18337 1486.123441 61.03733246 2.5068884690.014922292 0.016556432 0.01666745 0.016665991 0.016666018 0.016666017 0.0166660170.016556432 0.01666745 0.016665991 0.016666018 0.016666017 0.016666017 0.016666017
0.44965447 0.026152937 -0.00034024 6.17098E-06 -1.11507E-07 2.01503E-09 -3.64135E-11-275.162919 -235.572362 -233.231297 -233.261806 -233.261253 -233.261263 -233.261262
987011629 66608087.66 875315.1959 15873.72223 286.8329067 5.183312106 0.0936683080.015574788 0.017598007 0.017794983 0.017795288 0.017795286 0.017795286 0.0177952860.017598007 0.017794983 0.017795288 0.017795286 0.017795286 0.017795286 0.0177952860.522208273 0.04235919 6.44717E-05 -4.36714E-07 2.96383E-09 -2.01146E-11 1.37668E-13-258.107707 -215.046693 -211.500375 -211.494963 -211.495 -211.495 -211.4951149686137 110692268 171298.2285 1160.357963 7.874946655 0.053445586 0.000366533
0.014922292 0.016556432 0.01666745 0.016665991 0.016666018 0.016666017 0.0166660170.016556432 0.01666745 0.016665991 0.016666018 0.016666017 0.016666017 0.016666017
0.44965447 0.026152937 -0.00034024 6.17098E-06 -1.11507E-07 2.01503E-09 -3.64135E-11-275.162919 -235.572362 -233.231297 -233.261806 -233.261253 -233.261263 -233.261262
987011629 66608087.66 875315.1959 15873.72223 286.8329067 5.183312106 0.0936683080.015574788 0.017598007 0.017794983 0.017795288 0.017795286 0.017795286 0.0177952860.017598007 0.017794983 0.017795288 0.017795286 0.017795286 0.017795286 0.0177952860.522208273 0.04235919 6.44717E-05 -4.36714E-07 2.96383E-09 -2.01146E-11 1.37668E-13-258.107707 -215.046693 -211.500375 -211.494963 -211.495 -211.495 -211.4951149686137 110692268 171298.2285 1160.357963 7.874946655 0.053445586 0.000366533
0.014660663 0.016086236 0.016150677 0.016148936 0.016148988 0.016148986 0.0161489860.016086236 0.016150677 0.016148936 0.016148988 0.016148986 0.016148986 0.0161489860.402778394 0.01584861 -0.00042573 1.27794E-05 -3.82514E-07 1.14505E-08 -3.42766E-10-282.538003 -245.937653 -244.47237 -244.511775 -244.510592 -244.510627 -244.510626
886206374 39900232.37 1078346.103 32364.11132 968.7336809 28.99880439 0.8680692870.014589634 0.015895086 0.015930594 0.015929193 0.01592925 0.015929248 0.0159292480.015895086 0.015930594 0.015929193 0.01592925 0.015929248 0.015929248 0.0159292480.371528304 0.00889025 -0.00034968 1.43857E-05 -5.90801E-07 2.42651E-08 -9.96602E-10-284.597439 -250.371595 -249.537872 -249.570686 -249.569336 -249.569391 -249.569389
821292839 22289326.6 879705.2731 36186.18337 1486.123441 61.03733246 2.506888469
0.0159292480.0159292484.09317E-11-249.5693890.1029600980.0166660170.0166660176.59028E-13-233.2612620.0016945440.0177952860.017795286
0-211.495
00.0166660170.0166660176.59028E-13-233.2612620.0016945440.0177952860.017795286
0-211.495
00.0161489860.0161489861.02602E-11-244.5106260.0259848880.0159292480.0159292484.09317E-11-249.5693890.102960098
Octavo Paso PROCESO DE ITERACIÓN: SEGUNDA ITERACIÓN
Calculo de la Viscocidad Cinematica
Ѵ = m =r
Ѵ = 1.1409 x
Ks = 0.00006
Tuberia Q L D V
(i) (j) (m) (m) (m/s)1 2 0.114 500.00 0.25 2.327892 3 0.006 400.00 0.15 0.317744 3 0.034 200.00 0.10 4.378045 4 0.064 400.00 0.15 3.643452 5 0.049 200.00 0.10 6.194976 5 0.046 600.00 0.20 1.455631 6 0.086 300.00 0.25 1.74647
Calculo de la Matriz A11
1 2 3 4 5 6 71 76.16056 0 0 0 0 0 02 0 65.34927 0 0 0 0 0
A11 3 0 0 1050 0 0 0 04 0 0 0 477.5931 0 0 05 0 0 0 0 1462.112 0 06 0 0 0 0 0 122.167423 07 0 0 0 0 0 0 35.14234
Finalmente:
=
1 2 3 4 5 6 71 0.5 0 0 0 0 0 02 0 0.5 0 0 0 0 03 0 0 0.5 0 0 0 0
4 0 0 0 0.5 0 0 05 0 0 0 0 0.5 0 06 0 0 0 0 0 0.5 07 0 0 0 0 0 0 0.5
(1.14 - 0.031 (T-15) + 0.00068 (T - 15)2)
10-6 m2/s
(m3/s)
A11 = αij x Qij(nj-1)+βi+(gi/Qi)
H(next) [(A21 x Ndw-1 x A11
-1 x A12)] [A21 x Ndw-1 x (Qa x A11
-1 x A10 x Hn) + q - A21 x Qa]
Calculo de Matrices por Partes para el calculo del (H next)
Ndw-1
1 2 3 4 5 6 71 76.16056 0 0 0 0 0 02 0 65.34927 0 0 0 0 0
A11 ' 3 0 0 1050 0 0 0 04 0 0 0 477.5931 0 0 05 0 0 0 0 1462.112 0 06 0 0 0 0 0 122.167423 07 0 0 0 0 0 0 35.14234
1 2 3 4 5 6 71 152.3211 0 0 0 0 0 02 0 130.6985 0 0 0 0 03 0 0 2100 0 0 0 0
4 0 0 0 955.1861 0 0 05 0 0 0 0 2924.225 0 06 0 0 0 0 0 244.33484599 07 0 0 0 0 0 0 70.28467
1 2 3 4 5 6 71 0.0066 0 0 0 0 0 02 0 0.0077 0 0 0 0 03 0 0 0.0005 0 0 0 0
4 0 0 0 0.0010 0 0 05 0 0 0 0 0.0003 0 06 0 0 0 0 0 0.0041 07 0 0 0 0 0 0 0.0142
[A21] [([N] x [A11]')-1]1 2 3 4 5 6 7
1 0.006565 -0.00765 0 0 -0.00034 0 02 0 0.007651 0.000476 0 0 0 03 0 0 -0.00048 0.001047 0 0 04 0 0 0 -0.00105 0.000342 0.0040927441 05 0 0 0 0 0 -0.0040927441 0.014228
[A21] [([N] x [A11])-1][A12]1 2 3 4 5 6 7
1 0.014558 -0.00765 0 -0.00034 02 -0.00765 0.008127 -0.00048 0 03 0 -0.00048 0.001523 -0.00105 04 -0.00034 0 -0.00105 0.005482 -0.004095 0 0 0 -0.00409 0.018321
[N] x [A11']
[N] x [A11']
([N] x [A11])-1
([N] x [A11])-1
[A21] [([N] x [A11])-1]
.-([A12])([N][A11]')-1[A12])-11 2 3 4 5 6 7
1 -140.672 -135.888 -59.0236 -24.0619 -5.375322 -135.888 -257.042 -103.694 -33.9429 -7.582693 -59.0236 -103.694 -821.43 -192.706 -43.04974 -24.0619 -33.9429 -192.706 -264.92 -59.18195 -5.37532 -7.58269 -43.0497 -59.1819 -67.8044
[A11][Q] [A10][Ho]1 1
1 8.70288 1 -100 12 0.366935 2 0 23 36.10428 3 0 34 30.74984 4 0 45 71.13934 5 0 56 5.586695 6 0 67 3.012746 7 -100 7
[A21][Q]
1 11 -0.627 1 0.06 12 0.020 2 0.04 23 0.015 3 0.03 34 0.015 4 0.03 45 -1.403 5 0.04 5
Hi+1=-([A12])([N][A11]')-1[A12])-1(([A21][N][A11'])-1([A11][Q]+[A10][Ho])-[A21][Q]-[q])
H2 91.7083H3 88.56631H4 = 80.08239H5 90.55126H6 96.79752
Cálculo de Qi+1Para el cálculo de Qi+1 se utilizará la Ecuación
de la resolución sistemática de esta ecuación resultan las siguientes matrices:
([A21][N][A11'])-1([A11][Q]+[A10][Ho])
([A21][N][A11'])-1([A11][Q]+[A10][Ho])-[A21][Q]-[q]
[A12][Hi+1] [A12][Hi+1]+[A10][Ho]91.7083 -8.2917
-3.14199 -3.141998.483929 8.483929-10.4689 -10.4689-1.15704 -1.15704-6.24626 -6.2462696.79752 -3.20248
([N] x [A11])-1[A11]
0.5 0 0 0 0 0 00 0.5 0 0 0 0 00 0 0.5 0 0 0 00 0 0 0.5 0 0 00 0 0 0 0.5 0 00 0 0 0 0 0.5 00 0 0 0 0 0 0.5
[I]-(([N] x [A11])-1[A11])0.5 0 0 0 0 0 0
0 0.5 0 0 0 0 00 0 0.5 0 0 0 00 0 0 0.5 0 0 00 0 0 0 0.5 0 00 0 0 0 0 0.5 00 0 0 0 0 0 0.5
Luego
Tuberia No Q(m3/s)1 2 0.11162 3 0.02684 3 0.01325 4 0.04322 5 0.02476 5 0.04841 6 0.0884
x
V Re f hf hf+hm B=hl
(m/s) (m) (m) (m)2.32789 510100.28973 0.01576 6.665 6.665 0.0000.31774 41775.37409 0.02299 100.062 116.384 16.3214.37804 383735.40411 0.01848 305.366 305.366 0.0003.64345 479022.83537 0.01704 74.178 74.178 0.0006.19497 542989.96531 0.01819 300.505 300.505 0.0001.45563 255171.56834 0.01724 26.715 26.715 0.0001.74647 382696.64077 0.01615 4.099 4.099 0.000
510100.28973
Q(m3/s)1
1 0.11432 0.00563 0.03444 0.06445 0.04876 0.04577 0.0857
10-6 m2/s
[A21 x Ndw-1 x (Qa x A11
-1 x A10 x Hn) + q - A21 x Qa]
([A11][Q]+[A10][Ho])1
-91.2970.366936.104
30.7571.1395.5867
-96.987
1-0.630.020.020.01-1.40
Hi+1=-([A12])([N][A11]')-1[A12])-1(([A21][N][A11'])-1([A11][Q]+[A10][Ho])-[A21][Q]-[q])
([A21][N][A11'])-1([A11][Q]+[A10][Ho])-[A21][Q]-[q]
([N] x [A11])-1([A12][Hi+1]+[A10][Ho])-0.0544-0.02400.0040
-0.0110-0.0004-0.0256-0.0456
([I]-(([N] x [A11])-1)[A11])[Q]0.060.000.020.030.020.020.04
α = hf
(m) (m)666.496 0
11638.362 030536.578 07417.768 0
30050.497 02671.504 0409.920 0
g = hBomba
Re D K f X0 0.001 0.00253734 0.00567397510100.29 0.25 0.00006 0.01575535 X1 0.00253734 0.00567397 0.01037496
41775.3741 0.15 0.00006 0.0229915 F(X) 24.3087784 12.2733415 5.50365175383735.404 0.10 0.00006 0.01847954 F'(X) -15812.2569 -3912.90247 -1170.74322479022.835 0.15 0.00006 0.01704395 ERROR 6058861187 5528109786 4531091414542989.965 0.10 0.00006 0.01818538 X0 0.001 0.00265873 0.00638769255171.568 0.20 0.00006 0.01724468 X1 0.00265873 0.00638769 0.01289682382696.641 0.25 0.00006 0.01615021 F(X) 26.2282243 13.6035055 6.38061114
F'(X) -15812.257 -3648.06618 -980.255303ERROR 6238802102 5837733117 5047081785X0 0.001 0.00256561 0.00585787X1 0.00256561 0.00585787 0.01110089F(X) 24.7558132 12.6699893 5.85167695F'(X) -15812.257 -3848.41879 -1116.08908ERROR 6102290063 5620233699 4723063624X0 0.001 0.00254922 0.00575518X1 0.00254922 0.00575518 0.01070869F(X) 24.4967383 12.4569798 5.67705964F'(X) -15812.257 -3885.57186 -1146.06871ERROR 6077238620 5570558141 4625689359X0 0.001 0.00255573 0.00580769X1 0.00255573 0.00580769 0.01095212F(X) 24.5996045 12.5875377 5.81614114F'(X) -15812.257 -3870.7489 -1130.57192ERROR 6087223796 5599406775 4697195249X0 0.001 0.00256898 0.00585163X1 0.00256898 0.00585163 0.01096379F(X) 24.8091727 12.6081033 5.71475897F'(X) -15812.257 -3840.84008 -1117.87385ERROR 6107410035 5609794996 4662772885X0 0.001 0.00254894 0.00573593X1 0.00254894 0.00573593 0.01056593F(X) 24.4922176 12.3853544 5.56339733F'(X) -15812.2569 -3886.22541 -1151.8402ERROR 6076798635 5556186835 4571302031
0.01037496 0.01443349 0.01571758 0.0157567 0.0157553 0.01575535 0.01575535 0.015755350.01443349 0.01571758 0.0157567 0.0157553 0.01575535 0.01575535 0.01575535 0.015755351.92377907 0.37137873 0.00995838 -0.00035497 1.33622E-05 -5.0204E-07 1.88635E-08 -7.0878E-10
-474.009333 -289.214107 -254.610066 -253.665872 -253.699552 -253.698285 -253.698332 -253.698332811881710 816980687 24822650.5 888185.22 33429.4117 1255.99731 47.1929911 1.773232660.01289682 0.01994922 0.02294303 0.02299611 0.02299105 0.02299154 0.0229915 0.02299150.01994922 0.02294303 0.02299611 0.02299105 0.02299154 0.0229915 0.0229915 0.02299152.41371599 0.53385847 0.00768416 -0.00072978 7.08413E-05 -6.8625E-06 6.64918E-07 -6.4423E-08
-342.254836 -178.320815 -144.746539 -144.248609 -144.295937 -144.291344 -144.291789 -144.2917453535173397 1304888488 23085203.5 2200497.81 213532.538 20685.9768 2004.28293 194.1937040.01110089 0.01621555 0.01831464 0.01848214 0.01847948 0.01847954 0.01847954 0.018479540.01621555 0.01831464 0.01848214 0.01847948 0.01847954 0.01847954 0.01847954 0.018479542.19094678 0.51010547 0.03393557 -0.00053263 1.21021E-05 -2.7361E-07 6.18681E-09 -1.3989E-10
-428.366124 -243.012121 -202.599609 -199.86345 -199.906498 -199.90552 -199.905542 -199.9055413154170170 1146129342 90628391 1442130.19 32759.8314 740.666591 16.7475309 0.3786880.01070869 0.01527271 0.0169477 0.01704611 0.01704389 0.01704395 0.01704395 0.017043950.01527271 0.0169477 0.01704611 0.01704389 0.01704395 0.01704395 0.01704395 0.017043952.06323463 0.44517276 0.02238824 -0.00050068 1.34644E-05 -3.607E-07 9.66409E-09 -2.5892E-10
-452.064949 -265.777093 -227.491659 -225.531927 -225.575823 -225.574643 -225.574675 -225.5746742988351025 988326230 57733672.9 1302527.66 35020.6359 938.190613 25.1362464 0.673456180.01095212 0.01594573 0.01800814 0.01818693 0.01818535 0.01818538 0.01818538 0.018185380.01594573 0.01800814 0.01818693 0.01818535 0.01818538 0.01818538 0.01818538 0.018185382.18273963 0.51391912 0.03714744 -0.00032335 5.24501E-06 -8.4728E-08 1.3688E-09 -2.2114E-11
-437.106044 -249.183885 -207.77164 -204.728159 -204.754717 -204.754286 -204.754293 -204.7542933131631145 1145264722 98306708.9 868506.835 14086.0652 227.547698 3.67607005 0.05938860.01096379 0.01562791 0.01720516 0.01724662 0.01724459 0.01724469 0.01724468 0.017244680.01562791 0.01720516 0.01724662 0.01724459 0.01724469 0.01724468 0.01724468 0.017244682.03546292 0.40503497 0.00922025 -0.00045014 2.28714E-05 -1.1598E-06 5.88234E-08 -2.9833E-09
-436.409333 -256.797213 -222.423775 -221.625469 -221.664472 -221.66249 -221.662591 -221.6625852984477600 916734125 24035737 1177820.34 59833.1376 3034.26172 153.887202 7.804585720.01056593 0.01478562 0.01612024 0.01615152 0.01615015 0.01615021 0.01615021 0.016150210.01478562 0.01612024 0.01615152 0.01615015 0.01615021 0.01615021 0.01615021 0.016150211.94628637 0.37232453 0.00767021 -0.00033549 1.52054E-05 -6.8811E-07 3.11419E-08 -1.4094E-09
-461.239806 -278.974883 -245.162711 -244.453242 -244.484291 -244.482884 -244.482948 -244.4829452853911123 827913865 19370437.5 849770.369 38509.6731 1742.72978 78.8710912 3.56947547
0.015755350.015755352.6632E-11
-253.6983310.06662821
0.02299150.0229915
6.24196E-09-144.2917518.81533410.018479540.01847954
3.16369E-12-199.9055410.008564940.017043950.01704395
6.93667E-12-225.5746740.018041420.018185380.01818538
3.58824E-13-204.7542930.000963450.017244680.01724468
1.51301E-10-221.6625860.395817920.016150210.01615021
6.37836E-11-244.4829450.16154094
Octavo Paso PROCESO DE ITERACIÓN: SEGUNDA ITERACIÓN
Calculo de la Viscocidad Cinematica
Ѵ = m =r
Ѵ = 1.1409 x
Ks = 0.00006
Tuberia Q L D V
(i) (j) (m) (m) (m/s)1 2 0.1116 500.00 0.25 2.272902 3 0.0268 400.00 0.15 1.519264 3 0.0132 200.00 0.10 1.674635 4 0.0432 400.00 0.15 2.441932 5 0.0247 200.00 0.10 3.147866 5 0.0484 600.00 0.20 1.541551 6 0.0884 300.00 0.25 1.80147
Calculo de la Matriz A11
1 2 3 4 5 6 71 74.50304 0 0 0 0 0 02 0 257.4973 0 0 0 0 0
A11 3 0 0 431.6049 0 0 0 04 0 0 0 329.0185 0 0 05 0 0 0 0 769.9726 0 06 0 0 0 0 0 128.62093865 07 0 0 0 0 0 0 36.14498
Finalmente:
=
1 2 3 4 5 6 71 0.5 0 0 0 0 0 02 0 0.5 0 0 0 0 03 0 0 0.5 0 0 0 0
4 0 0 0 0.5 0 0 05 0 0 0 0 0.5 0 06 0 0 0 0 0 0.5 07 0 0 0 0 0 0 0.5
(1.14 - 0.031 (T-15) + 0.00068 (T - 15)2)
10-6 m2/s
(m3/s)
A11 = αij x Qij(nj-1)+βi+(gi/Qi)
H(next) [(A21 x Ndw-1 x A11
-1 x A12)] [A21 x Ndw-1 x (Qa x A11
-1 x A10 x Hn) + q - A21 x Qa]
Calculo de Matrices por Partes para el calculo del (H next)
Ndw-1
1 2 3 4 5 6 71 74.50304 0 0 0 0 0 02 0 257.4973 0 0 0 0 0
A11 ' 3 0 0 431.6049 0 0 0 04 0 0 0 329.0185 0 0 05 0 0 0 0 769.9726 0 06 0 0 0 0 0 128.62093865 07 0 0 0 0 0 0 36.14498
1 2 3 4 5 6 71 149.0061 0 0 0 0 0 02 0 514.9945 0 0 0 0 03 0 0 863.2099 0 0 0 0
4 0 0 0 658.037 0 0 05 0 0 0 0 1539.945 0 06 0 0 0 0 0 257.2418773 07 0 0 0 0 0 0 72.28996
1 2 3 4 5 6 71 0.0067 0 0 0 0 0 02 0 0.0019 0 0 0 0 03 0 0 0.0012 0 0 0 0
4 0 0 0 0.0015 0 0 05 0 0 0 0 0.0006 0 06 0 0 0 0 0 0.0039 07 0 0 0 0 0 0 0.0138
[A21] [([N] x [A11]')-1]1 2 3 4 5 6 7
1 0.006711 -0.00194 0 0 -0.00065 0 02 0 0.001942 0.001158 0 0 0 03 0 0 -0.00116 0.00152 0 0 04 0 0 0 -0.00152 0.000649 0.0038873919 05 0 0 0 0 0 -0.0038873919 0.013833
[A21] [([N] x [A11])-1][A12]1 2 3 4 5 6 7
1 0.009302 -0.00194 0 -0.00065 02 -0.00194 0.0031 -0.00116 0 03 0 -0.00116 0.002678 -0.00152 04 -0.00065 0 -0.00152 0.006056 -0.003895 0 0 0 -0.00389 0.017721
[N] x [A11']
[N] x [A11']
([N] x [A11])-1
([N] x [A11])-1
[A21] [([N] x [A11])-1]
.-([A12])([N][A11]')-1[A12])-11 2 3 4 5 6 7
1 -132.625 -108.245 -67.3798 -36.228 -7.947412 -108.245 -488.412 -262.421 -90.1454 -19.77533 -67.3798 -262.421 -589.341 -180.519 -39.60084 -36.228 -90.1454 -180.519 -249.412 -54.7145 -7.94741 -19.7753 -39.6008 -54.714 -68.4343
[A11][Q] [A10][Ho]1 1
1 8.312358 1 -100 12 6.913147 2 0 23 5.676702 3 0 34 14.19798 4 0 45 19.03624 5 0 56 6.229019 6 0 67 3.196274 7 -100 7
[A21][Q]
1 11 -0.641 1 0.06 12 0.020 2 0.04 23 0.015 3 0.03 34 0.015 4 0.03 45 -1.363 5 0.04 5
Hi+1=-([A12])([N][A11]')-1[A12])-1(([A21][N][A11'])-1([A11][Q]+[A10][Ho])-[A21][Q]-[q])
H2 92.1433H3 81.30041H4 = 80.39026H5 89.567H6 96.58266
Cálculo de Qi+1Para el cálculo de Qi+1 se utilizará la Ecuación
de la resolución sistemática de esta ecuación resultan las siguientes matrices:
([A21][N][A11'])-1([A11][Q]+[A10][Ho])
([A21][N][A11'])-1([A11][Q]+[A10][Ho])-[A21][Q]-[q]
[A12][Hi+1] [A12][Hi+1]+[A10][Ho]92.1433 -7.8567
-10.8429 -10.84290.910149 0.910149-9.17673 -9.17673
-2.5763 -2.5763-7.01566 -7.0156696.58266 -3.41734
([N] x [A11])-1[A11]
0.5 0 0 0 0 0 00 0.5 0 0 0 0 00 0 0.5 0 0 0 00 0 0 0.5 0 0 00 0 0 0 0.5 0 00 0 0 0 0 0.5 00 0 0 0 0 0 0.5
[I]-(([N] x [A11])-1[A11])0.5 0 0 0 0 0 0
0 0.5 0 0 0 0 00 0 0.5 0 0 0 00 0 0 0.5 0 0 00 0 0 0 0.5 0 00 0 0 0 0 0.5 00 0 0 0 0 0 0.5
Luego
Tuberia No Q(m3/s)1 2 0.10852 3 0.03454 3 0.00555 4 0.03552 5 0.01406 5 0.05151 6 0.0915
x
V Re f hf hf+hm B=hl
(m/s) (m) (m) (m)2.27290 498050.00292 0.01579 6.678 6.678 0.0001.51926 199744.40459 0.01829 79.590 95.911 16.3211.67463 146781.85837 0.01986 328.153 328.153 0.0002.44193 321053.80487 0.01752 76.245 76.245 0.0003.14786 275910.70254 0.01885 311.436 311.436 0.0001.54155 270234.42685 0.01714 26.559 26.559 0.0001.80147 394746.92758 0.01610 4.087 4.087 0.000
498050.00292
Q(m3/s)1
1 0.11162 0.02683 0.01324 0.04325 0.02476 0.04847 0.0884
10-6 m2/s
[A21 x Ndw-1 x (Qa x A11
-1 x A10 x Hn) + q - A21 x Qa]
([A11][Q]+[A10][Ho])1
-91.6886.91315.676714.19819.036
6.229-96.804
1-0.640.020.020.01-1.36
Hi+1=-([A12])([N][A11]')-1[A12])-1(([A21][N][A11'])-1([A11][Q]+[A10][Ho])-[A21][Q]-[q])
([A21][N][A11'])-1([A11][Q]+[A10][Ho])-[A21][Q]-[q]
([N] x [A11])-1([A12][Hi+1]+[A10][Ho])-0.0527-0.02110.0011
-0.0139-0.0017-0.0273-0.0473
([I]-(([N] x [A11])-1)[A11])[Q]0.060.010.010.020.010.020.04
α = hf
(m) (m)667.765 0
9591.122 032815.327 07624.545 0
31143.645 02655.851 0408.744 0
g = hBomba
Re D K f X0 0.001 0.00253827 0.00567888498050.003 0.25 0.00006 0.01578536 X1 0.00253827 0.00567888 0.01038987199744.405 0.15 0.00006 0.01828752 F(X) 24.3234971 12.2821561 5.50821501146781.858 0.10 0.00006 0.01985855 F'(X) -15812.2569 -3910.75072 -1169.22614321053.805 0.15 0.00006 0.01751906 ERROR 6060306499 5530337555 4534214812275910.703 0.10 0.00006 0.01884691 X0 0.001 0.00258293 0.00593665270234.427 0.20 0.00006 0.01714364 X1 0.00258293 0.00593665 0.01127895394746.928 0.25 0.00006 0.01610391 F(X) 25.0296868 12.7769424 5.84428502
F'(X) -15812.257 -3809.78294 -1093.96387ERROR 6128426923 5649179254 4736523803X0 0.001 0.00260104 0.00604937X1 0.00260104 0.00604937 0.01170995F(X) 25.3160458 13.0004437 6.02034293F'(X) -15812.257 -3770.07252 -1063.55519ERROR 6155383051 5700311231 4833994533X0 0.001 0.00256356 0.00583055X1 0.00256356 0.00583055 0.01093892F(X) 24.7233403 12.5878778 5.7414732F'(X) -15812.257 -3853.04304 -1123.93528ERROR 6099167630 5603237056 4669900868X0 0.001 0.0025765 0.00591491X1 0.0025765 0.00591491 0.01127567F(X) 24.9280468 12.7662151 5.89682405F'(X) -15812.257 -3824.04575 -1099.99638ERROR 6118768013 5644054039 4754276268X0 0.001 0.0025665 0.00583787X1 0.0025665 0.00583787 0.01091935F(X) 24.7698709 12.5830803 5.70051756F'(X) -15812.257 -3846.41967 -1121.82333ERROR 6103640250 5603710175 4653643437X0 0.001 0.00254765 0.00572894X1 0.00254765 0.00572894 0.0105441F(X) 24.4717675 12.3726433 5.55643307F'(X) -15812.2569 -3889.18437 -1153.94622ERROR 6074807037 5553025175 4566685158
0.01038987 0.01446056 0.01574824 0.01578671 0.01578531 0.01578536 0.01578536 0.015785360.01446056 0.01574824 0.01578671 0.01578531 0.01578536 0.01578536 0.01578536 0.015785361.92539872 0.37137199 0.00976665 -0.00035449 1.3563E-05 -5.1795E-07 1.97811E-08 -7.5546E-10
-472.991023 -288.40467 -253.869527 -252.945272 -252.978843 -252.977558 -252.977607 -252.9776062815027357 817663996 24369322.4 887828.04 33963.7583 1297.03009 49.535114 1.891804450.01127895 0.01635861 0.01822054 0.01829067 0.01828736 0.01828753 0.01828752 0.018287520.01635861 0.01822054 0.01829067 0.01828736 0.01828753 0.01828752 0.01828752 0.018287522.12473187 0.4465708 0.01431743 -0.00067068 3.35368E-05 -1.672E-06 8.33681E-08 -4.1569E-09-418.28265 -239.842632 -204.16438 -202.996338 -203.051117 -203.048378 -203.048514 -203.048508
3105188622 1021886665 38340315.2 1806665.09 90315.2682 4502.70922 224.51494 11.19473020.01170995 0.01740141 0.01973133 0.01986393 0.01985829 0.01985856 0.01985854 0.019858550.01740141 0.01973133 0.01986393 0.01985829 0.01985856 0.01985854 0.01985855 0.019858552.25069399 0.50952101 0.02403703 -0.00101298 4.82191E-05 -2.284E-06 1.08215E-07 -5.127E-09
-395.450885 -218.686465 -181.268307 -179.464898 -179.541049 -179.537425 -179.537596 -179.5375883270690051 1180820443 66756520.1 2842375.95 135240.84 6406.19401 303.51808 14.38019040.01093892 0.01569816 0.01743616 0.01752179 0.01751896 0.01751907 0.01751906 0.017519060.01569816 0.01743616 0.01752179 0.01751896 0.01751907 0.01751906 0.01751906 0.017519062.08405017 0.44333263 0.01866975 -0.00061099 2.23866E-05 -8.1735E-07 2.98458E-08 -1.0898E-09
-437.895856 -255.081284 -218.035624 -216.445664 -216.49777 -216.495861 -216.49593 -216.4959283031717390 996782127 48868913.5 1611295.87 59023.3834 2155.00103 78.6906524 2.873406010.01127567 0.01654287 0.01869486 0.01885053 0.0188468 0.01884691 0.01884691 0.018846910.01654287 0.01869486 0.01885053 0.0188468 0.01884691 0.01884691 0.01884691 0.018846912.20413648 0.50757078 0.03058513 -0.0007241 2.1853E-05 -6.5609E-07 1.97009E-08 -5.9157E-10
-418.464656 -235.861026 -196.476708 -194.058717 -194.116092 -194.114361 -194.114413 -194.1144113183968626 1151113461 82580150.1 1979823.6 59732.2832 1793.35514 53.8502567 1.616986920.01091935 0.01554135 0.01710243 0.01714559 0.01714355 0.01714365 0.01714364 0.017143640.01554135 0.01710243 0.01714559 0.01714355 0.01714365 0.01714364 0.01714364 0.017143642.02938657 0.40422534 0.00968457 -0.0004559 2.24068E-05 -1.0991E-06 5.39154E-08 -2.6448E-09
-439.071239 -258.938369 -224.423012 -223.579558 -223.619293 -223.61734 -223.617436 -223.6174312974001241 912786512 25168680.9 1189418.38 58447.7634 2866.92686 140.638395 6.89904691
0.0105441 0.01474477 0.01607309 0.01610523 0.01610385 0.01610391 0.01610391 0.016103910.01474477 0.01607309 0.01610523 0.01610385 0.01610391 0.01610391 0.01610391 0.016103911.94352702 0.37210576 0.00791412 -0.00033904 1.50772E-05 -6.6942E-07 2.97244E-08 -1.3198E-09
-462.670673 -280.131425 -246.238249 -245.504116 -245.535585 -245.534185 -245.534247 -245.5342452848922566 826428075 19956294.1 857560.242 38130.6283 1693.00366 75.1743433 3.3379519
0.015785360.01578536
2.88525E-11-252.9776060.072251210.018287520.01828752
2.07269E-10-203.0485080.558186240.019858550.01985855
2.42911E-10-179.5375890.681310590.017519060.01751906
3.97957E-11-216.4959280.104924690.018846910.01884691
1.77627E-11-194.1144110.048552610.017143640.01714364
1.29743E-10-223.6174320.338435970.016103910.01610391
5.86056E-11-245.5342450.14821712
Octavo Paso PROCESO DE ITERACIÓN: SEGUNDA ITERACIÓN
Calculo de la Viscocidad Cinematica
Ѵ = m =r
Ѵ = 1.1409 x
Ks = 0.00006
Tuberia Q L D V
(i) (j) (m) (m) (m/s)1 2 0.1085 500.00 0.25 2.210602 3 0.0345 400.00 0.15 1.951064 3 0.0055 200.00 0.10 0.703075 4 0.0355 400.00 0.15 2.010132 5 0.0140 200.00 0.10 1.786946 5 0.0515 600.00 0.20 1.638891 6 0.0915 300.00 0.25 1.86376
Calculo de la Matriz A11
1 2 3 4 5 6 71 72.46102 0 0 0 0 0 02 0 330.6837 0 0 0 0 0
A11 3 0 0 181.2027 0 0 0 04 0 0 0 270.8383 0 0 05 0 0 0 0 437.0891 0 06 0 0 0 0 0 136.74253199 07 0 0 0 0 0 0 37.39492
Finalmente:
=
1 2 3 4 5 6 71 0.5 0 0 0 0 0 02 0 0.5 0 0 0 0 03 0 0 0.5 0 0 0 0
4 0 0 0 0.5 0 0 05 0 0 0 0 0.5 0 06 0 0 0 0 0 0.5 07 0 0 0 0 0 0 0.5
(1.14 - 0.031 (T-15) + 0.00068 (T - 15)2)
10-6 m2/s
(m3/s)
A11 = αij x Qij(nj-1)+βi+(gi/Qi)
H(next) [(A21 x Ndw-1 x A11
-1 x A12)] [A21 x Ndw-1 x (Qa x A11
-1 x A10 x Hn) + q - A21 x Qa]
Calculo de Matrices por Partes para el calculo del (H next)
Ndw-1
1 2 3 4 5 6 71 72.46102 0 0 0 0 0 02 0 330.6837 0 0 0 0 0
A11 ' 3 0 0 181.2027 0 0 0 04 0 0 0 270.8383 0 0 05 0 0 0 0 437.0891 0 06 0 0 0 0 0 136.74253199 07 0 0 0 0 0 0 37.39492
1 2 3 4 5 6 71 144.922 0 0 0 0 0 02 0 661.3675 0 0 0 0 03 0 0 362.4054 0 0 0 0
4 0 0 0 541.6765 0 0 05 0 0 0 0 874.1783 0 06 0 0 0 0 0 273.48506398 07 0 0 0 0 0 0 74.78984
1 2 3 4 5 6 71 0.0069 0 0 0 0 0 02 0 0.0015 0 0 0 0 03 0 0 0.0028 0 0 0 0
4 0 0 0 0.0018 0 0 05 0 0 0 0 0.0011 0 06 0 0 0 0 0 0.0037 07 0 0 0 0 0 0 0.0134
[A21] [([N] x [A11]')-1]1 2 3 4 5 6 7
1 0.0069 -0.00151 0 0 -0.00114 0 02 0 0.001512 0.002759 0 0 0 03 0 0 -0.00276 0.001846 0 0 04 0 0 0 -0.00185 0.001144 0.0036565068 05 0 0 0 0 0 -0.0036565068 0.013371
[A21] [([N] x [A11])-1][A12]1 2 3 4 5 6 7
1 0.009556 -0.00151 0 -0.00114 02 -0.00151 0.004271 -0.00276 0 03 0 -0.00276 0.004605 -0.00185 04 -0.00114 0 -0.00185 0.006647 -0.003665 0 0 0 -0.00366 0.017027
[N] x [A11']
[N] x [A11']
([N] x [A11])-1
([N] x [A11])-1
[A21] [([N] x [A11])-1]
.-([A12])([N][A11]')-1[A12])-11 2 3 4 5 6 7
1 -124.998 -92.4178 -74.5649 -47.8807 -10.28212 -92.4178 -488.635 -343.342 -126.178 -27.09583 -74.5649 -343.342 -490.623 -169.082 -36.30924 -47.8807 -126.178 -169.082 -233.209 -50.08015 -10.2821 -27.0958 -36.3092 -50.0801 -69.4836
[A11][Q] [A10][Ho]1 1
1 7.862942 1 -100 12 11.40135 2 0 23 1.000582 3 0 34 9.620688 4 0 45 6.134379 5 0 56 7.0405 6 0 67 3.421159 7 -100 7
[A21][Q]
1 11 -0.660 1 0.06 12 0.020 2 0.04 23 0.015 3 0.03 34 0.015 4 0.03 45 -1.317 5 0.04 5
Hi+1=-([A12])([N][A11]')-1[A12])-1(([A21][N][A11'])-1([A11][Q]+[A10][Ho])-[A21][Q]-[q])
H2 92.35937H3 79.87005H4 = 80.27446H5 89.00407H6 96.46411
Cálculo de Qi+1Para el cálculo de Qi+1 se utilizará la Ecuación
de la resolución sistemática de esta ecuación resultan las siguientes matrices:
([A21][N][A11'])-1([A11][Q]+[A10][Ho])
([A21][N][A11'])-1([A11][Q]+[A10][Ho])-[A21][Q]-[q]
[A12][Hi+1] [A12][Hi+1]+[A10][Ho]92.35937 -7.64063-12.4893 -12.4893-0.40441 -0.40441-8.72961 -8.72961
-3.3553 -3.3553-7.46004 -7.4600496.46411 -3.53589
([N] x [A11])-1[A11]
0.5 0 0 0 0 0 00 0.5 0 0 0 0 00 0 0.5 0 0 0 00 0 0 0.5 0 0 00 0 0 0 0.5 0 00 0 0 0 0 0.5 00 0 0 0 0 0 0.5
[I]-(([N] x [A11])-1[A11])0.5 0 0 0 0 0 0
0 0.5 0 0 0 0 00 0 0.5 0 0 0 00 0 0 0.5 0 0 00 0 0 0 0.5 0 00 0 0 0 0 0.5 00 0 0 0 0 0 0.5
Luego
Tuberia No Q(m3/s)1 2 0.10702 3 0.03614 3 0.00395 4 0.03392 5 0.01096 5 0.05301 6 0.0930
x
V Re f hf hf+hm B=hl
(m/s) (m) (m) (m)2.21060 484399.13615 0.01579 6.678 6.678 0.0001.95106 256516.23536 0.01829 79.590 95.911 16.3210.70307 61624.11222 0.01986 328.153 328.153 0.0002.01013 264281.97410 0.01752 76.245 76.245 0.0001.78694 156625.78946 0.01885 311.436 311.436 0.0001.63889 287298.01032 0.01714 26.559 26.559 0.0001.86376 408397.79436 0.01610 4.087 4.087 0.000
Q(m3/s)1
1 0.10852 0.03453 0.00554 0.03555 0.01406 0.05157 0.0915
10-6 m2/s
[A21 x Ndw-1 x (Qa x A11
-1 x A10 x Hn) + q - A21 x Qa]
([A11][Q]+[A10][Ho])1
-92.13711.4011.00069.62076.13447.0405
-96.579
1-0.660.020.020.01-1.32
Hi+1=-([A12])([N][A11]')-1[A12])-1(([A21][N][A11'])-1([A11][Q]+[A10][Ho])-[A21][Q]-[q])
([A21][N][A11'])-1([A11][Q]+[A10][Ho])-[A21][Q]-[q]
([N] x [A11])-1([A12][Hi+1]+[A10][Ho])-0.0527-0.0189-0.0011-0.0161-0.0038-0.0273-0.0473
([I]-(([N] x [A11])-1)[A11])[Q]0.050.020.000.020.010.030.05
α = hf
(m) (m)667.765 0
9591.122 032815.327 07624.545 0
31143.645 02655.851 0408.744 0
g = hBomba
Re D K f X0 0.001 0.00253936 0.00568465484399.136 0.25 0.00006 0.01582087 X1 0.00253936 0.00568465 0.01040743256516.235 0.15 0.00006 0.01785198 F(X) 24.3407354 12.2925194 5.5136115161624.1122 0.10 0.00006 0.02213117 F'(X) -15812.2569 -3908.23312 -1167.44929264281.974 0.15 0.00006 0.01780471 ERROR 6061997872 5532952590 4537896411156625.789 0.10 0.00006 0.01973275 X0 0.001 0.00257242 0.00587855287298.01 0.20 0.00006 0.01703972 X1 0.00257242 0.00587855 0.01109052
408397.794 0.25 0.00006 0.0160542 F(X) 24.8635572 12.67284 5.78637905F'(X) -15812.257 -3833.1415 -1110.20962ERROR 6112614508 5624049369 4699483380X0 0.001 0.00264084 0.00628211X1 0.00264084 0.00628211 0.01252672F(X) 25.9453607 13.4187729 6.27614001F'(X) -15812.257 -3685.18778 -1005.04879ERROR 6213323962 5796256186 4985032502X0 0.001 0.00257121 0.00587194X1 0.00257121 0.00587194 0.01106942F(X) 24.8444202 12.6610803 5.78003111F'(X) -15812.257 -3835.84758 -1112.08285ERROR 6110784726 5621185695 4695351756X0 0.001 0.00259832 0.00603406X1 0.00259832 0.00603406 0.01165903F(X) 25.2729723 12.9733887 6.00521562F'(X) -15812.257 -3776.00148 -1067.60052ERROR 6151352378 5693920882 4824557421X0 0.001 0.00256388 0.00582345X1 0.00256388 0.00582345 0.01087305F(X) 24.7284468 12.5569065 5.68579505F'(X) -15812.257 -3852.31519 -1125.98961ERROR 6099658990 5597322325 4644141160X0 0.001 0.00254624 0.00572136X1 0.00254624 0.00572136 0.0105205F(X) 24.449519 12.3588758 5.54894132F'(X) -15812.2569 -3892.40782 -1156.23806ERROR 6072637990 5549593922 4561699356
0.01040743 0.01449253 0.0157845 0.01582223 0.01582082 0.01582088 0.01582087 0.015820870.01449253 0.0157845 0.01582223 0.01582082 0.01582088 0.01582087 0.01582087 0.015820871.92733687 0.371382 0.00954385 -0.00035368 1.37876E-05 -5.3649E-07 2.0877E-08 -8.1241E-10-471.79681 -287.453776 -252.998152 -252.097007 -252.130426 -252.129123 -252.129174 -252.129172
2818761915 818506148 23841792.4 886781.435 34564.5921 1344.95741 52.3376718 2.036665470.01109052 0.01598803 0.0177767 0.01785494 0.01785185 0.01785198 0.01785198 0.017851980.01598803 0.0177767 0.01785494 0.01785185 0.01785198 0.01785198 0.01785198 0.01785198
2.1008665 0.44394652 0.01657248 -0.00064967 2.7778E-05 -1.1838E-06 5.04571E-08 -2.1506E-09-428.965836 -248.199093 -211.825324 -210.440294 -210.494659 -210.492334 -210.492434 -210.4924293063238140 1006188314 43817868.5 1729330.59 73921.9766 3150.3461 134.276218 5.723181540.01252672 0.01917327 0.02202529 0.02213871 0.0221306 0.02213121 0.02213117 0.022131170.01917327 0.02202529 0.02213871 0.0221306 0.02213121 0.02213117 0.02213117 0.022131172.37610934 0.53960697 0.0174468 -0.00123761 9.32902E-05 -7.0024E-06 5.25776E-07 -3.9477E-08
-357.495366 -189.201438 -153.832109 -152.65819 -152.741605 -152.735318 -152.73579 -152.7357543466568893 1294885674 51229069.5 3663282.29 275977.334 20715.969 1555.44876 116.7877430.01106942 0.01594724 0.01772843 0.01780764 0.01780459 0.01780472 0.01780471 0.017804710.01594724 0.01772843 0.01780764 0.01780459 0.01780472 0.01780471 0.01780471 0.017804712.09839206 0.4437787 0.01684867 -0.0006456 2.70644E-05 -1.1308E-06 4.72536E-08 -1.9746E-09
-430.190201 -249.148555 -212.687598 -211.275746 -211.329915 -211.327644 -211.327739 -211.3277353058725199 1004703472 44485351 1716260.07 71928.7378 3005.3487 125.586517 5.247944720.01165903 0.01729755 0.01960312 0.01973798 0.01973251 0.01973276 0.01973275 0.019732750.01729755 0.01960312 0.01973798 0.01973251 0.01973276 0.01973275 0.01973275 0.019732752.24435046 0.50872726 0.02468375 -0.00098949 4.51701E-05 -2.0518E-06 9.32208E-08 -4.2353E-09
-398.038767 -220.651222 -183.04094 -181.177178 -181.252041 -181.248623 -181.248779 -181.2487723259722997 1176124840 68321948.2 2767744.24 126293.219 5736.80599 260.645439 11.84202840.01087305 0.01545182 0.0169967 0.01704167 0.01703963 0.01703973 0.01703972 0.017039720.01545182 0.0169967 0.01704167 0.01703963 0.01703973 0.01703972 0.01703972 0.01703972
2.0232352 0.40349732 0.01018775 -0.00046075 2.18366E-05 -1.0328E-06 4.88485E-08 -2.3105E-09-441.87303 -261.184441 -226.512374 -225.619682 -225.660087 -225.658172 -225.658263 -225.658259
2963256237 908926661 26392100.1 1198485.53 56789.4828 2685.85899 127.0391 6.008833720.0105205 0.01470078 0.01602246 0.01605553 0.01605414 0.0160542 0.0160542 0.0160542
0.01470078 0.01602246 0.01605553 0.01605414 0.0160542 0.0160542 0.0160542 0.01605421.94059629 0.37190067 0.00818273 -0.00034254 1.49141E-05 -6.4831E-07 2.81836E-08 -1.2252E-09
-464.2256 -281.385721 -247.402327 -246.640926 -246.672819 -246.67143 -246.67149 -246.6714882843581256 824889448 20600114.6 865078.679 37660.5527 1637.09327 71.168574 3.09387175
0.015820870.01582087
3.16147E-11-252.1291720.079255590.017851980.01785198
9.16653E-11-210.492429
0.24394020.022131170.02213117
2.96404E-09-152.735757
8.76878920.017804710.01780471
8.25153E-11-211.3277350.219302620.019732750.01973275
1.92428E-10-181.2487720.538030350.017039720.01703972
1.09285E-10-225.6582590.28421422
0.01605420.0160542
5.32623E-11-246.6714880.13449718
Octavo Paso PROCESO DE ITERACIÓN: SEGUNDA ITERACIÓN
Calculo de la Viscocidad Cinematica
Ѵ = m =r
Ѵ = 1.1409 x
Ks = 0.00006
Tuberia Q L D V
(i) (j) (m) (m) (m/s)1 2 0.1070 500.00 0.25 2.179352 3 0.0361 400.00 0.15 2.044154 3 0.0039 200.00 0.10 0.493625 4 0.0339 400.00 0.15 1.917042 5 0.0109 200.00 0.10 1.382176 5 0.0530 600.00 0.20 1.687721 6 0.0930 300.00 0.25 1.89501
Calculo de la Matriz A11
1 2 3 4 5 6 71 71.43664 0 0 0 0 0 02 0 346.4615 0 0 0 0 0
A11 3 0 0 127.2203 0 0 0 04 0 0 0 258.2956 0 0 05 0 0 0 0 338.0812 0 06 0 0 0 0 0 140.81671011 07 0 0 0 0 0 0 38.02195
Finalmente:
=
1 2 3 4 5 6 71 0.5 0 0 0 0 0 02 0 0.5 0 0 0 0 03 0 0 0.5 0 0 0 0
4 0 0 0 0.5 0 0 05 0 0 0 0 0.5 0 06 0 0 0 0 0 0.5 07 0 0 0 0 0 0 0.5
(1.14 - 0.031 (T-15) + 0.00068 (T - 15)2)
10-6 m2/s
(m3/s)
A11 = αij x Qij(nj-1)+βi+(gi/Qi)
H(next) [(A21 x Ndw-1 x A11
-1 x A12)] [A21 x Ndw-1 x (Qa x A11
-1 x A10 x Hn) + q - A21 x Qa]
Calculo de Matrices por Partes para el calculo del (H next)
Ndw-1
1 2 3 4 5 6 71 71.43664 0 0 0 0 0 02 0 346.4615 0 0 0 0 0
A11 ' 3 0 0 127.2203 0 0 0 04 0 0 0 258.2956 0 0 05 0 0 0 0 338.0812 0 06 0 0 0 0 0 140.81671011 07 0 0 0 0 0 0 38.02195
1 2 3 4 5 6 71 142.8733 0 0 0 0 0 02 0 692.923 0 0 0 0 03 0 0 254.4406 0 0 0 0
4 0 0 0 516.5912 0 0 05 0 0 0 0 676.1623 0 06 0 0 0 0 0 281.63342022 07 0 0 0 0 0 0 76.0439
1 2 3 4 5 6 71 0.0070 0 0 0 0 0 02 0 0.0014 0 0 0 0 03 0 0 0.0039 0 0 0 0
4 0 0 0 0.0019 0 0 05 0 0 0 0 0.0015 0 06 0 0 0 0 0 0.0036 07 0 0 0 0 0 0 0.0132
[A21] [([N] x [A11]')-1]1 2 3 4 5 6 7
1 0.006999 -0.00144 0 0 -0.00148 0 02 0 0.001443 0.00393 0 0 0 03 0 0 -0.00393 0.001936 0 0 04 0 0 0 -0.00194 0.001479 0.003550715 05 0 0 0 0 0 -0.003550715 0.01315
[A21] [([N] x [A11])-1][A12]1 2 3 4 5 6 7
1 0.009921 -0.00144 0 -0.00148 02 -0.00144 0.005373 -0.00393 0 03 0 -0.00393 0.005866 -0.00194 04 -0.00148 0 -0.00194 0.006965 -0.003555 0 0 0 -0.00355 0.016701
[N] x [A11']
[N] x [A11']
([N] x [A11])-1
([N] x [A11])-1
[A21] [([N] x [A11])-1]
.-([A12])([N][A11]')-1[A12])-11 2 3 4 5 6 7
1 -121.678 -89.2002 -77.2744 -53.0615 -11.28112 -89.2002 -475.526 -362.944 -134.368 -28.56733 -77.2744 -362.944 -467.842 -164.224 -34.91484 -53.0615 -134.368 -164.224 -224.84 -47.80215 -11.2811 -28.5673 -34.9148 -47.8021 -70.0396
[A11][Q] [A10][Ho]1 1
1 7.642198 1 -100 12 12.51528 2 0 23 0.493215 3 0 34 8.750243 4 0 45 3.670054 5 0 56 7.466287 6 0 67 3.536852 7 -100 7
[A21][Q]
1 11 -0.670 1 0.06 12 0.020 2 0.04 23 0.015 3 0.03 34 0.015 4 0.03 45 -1.295 5 0.04 5
Hi+1=-([A12])([N][A11]')-1[A12])-1(([A21][N][A11'])-1([A11][Q]+[A10][Ho])-[A21][Q]-[q])
H2 92.38499H3 79.78244H4 = 80.24361H5 88.92879H6 96.44868
Cálculo de Qi+1Para el cálculo de Qi+1 se utilizará la Ecuación
de la resolución sistemática de esta ecuación resultan las siguientes matrices:
([A21][N][A11'])-1([A11][Q]+[A10][Ho])
([A21][N][A11'])-1([A11][Q]+[A10][Ho])-[A21][Q]-[q]
[A12][Hi+1] [A12][Hi+1]+[A10][Ho]92.38499 -7.61501-12.6026 -12.6026-0.46117 -0.46117-8.68518 -8.68518-3.45621 -3.45621-7.51989 -7.5198996.44868 -3.55132
([N] x [A11])-1[A11]
0.5 0 0 0 0 0 00 0.5 0 0 0 0 00 0 0.5 0 0 0 00 0 0 0.5 0 0 00 0 0 0 0.5 0 00 0 0 0 0 0.5 00 0 0 0 0 0 0.5
[I]-(([N] x [A11])-1[A11])0.5 0 0 0 0 0 0
0 0.5 0 0 0 0 00 0 0.5 0 0 0 00 0 0 0.5 0 0 00 0 0 0 0.5 0 00 0 0 0 0 0.5 00 0 0 0 0 0 0.5
Luego
Tuberia No Q(m3/s)1 2 0.10682 3 0.03624 3 0.00385 4 0.03382 5 0.01056 5 0.05321 6 0.0932
x
V Re f hf hf+hm B=hl
(m/s) (m) (m) (m)2.17935 477551.21107 0.01579 6.678 6.678 0.0002.04415 268755.26110 0.01829 79.590 95.911 16.3210.49362 43265.57360 0.01986 328.153 328.153 0.0001.91704 252042.94836 0.01752 76.245 76.245 0.0001.38217 121147.43815 0.01885 311.436 311.436 0.0001.68772 295857.91666 0.01714 26.559 26.559 0.0001.89501 415245.71943 0.01610 4.087 4.087 0.000
Q(m3/s)1
1 0.10702 0.03613 0.00394 0.03395 0.01096 0.05307 0.0930
10-6 m2/s
[A21 x Ndw-1 x (Qa x A11
-1 x A10 x Hn) + q - A21 x Qa]
([A11][Q]+[A10][Ho])1
-92.35812.5150.49328.75023.67017.4663
-96.463
1-0.670.020.010.02-1.30
Hi+1=-([A12])([N][A11]')-1[A12])-1(([A21][N][A11'])-1([A11][Q]+[A10][Ho])-[A21][Q]-[q])
([A21][N][A11'])-1([A11][Q]+[A10][Ho])-[A21][Q]-[q]
([N] x [A11])-1([A12][Hi+1]+[A10][Ho])-0.0533-0.0182-0.0018-0.0168-0.0051-0.0267-0.0467
([I]-(([N] x [A11])-1)[A11])[Q]0.050.020.000.020.010.030.05
α = hf
(m) (m)667.765 0
9591.122 032815.327 07624.545 0
31143.645 02655.851 0408.744 0
g = hBomba
Re D K f X0 0.001 0.00253992 0.00568762477551.211 0.25 0.00006 0.01583933 X1 0.00253992 0.00568762 0.01041652268755.261 0.15 0.00006 0.01777853 F(X) 24.3496197 12.297877 5.516414643265.5736 0.10 0.00006 0.0234233 F'(X) -15812.2569 -3906.93667 -1166.53353252042.948 0.15 0.00006 0.01788031 ERROR 6062869003 5534302774 4539803667121147.438 0.10 0.00006 0.02026343 X0 0.001 0.00257054 0.00586825295857.917 0.20 0.00006 0.01699131 X1 0.00257054 0.00586825 0.01105768415245.719 0.25 0.00006 0.01603029 F(X) 24.8337163 12.6545247 5.77651032
F'(X) -15812.257 -3837.36256 -1113.13068ERROR 6109760523 5619587006 4693053512X0 0.001 0.00265841 0.0063896X1 0.00265841 0.0063896 0.01292806F(X) 26.2232205 13.6140522 6.40649374F'(X) -15812.257 -3648.71749 -979.816603ERROR 6238354371 5839471556 5057573522X0 0.001 0.00257314 0.00588248X1 0.00257314 0.00588248 0.0111031F(X) 24.8749149 12.679843 5.79017869F'(X) -15812.257 -3831.53695 -1109.09795ERROR 6113699665 5625752203 4701949142X0 0.001 0.00260933 0.00609647X1 0.00260933 0.00609647 0.01186896F(X) 25.4471179 13.0841852 6.06840655F'(X) -15812.257 -3752.12587 -1051.26356ERROR 6167596567 5719933730 4863518088X0 0.001 0.00256263 0.00581664X1 0.00256263 0.00581664 0.01085127F(X) 24.7087855 12.5445573 5.6789122F'(X) -15812.257 -3855.11869 -1127.96816ERROR 6097766498 5594300053 4639675252X0 0.001 0.00254555 0.00571769X1 0.00254555 0.00571769 0.01050908F(X) 24.438705 12.3522075 5.54533212F'(X) -15812.2569 -3893.97621 -1157.35221ERROR 6071582844 5547929399 4559290100
0.01041652 0.01450912 0.01580334 0.01584068 0.01583928 0.01583933 0.01583933 0.015839330.01450912 0.01580334 0.01584068 0.01583928 0.01583933 0.01583933 0.01583933 0.015839331.92835314 0.37139475 0.00942978 -0.00035316 1.38987E-05 -5.4599E-07 2.14502E-08 -8.427E-10
-471.180691 -286.962507 -252.54737 -251.658034 -251.691363 -251.690052 -251.690103 -251.6901012820707865 818957949 23571360.5 885979.845 34863.3433 1369.56963 53.8056573 2.113834280.01105768 0.0159246 0.01770167 0.01778145 0.01777841 0.01777853 0.01777853 0.01777853
0.0159246 0.01770167 0.01778145 0.01777841 0.01777853 0.01777853 0.01777853 0.017778532.09703279 0.44369662 0.01700457 -0.00064317 2.66616E-05 -1.1015E-06 4.55157E-08 -1.8807E-09-430.87433 -249.678294 -213.16794 -211.740925 -211.79497 -211.792729 -211.792822 -211.792818
3056229984 1003901210 44861810.3 1708544.52 70806.7201 2925.41036 120.880034 4.994820750.01292806 0.02011133 0.02331515 0.02343224 0.02342253 0.02342337 0.0234233 0.02342330.02011133 0.02331515 0.02343224 0.02342253 0.02342337 0.0234233 0.0234233 0.0234233
2.4496267 0.56444796 0.01654593 -0.00136199 0.00011816 -1.0207E-05 8.82022E-07 -7.6218E-08-341.018274 -176.179555 -141.315758 -140.264408 -140.3511 -140.34358 -140.34423 -140.3441733571752921 1374137198 49967415.1 4145657.53 359411.185 31048.9587 2683.09793 231.853908
0.0111031 0.01601242 0.01780563 0.01788329 0.01788018 0.01788032 0.01788031 0.017880310.01601242 0.01780563 0.01788329 0.01788018 0.01788032 0.01788031 0.01788031 0.017880312.10236193 0.44405899 0.01641012 -0.00065191 2.81973E-05 -1.2156E-06 5.24168E-08 -2.2601E-09
-428.238455 -247.634185 -211.311478 -209.942191 -209.996657 -209.994301 -209.994402 -209.9943983065947973 1007100411 43425137.9 1736655.22 75096.6241 3237.62046 139.600767 6.019314320.01186896 0.01773095 0.02014293 0.02026929 0.02026312 0.02026345 0.02026343 0.020263430.01773095 0.02014293 0.02026929 0.02026312 0.02026345 0.02026343 0.02026343 0.02026343
2.271804 0.51289126 0.02220885 -0.00107415 5.74972E-05 -3.0632E-06 1.63232E-07 -8.6983E-09-387.548293 -212.642496 -175.767158 -174.134298 -174.213423 -174.209188 -174.209413 -174.2094013306078312 1197436529 62337575.5 3044213.29 162874.113 8677.35565 462.403905 24.64054150.01085127 0.01540994 0.01694741 0.01699327 0.01699122 0.01699132 0.01699131 0.016991310.01540994 0.01694741 0.01699327 0.01699122 0.01699132 0.01699131 0.01699131 0.016991312.02040668 0.40319629 0.01043145 -0.0004626 2.15378E-05 -1.0006E-06 4.64937E-08 -2.1603E-09
-443.201221 -262.24637 -227.497364 -226.580713 -226.621396 -226.619502 -226.61959 -226.6195862958263659 907201268 26983074.1 1201598.73 55933.7868 2598.67684 120.745048 5.610280450.01050908 0.01467958 0.01599809 0.01603162 0.01603023 0.01603029 0.01603029 0.016030290.01467958 0.01599809 0.01603162 0.01603023 0.01603029 0.01603029 0.01603029 0.016030291.93919863 0.3718133 0.00831451 -0.00034409 1.48262E-05 -6.3778E-07 2.74371E-08 -1.1803E-09
-464.980671 -281.993842 -247.965812 -247.190995 -247.223081 -247.221698 -247.221758 -247.2217552841017501 824170638 20915446.7 868366.544 37410.9174 1609.31123 69.2324847 2.9783727
0.015839330.015839333.3106E-11
-251.6901010.083042430.017778530.01777853
7.77121E-11-211.7928180.20638673
0.02342330.0234233
6.58621E-09-140.344178
20.0351820.017880310.01788031
9.74518E-11-209.9943980.259542340.020263430.02026343
4.63514E-10-174.2094021.313040260.016991310.01699131
1.00374E-10-226.6195860.260672320.016030290.016030295.0778E-11
-247.2217550.12812916
Octavo Paso PROCESO DE ITERACIÓN: SEGUNDA ITERACIÓN
Calculo de la Viscocidad Cinematica
Ѵ = m =r
Ѵ = 1.1409 x
Ks = 0.00006
Tuberia Q L D V
(i) (j) (m) (m) (m/s)1 2 0.1068 500.00 0.25 2.175472 3 0.0362 400.00 0.15 2.051284 3 0.0038 200.00 0.10 0.477585 4 0.0338 400.00 0.15 1.909912 5 0.0105 200.00 0.10 1.341906 5 0.0532 600.00 0.20 1.693781 6 0.0932 300.00 0.25 1.89889
Calculo de la Matriz A11
1 2 3 4 5 6 71 71.30955 0 0 0 0 0 02 0 347.6695 0 0 0 0 0
A11 3 0 0 123.0872 0 0 0 04 0 0 0 257.3353 0 0 05 0 0 0 0 328.2314 0 06 0 0 0 0 0 141.32216814 07 0 0 0 0 0 0 38.09974
Finalmente:
=
1 2 3 4 5 6 71 0.5 0 0 0 0 0 02 0 0.5 0 0 0 0 03 0 0 0.5 0 0 0 0
4 0 0 0 0.5 0 0 05 0 0 0 0 0.5 0 06 0 0 0 0 0 0.5 07 0 0 0 0 0 0 0.5
(1.14 - 0.031 (T-15) + 0.00068 (T - 15)2)
10-6 m2/s
(m3/s)
A11 = αij x Qij(nj-1)+βi+(gi/Qi)
H(next) [(A21 x Ndw-1 x A11
-1 x A12)] [A21 x Ndw-1 x (Qa x A11
-1 x A10 x Hn) + q - A21 x Qa]
Calculo de Matrices por Partes para el calculo del (H next)
Ndw-1
1 2 3 4 5 6 71 71.30955 0 0 0 0 0 02 0 347.6695 0 0 0 0 0
A11 ' 3 0 0 123.0872 0 0 0 04 0 0 0 257.3353 0 0 05 0 0 0 0 328.2314 0 06 0 0 0 0 0 141.32216814 07 0 0 0 0 0 0 38.09974
1 2 3 4 5 6 71 142.6191 0 0 0 0 0 02 0 695.339 0 0 0 0 03 0 0 246.1744 0 0 0 0
4 0 0 0 514.6706 0 0 05 0 0 0 0 656.4628 0 06 0 0 0 0 0 282.64433628 07 0 0 0 0 0 0 76.19948
1 2 3 4 5 6 71 0.0070 0 0 0 0 0 02 0 0.0014 0 0 0 0 03 0 0 0.0041 0 0 0 0
4 0 0 0 0.0019 0 0 05 0 0 0 0 0.0015 0 06 0 0 0 0 0 0.0035 07 0 0 0 0 0 0 0.0131
[A21] [([N] x [A11]')-1]1 2 3 4 5 6 7
1 0.007012 -0.00144 0 0 -0.00152 0 02 0 0.001438 0.004062 0 0 0 03 0 0 -0.00406 0.001943 0 0 04 0 0 0 -0.00194 0.001523 0.0035380153 05 0 0 0 0 0 -0.0035380153 0.013123
[A21] [([N] x [A11])-1][A12]1 2 3 4 5 6 7
1 0.009973 -0.00144 0 -0.00152 02 -0.00144 0.0055 -0.00406 0 03 0 -0.00406 0.006005 -0.00194 04 -0.00152 0 -0.00194 0.007004 -0.003545 0 0 0 -0.00354 0.016661
[N] x [A11']
[N] x [A11']
([N] x [A11])-1
([N] x [A11])-1
[A21] [([N] x [A11])-1]
.-([A12])([N][A11]')-1[A12])-11 2 3 4 5 6 7
1 -121.297 -88.9944 -77.5582 -53.6489 -11.39222 -88.9944 -474.236 -364.451 -134.925 -28.65093 -77.5582 -364.451 -466.02 -163.7 -34.76114 -53.6489 -134.925 -163.7 -223.858 -47.53565 -11.3922 -28.6509 -34.7611 -47.5356 -70.1128
[A11][Q] [A10][Ho]1 1
1 7.61503 1 -100 12 12.6027 2 0 23 0.461689 3 0 34 8.6853 4 0 45 3.45932 5 0 56 7.519983 6 0 67 3.551339 7 -100 7
[A21][Q]
1 11 -0.671 1 0.06 12 0.020 2 0.04 23 0.015 3 0.03 34 0.015 4 0.03 45 -1.292 5 0.04 5
Hi+1=-([A12])([N][A11]')-1[A12])-1(([A21][N][A11'])-1([A11][Q]+[A10][Ho])-[A21][Q]-[q])
H2 92.38525H3 79.7818H4 = 80.24322H5 88.92796H6 96.44851
Cálculo de Qi+1Para el cálculo de Qi+1 se utilizará la Ecuación
de la resolución sistemática de esta ecuación resultan las siguientes matrices:
([A21][N][A11'])-1([A11][Q]+[A10][Ho])
([A21][N][A11'])-1([A11][Q]+[A10][Ho])-[A21][Q]-[q]
[A12][Hi+1] [A12][Hi+1]+[A10][Ho]92.38525 -7.61475-12.6035 -12.6035-0.46142 -0.46142-8.68474 -8.68474
-3.4573 -3.4573-7.52055 -7.5205596.44851 -3.55149
([N] x [A11])-1[A11]
0.5 0 0 0 0 0 00 0.5 0 0 0 0 00 0 0.5 0 0 0 00 0 0 0.5 0 0 00 0 0 0 0.5 0 00 0 0 0 0 0.5 00 0 0 0 0 0 0.5
[I]-(([N] x [A11])-1[A11])0.5 0 0 0 0 0 0
0 0.5 0 0 0 0 00 0 0.5 0 0 0 00 0 0 0.5 0 0 00 0 0 0 0.5 0 00 0 0 0 0 0.5 00 0 0 0 0 0 0.5
Luego
Tuberia No Q(m3/s)1 2 0.10682 3 0.03634 3 0.00375 4 0.03372 5 0.01056 5 0.05321 6 0.0932
x
V Re f hf hf+hm B=hl
(m/s) (m) (m) (m)2.17547 476701.63145 0.01579 6.678 6.678 0.0002.05128 269692.32868 0.01829 79.590 95.911 16.3210.47758 41859.97223 0.01986 328.153 328.153 0.0001.90991 251105.88078 0.01752 76.245 76.245 0.0001.34190 117617.88772 0.01885 311.436 311.436 0.0001.69378 296919.89120 0.01714 26.559 26.559 0.0001.89889 416095.29906 0.01610 4.087 4.087 0.000
Q(m3/s)1
1 0.10682 0.03623 0.00384 0.03385 0.01056 0.05327 0.0932
10-6 m2/s
[A21 x Ndw-1 x (Qa x A11
-1 x A10 x Hn) + q - A21 x Qa]
([A11][Q]+[A10][Ho])1
-92.38512.6030.46178.68533.4593
7.52-96.449
1-0.670.020.010.01-1.29
Hi+1=-([A12])([N][A11]')-1[A12])-1(([A21][N][A11'])-1([A11][Q]+[A10][Ho])-[A21][Q]-[q])
([A21][N][A11'])-1([A11][Q]+[A10][Ho])-[A21][Q]-[q]
([N] x [A11])-1([A12][Hi+1]+[A10][Ho])-0.0534-0.0181-0.0019-0.0169-0.0053-0.0266-0.0466
([I]-(([N] x [A11])-1)[A11])[Q]0.050.020.000.020.010.030.05
α = hf
(m) (m)667.765 0
9591.122 032815.327 07624.545 0
31143.645 02655.851 0408.744 0
g = hBomba
Re D K f X0 0.001 0.002539991476701.6314 0.25 0.00006 0.015841654 X1 0.002539991 0.005687997269692.3287 0.15 0.00006 0.017773137 F(X) 24.3507333 12.2985493841859.97223 0.10 0.00006 0.023556274 F'(X) -15812.2569 -3906.77421251105.8808 0.15 0.00006 0.017886352 ERROR 6062978167 5534472127117617.8877 0.10 0.00006 0.020330351 X0 0.001 0.002570396296919.8912 0.20 0.00006 0.016985469 X1 0.002570396 0.005867488416095.2991 0.25 0.00006 0.016027366 F(X) 24.83150261 12.65317092
F'(X) -15812.257 -3837.676ERROR 6109548639 5619256656X0 0.001 0.00266008X1 0.00266008 0.006399943F(X) 26.24961847 13.6328593F'(X) -15812.257 -3645.28395ERROR 6240715175 5843587006X0 0.001 0.002573294X1 0.002573294 0.005883313F(X) 24.87732626 12.68133199F'(X) -15812.257 -3831.19644ERROR 6113929973 5626114033X0 0.001 0.002610635X1 0.002610635 0.006103962F(X) 25.46777529 13.09756737F'(X) -15812.257 -3749.31042ERROR 6169514378 5723048377X0 0.001 0.002562484X1 0.002562484 0.005815808F(X) 24.70639513 12.54305921F'(X) -15812.257 -3855.45977ERROR 6097536284 5593933042X0 0.001 0.002545471X1 0.002545471 0.005717236F(X) 24.43737895 12.35139084F'(X) -15812.2569 -3894.1686ERROR 6071453419 5547725438
0.005687997 0.01041766 0.014511201 0.015805713 0.015843004 0.0158416 0.0158416560.01041766 0.014511201 0.015805713 0.015843004 0.0158416 0.015841656 0.015841654
5.516766993 1.928481361 0.371396714 0.009415513 -0.00035309 1.39124E-05 -5.47181E-07-1166.41874 -471.103434 -286.900873 -252.490787 -251.602925 -251.636244 -251.6349314540043200 2820952797 819015437 23537533.22 885866.8741 34900.25491 1372.649296
0.005867488 0.011055253 0.015919934 0.017696164 0.01777605 0.017773016 0.0177731420.011055253 0.015919934 0.017696164 0.01777605 0.017773016 0.017773142 0.017773137
5.77578486 2.096753895 0.443680692 0.017036942 -0.00064265 2.6578E-05 -1.0955E-06-1113.34738 -431.015752 -249.787729 -213.267104 -211.836938 -211.890956 -211.8887224692579353 3055716543 1003737809 44939943 1706912.226 70574.0737 2908.984979
0.006399943 0.012967408 0.020205523 0.023447387 0.023565382 0.023555475 0.0235563440.012967408 0.020205523 0.023447387 0.023565382 0.023555475 0.023556344 0.0235562686.419332294 2.457132347 0.567180672 0.016534624 -0.00137801 0.000120985 -1.05766E-05-977.444382 -339.47129 -174.95513 -140.12935 -139.084712 -139.171924 -139.1642685064593865 3582245898 1382611893 50071513.93 4206125.034 369037.8383 32263.63238
0.005883313 0.011105774 0.016017619 0.017811795 0.017889331 0.017886223 0.0178863570.011105774 0.016017619 0.017811795 0.017889331 0.017886223 0.017886357 0.017886352
5.79098845 2.102681993 0.444084104 0.016375794 -0.00065237 2.82859E-05 -1.22245E-06-1108.86195 -428.08396 -247.514119 -211.202187 -209.836226 -209.890711 -209.8883494702473939 3066526295 1007297028 43342089.52 1738169.3 75345.16609 3256.262898
0.006103962 0.011894566 0.017784747 0.020210819 0.020336276 0.020330028 0.0203303680.011894566 0.017784747 0.020210819 0.020336276 0.020330028 0.020330368 0.020330356.076252417 2.275377864 0.5135564 0.021940715 -0.00108256 5.8955E-05 -3.19555E-06-1049.32969 -386.300151 -211.682255 -174.886715 -173.278897 -173.358376 -173.3540484868276673 3311928572 1200382850 61691102.67 3073038.844 167274.9391 9067.059755
0.005815808 0.010848635 0.015404876 0.01694146 0.01698742 0.016985378 0.0169854730.010848635 0.015404876 0.01694146 0.01698742 0.016985378 0.016985473 0.0169854695.678080036 2.020066794 0.403161628 0.01046129 -0.00046281 2.15003E-05 -9.96709E-07-1128.20876 -443.362623 -262.37529 -227.616817 -226.697227 -226.737942 -226.7360514639134258 2957661393 906996134 27055370.06 1201923.476 55826.82071 2588.035362
0.005717236 0.010507685 0.014676982 0.015995114 0.016028701 0.016027308 0.0160273680.010507685 0.014676982 0.015995114 0.016028701 0.016027308 0.016027368 0.0160273665.544891005 1.939028458 0.371803139 0.008330719 -0.00034428 1.4815E-05 -6.36473E-07-1157.48884 -465.073227 -282.068341 -248.034802 -247.258333 -247.290442 -247.289064558995310 2840704587 824083796 20954221 868753.0264 37379.37085 1605.879372
0.015841654 0.015841654 0.0158416540.015841654 0.015841654 0.0158416542.15224E-08 -8.46544E-10 3.3296E-11-251.634982 -251.63498 -251.6349853.99074411 2.12362522 0.0835252250.017773137 0.017773137 0.0177731370.017773137 0.017773137 0.0177731374.51612E-08 -1.86172E-09 7.67493E-11-211.888814 -211.88881 -211.88881119.9204245 4.943591047 0.2037984270.023556268 0.023556275 0.0235562740.023556275 0.023556274 0.0235562749.24971E-07 -8.08899E-08 7.07395E-09-139.164938 -139.164879 -139.1648842821.574948 246.7504953 21.578708820.017886352 0.017886352 0.0178863520.017886352 0.017886352 0.0178863525.28385E-08 -2.28386E-09 9.87166E-11-209.888451 -209.888447 -209.888447140.7472557 6.083568973 0.262953924
0.02033035 0.020330351 0.0203303510.020330351 0.020330351 0.0203303511.73253E-07 -9.39315E-09 5.09262E-10-173.354283 -173.35427 -173.354271491.5885602 26.65211322 1.4449800990.016985469 0.016985469 0.0169854690.016985469 0.016985469 0.0169854694.62099E-08 -2.14239E-09 9.93268E-11-226.736139 -226.736135 -226.736135119.9876428 5.562896811 0.2579105670.016027366 0.016027366 0.0160273660.016027366 0.016027366 0.0160273662.73457E-08 -1.17489E-09 5.04787E-11
-247.28912 -247.289117 -247.28911768.99570061 2.964353653 0.127362403
Octavo Paso PROCESO DE ITERACIÓN: SEGUNDA ITERACIÓN
Calculo de la Viscocidad Cinematica
Ѵ = m =r
Ѵ = 1.1409 x
Ks = 0.00006
Tuberia Q L D V
(i) (j) (m) (m) (m/s)1 2 0.1068 500.00 0.25 2.175432 3 0.0363 400.00 0.15 2.051344 3 0.0037 200.00 0.10 0.477445 4 0.0337 400.00 0.15 1.909852 5 0.0105 200.00 0.10 1.341516 5 0.0532 600.00 0.20 1.693841 6 0.0932 300.00 0.25 1.89893
Calculo de la Matriz A11
1 2 3 4 5 6 71 71.30821 0 0 0 0 0 02 0 347.6799 0 0 0 0 0
A11 3 0 0 123.0516 0 0 0 04 0 0 0 257.327 0 0 05 0 0 0 0 328.1353 0 06 0 0 0 0 0 141.32748105 07 0 0 0 0 0 0 38.10056
Finalmente:
=
1 2 3 4 5 6 71 0.5 0 0 0 0 0 02 0 0.5 0 0 0 0 03 0 0 0.5 0 0 0 0
4 0 0 0 0.5 0 0 05 0 0 0 0 0.5 0 06 0 0 0 0 0 0.5 07 0 0 0 0 0 0 0.5
(1.14 - 0.031 (T-15) + 0.00068 (T - 15)2)
10-6 m2/s
(m3/s)
A11 = αij x Qij(nj-1)+βi+(gi/Qi)
H(next) [(A21 x Ndw-1 x A11
-1 x A12)] [A21 x Ndw-1 x (Qa x A11
-1 x A10 x Hn) + q - A21 x Qa]
Calculo de Matrices por Partes para el calculo del (H next)
Ndw-1
1 2 3 4 5 6 71 71.30821 0 0 0 0 0 02 0 347.6799 0 0 0 0 0
A11 ' 3 0 0 123.0516 0 0 0 04 0 0 0 257.327 0 0 05 0 0 0 0 328.1353 0 06 0 0 0 0 0 141.32748105 07 0 0 0 0 0 0 38.10056
1 2 3 4 5 6 71 142.6164 0 0 0 0 0 02 0 695.3598 0 0 0 0 03 0 0 246.1033 0 0 0 0
4 0 0 0 514.6541 0 0 05 0 0 0 0 656.2706 0 06 0 0 0 0 0 282.65496211 07 0 0 0 0 0 0 76.20112
1 2 3 4 5 6 71 0.0070 0 0 0 0 0 02 0 0.0014 0 0 0 0 03 0 0 0.0041 0 0 0 0
4 0 0 0 0.0019 0 0 05 0 0 0 0 0.0015 0 06 0 0 0 0 0 0.0035 07 0 0 0 0 0 0 0.0131
[A21] [([N] x [A11]')-1]1 2 3 4 5 6 7
1 0.007012 -0.00144 0 0 -0.00152 0 02 0 0.001438 0.004063 0 0 0 03 0 0 -0.00406 0.001943 0 0 04 0 0 0 -0.00194 0.001524 0.0035378823 05 0 0 0 0 0 -0.0035378823 0.013123
[A21] [([N] x [A11])-1][A12]1 2 3 4 5 6 7
1 0.009974 -0.00144 0 -0.00152 02 -0.00144 0.005501 -0.00406 0 03 0 -0.00406 0.006006 -0.00194 04 -0.00152 0 -0.00194 0.007005 -0.003545 0 0 0 -0.00354 0.016661
[N] x [A11']
[N] x [A11']
([N] x [A11])-1
([N] x [A11])-1
[A21] [([N] x [A11])-1]
.-([A12])([N][A11]')-1[A12])-11 2 3 4 5 6 7
1 -121.293 -88.9927 -77.561 -53.6547 -11.39332 -88.9927 -474.225 -364.463 -134.93 -28.65163 -77.561 -364.463 -466.005 -163.695 -34.75974 -53.6547 -134.93 -163.695 -223.848 -47.5335 -11.3933 -28.6516 -34.7597 -47.533 -70.1136
[A11][Q] [A10][Ho]1 1
1 7.614745 1 -100 12 12.60346 2 0 23 0.461422 3 0 34 8.684741 4 0 45 3.457296 5 0 56 7.520549 6 0 67 3.551492 7 -100 7
[A21][Q]
1 11 -0.671 1 0.06 12 0.020 2 0.04 23 0.015 3 0.03 34 0.015 4 0.03 45 -1.292 5 0.04 5
Hi+1=-([A12])([N][A11]')-1[A12])-1(([A21][N][A11'])-1([A11][Q]+[A10][Ho])-[A21][Q]-[q])
H2 92.38525H3 79.7818H4 = 80.24322H5 88.92796H6 96.44851
Cálculo de Qi+1Para el cálculo de Qi+1 se utilizará la Ecuación
de la resolución sistemática de esta ecuación resultan las siguientes matrices:
([A21][N][A11'])-1([A11][Q]+[A10][Ho])
([A21][N][A11'])-1([A11][Q]+[A10][Ho])-[A21][Q]-[q]
[A12][Hi+1] [A12][Hi+1]+[A10][Ho]92.38525 -7.61475-12.6035 -12.6035-0.46142 -0.46142-8.68474 -8.68474
-3.4573 -3.4573-7.52055 -7.5205596.44851 -3.55149
([N] x [A11])-1[A11]
0.5 0 0 0 0 0 00 0.5 0 0 0 0 00 0 0.5 0 0 0 00 0 0 0.5 0 0 00 0 0 0 0.5 0 00 0 0 0 0 0.5 00 0 0 0 0 0 0.5
[I]-(([N] x [A11])-1[A11])0.5 0 0 0 0 0 0
0 0.5 0 0 0 0 00 0 0.5 0 0 0 00 0 0 0.5 0 0 00 0 0 0 0.5 0 00 0 0 0 0 0.5 00 0 0 0 0 0 0.5
Luego
Tuberia No Q(m3/s)1 2 0.10682 3 0.03634 3 0.00375 4 0.03372 5 0.01056 5 0.05321 6 0.0932
x
V Re f hf hf+hm B=hl
(m/s) (m) (m) (m)2.17543 476692.70144 0.01579 6.678 6.678 0.0002.05134 269700.39788 0.01829 79.590 95.911 16.3210.47744 41847.86843 0.01986 328.153 328.153 0.0001.90985 251097.81158 0.01752 76.245 76.245 0.0001.34151 117583.45891 0.01885 311.436 311.436 0.0001.69384 296931.05370 0.01714 26.559 26.559 0.0001.89893 416104.22906 0.01610 4.087 4.087 0.000
Q(m3/s)1
1 0.10682 0.03633 0.00374 0.03375 0.01056 0.05327 0.0932
10-6 m2/s
[A21 x Ndw-1 x (Qa x A11
-1 x A10 x Hn) + q - A21 x Qa]
([A11][Q]+[A10][Ho])1
-92.38512.6030.46148.68473.45737.5205
-96.449
1-0.670.020.020.01-1.29
Hi+1=-([A12])([N][A11]')-1[A12])-1(([A21][N][A11'])-1([A11][Q]+[A10][Ho])-[A21][Q]-[q])
([A21][N][A11'])-1([A11][Q]+[A10][Ho])-[A21][Q]-[q]
([N] x [A11])-1([A12][Hi+1]+[A10][Ho])-0.0534-0.0181-0.0019-0.0169-0.0053-0.0266-0.0466
([I]-(([N] x [A11])-1)[A11])[Q]0.050.020.000.020.010.030.05
α = hf
(m) (m)667.765 0
9591.122 032815.327 07624.545 0
31143.645 02655.851 0408.744 0
g = hBomba
Re D K f X0 0.001 0.00253999 0.005688476692.701 0.25 0.00006 0.01584168 X1 0.00253999 0.005688 0.01041767269700.398 0.15 0.00006 0.01777309 F(X) 24.350745 12.2985565 5.516770741847.8684 0.10 0.00006 0.02355745 F'(X) -15812.2569 -3906.7725 -1166.41754251097.812 0.15 0.00006 0.0178864 ERROR 6062979316 5534473910 4540045721117583.459 0.10 0.00006 0.02033102 X0 0.001 0.00257039 0.00586748296931.054 0.20 0.00006 0.01698541 X1 0.00257039 0.00586748 0.01105523416104.229 0.25 0.00006 0.01602734 F(X) 24.8314836 12.6531593 5.77577863
F'(X) -15812.257 -3837.67869 -1113.34924ERROR 6109546818 5619253818 4692575281X0 0.001 0.0026601 0.00640003X1 0.0026601 0.00640003 0.01296775F(X) 26.2498499 13.6330244 6.41944518F'(X) -15812.257 -3645.25387 -977.423603ERROR 6240735861 5843623093 5064655503X0 0.001 0.0025733 0.00588332X1 0.0025733 0.00588332 0.0111058F(X) 24.8773471 12.6813449 5.79099544F'(X) -15812.257 -3831.1935 -1108.85991ERROR 6113931961 5626117156 4702478470X0 0.001 0.00261065 0.00610404X1 0.00261065 0.00610404 0.01189482F(X) 25.4679804 13.0977005 6.07633069F'(X) -15812.257 -3749.28248 -1049.3105ERROR 6169533413 5723079334 4868324066X0 0.001 0.00256248 0.0058158X1 0.00256248 0.0058158 0.01084861F(X) 24.7063701 12.5430435 5.67807131F'(X) -15812.257 -3855.46334 -1128.21128ERROR 6097533870 5593929193 4639128587X0 0.001 0.00254547 0.00571723X1 0.00254547 0.00571723 0.01050767F(X) 24.437365 12.3513823 5.54488638F'(X) -15812.2569 -3894.17062 -1157.49028ERROR 6071452061 5547723297 4558992216
0.01041767 0.01451122 0.01580574 0.01584303 0.01584162 0.01584168 0.01584168 0.015841680.01451122 0.01580574 0.01584303 0.01584162 0.01584168 0.01584168 0.01584168 0.015841681.92848271 0.37139674 0.00941536 -0.00035309 1.39126E-05 -5.4719E-07 2.15232E-08 -8.4659E-10
-471.102621 -286.900224 -252.490191 -251.602345 -251.635663 -251.634351 -251.634402 -251.63442820955376 819016043 23537177.3 885865.671 34900.6427 1372.6817 53.9926998 2.123733640.01105523 0.01591989 0.01769612 0.017776 0.01777297 0.0177731 0.01777309 0.017773090.01591989 0.01769612 0.017776 0.01777297 0.0177731 0.01777309 0.01777309 0.01777309
2.0967515 0.44368056 0.01703722 -0.00064264 2.65773E-05 -1.0955E-06 4.51581E-08 -1.8616E-09-431.016967 -249.788669 -213.267956 -211.837763 -211.89178 -211.889546 -211.889639 -211.8896353055712135 1003736408 44940614.7 1706898.15 70572.0739 2908.84402 119.912204 4.943151040.01296775 0.02020635 0.02344855 0.02356656 0.02355665 0.02355752 0.02355744 0.023557450.02020635 0.02344855 0.02356656 0.02355665 0.02355752 0.02355744 0.02355745 0.023557452.45719854 0.56720492 0.01653458 -0.00137816 0.00012101 -1.058E-05 9.25356E-07 -8.0932E-08
-339.457742 -174.944407 -140.118954 -139.074371 -139.161588 -139.153931 -139.1546 -139.1545413582338255 1382686922 50072612.4 4206669.61 369123.943 32274.5083 2822.81904 246.884915
0.0111058 0.01601766 0.01781185 0.01788938 0.01788627 0.01788641 0.0178864 0.01788640.01601766 0.01781185 0.01788938 0.01788627 0.01788641 0.0178864 0.0178864 0.01788642.10268476 0.44408432 0.0163755 -0.00065237 2.82867E-05 -1.2225E-06 5.28421E-08 -2.2841E-09
-428.082627 -247.513082 -211.201243 -209.835311 -209.889796 -209.887434 -209.887536 -209.8875323066531292 1007298730 43341373.2 1738182.31 75347.3101 3256.42398 140.75718 6.084119560.01189482 0.01778528 0.0202115 0.02033695 0.0203307 0.02033104 0.02033102 0.020331020.01778528 0.0202115 0.02033695 0.0203307 0.02033104 0.02033102 0.02033102 0.020331022.27541369 0.51356319 0.02193808 -0.00108264 5.89695E-05 -3.1969E-06 1.73355E-07 -9.4002E-09
-386.287754 -211.67271 -174.877955 -173.270383 -173.349866 -173.345537 -173.345772 -173.3457593311987035 1200412563 61684754 3073321.58 167318.699 9070.97281 491.884293 26.67267660.01084861 0.01540482 0.0169414 0.01698736 0.01698532 0.01698541 0.01698541 0.016985410.01540482 0.0169414 0.01698736 0.01698532 0.01698541 0.01698541 0.01698541 0.016985412.02006323 0.40316127 0.0104616 -0.00046281 2.14999E-05 -9.9667E-07 4.62069E-08 -2.1422E-09
-443.364315 -262.376641 -227.61807 -226.698448 -226.739164 -226.737273 -226.737361 -226.7373562957655082 906993988 27056128.8 1201926.82 55825.6955 2587.92371 119.979707 5.56240010.01050767 0.01467696 0.01599508 0.01602867 0.01602728 0.01602734 0.01602733 0.016027340.01467696 0.01599508 0.01602867 0.01602728 0.01602734 0.01602733 0.01602734 0.016027341.93902667 0.37180303 0.00833089 -0.00034428 1.48149E-05 -6.3646E-07 2.73448E-08 -1.1748E-09
-465.074199 -282.069123 -248.035527 -247.25904 -247.291149 -247.289767 -247.289827 -247.2898242840701304 824082886 20954628.2 868757.064 37379.0386 1605.84332 68.9932176 2.9642013
0.015841680.01584168
3.33005E-11-251.6344
0.083536050.017773090.01777309
7.67404E-11-211.8896350.203775530.023557450.02355745
7.07836E-09-139.15454721.5927116
0.01788640.0178864
9.87264E-11-209.8875320.262980310.020331020.02033102
5.09733E-10-173.345761.4463387
0.016985410.01698541
9.93161E-11-226.7373570.257880860.016027340.01602734
5.04743E-11-247.2898240.12735182
Octavo Paso PROCESO DE ITERACIÓN: SEGUNDA ITERACIÓN
Calculo de la Viscocidad Cinematica
Ѵ = m =r
Ѵ = 1.1409 x
Ks = 0.00006
Tuberia Q L D V
(i) (j) (m) (m) (m/s)1 2 0.1068 500.00 0.25 2.175432 3 0.0363 400.00 0.15 2.051344 3 0.0037 200.00 0.10 0.477445 4 0.0337 400.00 0.15 1.909852 5 0.0105 200.00 0.10 1.341516 5 0.0532 600.00 0.20 1.693841 6 0.0932 300.00 0.25 1.89893
Calculo de la Matriz A11
1 2 3 4 5 6 71 71.30821 0 0 0 0 0 02 0 347.6799 0 0 0 0 0
A11 3 0 0 123.0516 0 0 0 04 0 0 0 257.327 0 0 05 0 0 0 0 328.1353 0 06 0 0 0 0 0 141.32748156 07 0 0 0 0 0 0 38.10056
Finalmente:
=
1 2 3 4 5 6 71 0.5 0 0 0 0 0 02 0 0.5 0 0 0 0 03 0 0 0.5 0 0 0 0
4 0 0 0 0.5 0 0 05 0 0 0 0 0.5 0 06 0 0 0 0 0 0.5 07 0 0 0 0 0 0 0.5
(1.14 - 0.031 (T-15) + 0.00068 (T - 15)2)
10-6 m2/s
(m3/s)
A11 = αij x Qij(nj-1)+βi+(gi/Qi)
H(next) [(A21 x Ndw-1 x A11
-1 x A12)] [A21 x Ndw-1 x (Qa x A11
-1 x A10 x Hn) + q - A21 x Qa]
Calculo de Matrices por Partes para el calculo del (H next)
Ndw-1
1 2 3 4 5 6 71 71.30821 0 0 0 0 0 02 0 347.6799 0 0 0 0 0
A11 ' 3 0 0 123.0516 0 0 0 04 0 0 0 257.327 0 0 05 0 0 0 0 328.1353 0 06 0 0 0 0 0 141.32748156 07 0 0 0 0 0 0 38.10056
1 2 3 4 5 6 71 142.6164 0 0 0 0 0 02 0 695.3598 0 0 0 0 03 0 0 246.1033 0 0 0 0
4 0 0 0 514.6541 0 0 05 0 0 0 0 656.2706 0 06 0 0 0 0 0 282.65496313 07 0 0 0 0 0 0 76.20112
1 2 3 4 5 6 71 0.0070 0 0 0 0 0 02 0 0.0014 0 0 0 0 03 0 0 0.0041 0 0 0 0
4 0 0 0 0.0019 0 0 05 0 0 0 0 0.0015 0 06 0 0 0 0 0 0.0035 07 0 0 0 0 0 0 0.0131
[A21] [([N] x [A11]')-1]1 2 3 4 5 6 7
1 0.007012 -0.00144 0 0 -0.00152 0 02 0 0.001438 0.004063 0 0 0 03 0 0 -0.00406 0.001943 0 0 04 0 0 0 -0.00194 0.001524 0.0035378823 05 0 0 0 0 0 -0.0035378823 0.013123
[A21] [([N] x [A11])-1][A12]1 2 3 4 5 6 7
1 0.009974 -0.00144 0 -0.00152 02 -0.00144 0.005501 -0.00406 0 03 0 -0.00406 0.006006 -0.00194 04 -0.00152 0 -0.00194 0.007005 -0.003545 0 0 0 -0.00354 0.016661
[N] x [A11']
[N] x [A11']
([N] x [A11])-1
([N] x [A11])-1
[A21] [([N] x [A11])-1]
.-([A12])([N][A11]')-1[A12])-11 2 3 4 5 6 7
1 -121.293 -88.9927 -77.561 -53.6547 -11.39332 -88.9927 -474.225 -364.463 -134.93 -28.65163 -77.561 -364.463 -466.005 -163.695 -34.75974 -53.6547 -134.93 -163.695 -223.848 -47.5335 -11.3933 -28.6516 -34.7597 -47.533 -70.1136
[A11][Q] [A10][Ho]1 1
1 7.614745 1 -100 12 12.60346 2 0 23 0.461422 3 0 34 8.684741 4 0 45 3.457295 5 0 56 7.520549 6 0 67 3.551492 7 -100 7
[A21][Q]
1 11 -0.671 1 0.06 12 0.020 2 0.04 23 0.015 3 0.03 34 0.015 4 0.03 45 -1.292 5 0.04 5
Hi+1=-([A12])([N][A11]')-1[A12])-1(([A21][N][A11'])-1([A11][Q]+[A10][Ho])-[A21][Q]-[q])
H2 92.38525H3 79.7818H4 = 80.24322H5 88.92796H6 96.44851
Cálculo de Qi+1Para el cálculo de Qi+1 se utilizará la Ecuación
de la resolución sistemática de esta ecuación resultan las siguientes matrices:
([A21][N][A11'])-1([A11][Q]+[A10][Ho])
([A21][N][A11'])-1([A11][Q]+[A10][Ho])-[A21][Q]-[q]
[A12][Hi+1] [A12][Hi+1]+[A10][Ho]92.38525 -7.61475-12.6035 -12.6035-0.46142 -0.46142-8.68474 -8.68474
-3.4573 -3.4573-7.52055 -7.5205596.44851 -3.55149
([N] x [A11])-1[A11]
0.5 0 0 0 0 0 00 0.5 0 0 0 0 00 0 0.5 0 0 0 00 0 0 0.5 0 0 00 0 0 0 0.5 0 00 0 0 0 0 0.5 00 0 0 0 0 0 0.5
[I]-(([N] x [A11])-1[A11])0.5 0 0 0 0 0 0
0 0.5 0 0 0 0 00 0 0.5 0 0 0 00 0 0 0.5 0 0 00 0 0 0 0.5 0 00 0 0 0 0 0.5 00 0 0 0 0 0 0.5
Luego
Tuberia No Q(m3/s)1 2 0.10682 3 0.03634 3 0.00375 4 0.03372 5 0.01056 5 0.05321 6 0.0932
x
V Re f hf hf+hm B=hl
(m/s) (m) (m) (m)2.17543 476692.70058 0.01579 6.678 6.678 0.0002.05134 269700.39861 0.01829 79.590 95.911 16.3210.47744 41847.86734 0.01986 328.153 328.153 0.0001.90985 251097.81085 0.01752 76.245 76.245 0.0001.34151 117583.45567 0.01885 311.436 311.436 0.0001.69384 296931.05477 0.01714 26.559 26.559 0.0001.89893 416104.22992 0.01610 4.087 4.087 0.000
Q(m3/s)1
1 0.10682 0.03633 0.00374 0.03375 0.01056 0.05327 0.0932
10-6 m2/s
[A21 x Ndw-1 x (Qa x A11
-1 x A10 x Hn) + q - A21 x Qa]
([A11][Q]+[A10][Ho])1
-92.38512.6030.46148.68473.45737.5205
-96.449
1-0.670.020.010.01-1.29
Hi+1=-([A12])([N][A11]')-1[A12])-1(([A21][N][A11'])-1([A11][Q]+[A10][Ho])-[A21][Q]-[q])
([A21][N][A11'])-1([A11][Q]+[A10][Ho])-[A21][Q]-[q]
([N] x [A11])-1([A12][Hi+1]+[A10][Ho])-0.0534-0.0181-0.0019-0.0169-0.0053-0.0266-0.0466
([I]-(([N] x [A11])-1)[A11])[Q]0.050.020.000.020.010.030.05
α = hf
(m) (m)667.765 0
9591.122 032815.327 07624.545 0
31143.645 02655.851 0408.744 0
g = hBomba
Re D K f X0 0.001 0.00253999 0.005688476692.701 0.25 0.00006 0.01584168 X1 0.00253999 0.005688 0.01041767269700.399 0.15 0.00006 0.01777309 F(X) 24.350745 12.2985565 5.516770741847.8673 0.10 0.00006 0.02355745 F'(X) -15812.2569 -3906.7725 -1166.41754251097.811 0.15 0.00006 0.0178864 ERROR 6062979316 5534473910 4540045721117583.456 0.10 0.00006 0.02033102 X0 0.001 0.00257039 0.00586748296931.055 0.20 0.00006 0.01698541 X1 0.00257039 0.00586748 0.01105523416104.23 0.25 0.00006 0.01602734 F(X) 24.8314836 12.6531593 5.77577863
F'(X) -15812.257 -3837.67869 -1113.34924ERROR 6109546818 5619253818 4692575280X0 0.001 0.0026601 0.00640003X1 0.0026601 0.00640003 0.01296775F(X) 26.2498499 13.6330244 6.41944519F'(X) -15812.257 -3645.25387 -977.423602ERROR 6240735862 5843623097 5064655509X0 0.001 0.0025733 0.00588332X1 0.0025733 0.00588332 0.0111058F(X) 24.8773471 12.6813449 5.79099544F'(X) -15812.257 -3831.1935 -1108.85991ERROR 6113931961 5626117157 4702478471X0 0.001 0.00261065 0.00610404X1 0.00261065 0.00610404 0.01189482F(X) 25.4679804 13.0977005 6.0763307F'(X) -15812.257 -3749.28247 -1049.31049ERROR 6169533414 5723079337 4868324070X0 0.001 0.00256248 0.0058158X1 0.00256248 0.0058158 0.01084861F(X) 24.7063701 12.5430435 5.67807131F'(X) -15812.257 -3855.46334 -1128.21128ERROR 6097533870 5593929193 4639128586X0 0.001 0.00254547 0.00571723X1 0.00254547 0.00571723 0.01050767F(X) 24.437365 12.3513823 5.54488638F'(X) -15812.2569 -3894.17062 -1157.49028ERROR 6071452060 5547723297 4558992216
0.01041767 0.01451122 0.01580574 0.01584303 0.01584162 0.01584168 0.01584168 0.015841680.01451122 0.01580574 0.01584303 0.01584162 0.01584168 0.01584168 0.01584168 0.015841681.92848271 0.37139674 0.00941536 -0.00035309 1.39126E-05 -5.4719E-07 2.15232E-08 -8.4658E-10
-471.102621 -286.900224 -252.490191 -251.602345 -251.635663 -251.634351 -251.634402 -251.63442820955376 819016043 23537177.3 885865.67 34900.6427 1372.68171 53.9926976 2.123729260.01105523 0.01591989 0.01769612 0.017776 0.01777297 0.0177731 0.01777309 0.017773090.01591989 0.01769612 0.017776 0.01777297 0.0177731 0.01777309 0.01777309 0.01777309
2.0967515 0.44368056 0.01703722 -0.00064264 2.65773E-05 -1.0955E-06 4.51581E-08 -1.8616E-09-431.016967 -249.788669 -213.267956 -211.837763 -211.89178 -211.889547 -211.889639 -211.8896353055712135 1003736408 44940614.8 1706898.15 70572.0738 2908.844 119.912202 4.94315690.01296775 0.02020635 0.02344855 0.02356656 0.02355665 0.02355752 0.02355744 0.023557450.02020635 0.02344855 0.02356656 0.02355665 0.02355752 0.02355744 0.02355745 0.023557452.45719854 0.56720492 0.01653458 -0.00137816 0.00012101 -1.058E-05 9.25356E-07 -8.0932E-08
-339.457741 -174.944407 -140.118953 -139.07437 -139.161587 -139.15393 -139.154599 -139.1545413582338264 1382686929 50072612.5 4206669.66 369123.95 32274.5093 2822.81915 246.884929
0.0111058 0.01601766 0.01781185 0.01788938 0.01788627 0.01788641 0.0178864 0.01788640.01601766 0.01781185 0.01788938 0.01788627 0.01788641 0.0178864 0.0178864 0.01788642.10268476 0.44408432 0.0163755 -0.00065237 2.82867E-05 -1.2225E-06 5.28421E-08 -2.2841E-09
-428.082626 -247.513082 -211.201243 -209.835311 -209.889796 -209.887434 -209.887536 -209.8875323066531292 1007298730 43341373.1 1738182.31 75347.3102 3256.42399 140.757174 6.08412150.01189482 0.01778528 0.0202115 0.02033695 0.0203307 0.02033104 0.02033102 0.020331020.01778528 0.0202115 0.02033695 0.0203307 0.02033104 0.02033102 0.02033102 0.020331022.27541369 0.51356319 0.02193808 -0.00108264 5.89695E-05 -3.1969E-06 1.73355E-07 -9.4002E-09
-386.287753 -211.672709 -174.877954 -173.270382 -173.349865 -173.345536 -173.345771 -173.3457583311987041 1200412566 61684753.4 3073321.6 167318.704 9070.97317 491.884323 26.67268680.01084861 0.01540482 0.0169414 0.01698736 0.01698532 0.01698541 0.01698541 0.016985410.01540482 0.0169414 0.01698736 0.01698532 0.01698541 0.01698541 0.01698541 0.016985412.02006323 0.40316127 0.0104616 -0.00046281 2.14999E-05 -9.9667E-07 4.62069E-08 -2.1422E-09
-443.364315 -262.376641 -227.61807 -226.698449 -226.739164 -226.737273 -226.737361 -226.7373572957655082 906993988 27056128.9 1201926.82 55825.6954 2587.9237 119.979707 5.562402140.01050767 0.01467696 0.01599508 0.01602867 0.01602728 0.01602734 0.01602733 0.016027340.01467696 0.01599508 0.01602867 0.01602728 0.01602734 0.01602733 0.01602734 0.016027341.93902667 0.37180303 0.00833089 -0.00034428 1.48149E-05 -6.3646E-07 2.73447E-08 -1.1748E-09
-465.074199 -282.069124 -248.035527 -247.25904 -247.291149 -247.289767 -247.289827 -247.2898242840701303 824082885 20954628.2 868757.064 37379.0386 1605.84332 68.9932133 2.9642013
0.015841680.01584168
3.32996E-11-251.6344
0.083533860.017773090.01777309
7.67404E-11-211.8896350.203775530.023557450.02355745
7.07836E-09-139.15454621.5927085
0.01788640.0178864
9.87281E-11-209.8875320.262986130.020331020.02033102
5.09735E-10-173.3457591.446347230.016985410.01698541
9.93152E-11-226.7373570.257878820.016027340.01602734
5.04761E-11-247.2898240.12735615
Octavo Paso PROCESO DE ITERACIÓN: SEGUNDA ITERACIÓN
Calculo de la Viscocidad Cinematica
Ѵ = m =r
Ѵ = 1.1409 x
Ks = 0.00006
Tuberia Q L D V
(i) (j) (m) (m) (m/s)1 2 0.1068 500.00 0.25 2.175432 3 0.0363 400.00 0.15 2.051344 3 0.0037 200.00 0.10 0.477445 4 0.0337 400.00 0.15 1.909852 5 0.0105 200.00 0.10 1.341516 5 0.0532 600.00 0.20 1.693841 6 0.0932 300.00 0.25 1.89893
Calculo de la Matriz A11
1 2 3 4 5 6 71 71.30821 0 0 0 0 0 02 0 347.6799 0 0 0 0 0
A11 3 0 0 123.0516 0 0 0 04 0 0 0 257.327 0 0 05 0 0 0 0 328.1353 0 06 0 0 0 0 0 141.32748156 07 0 0 0 0 0 0 38.10056
Finalmente:
=
1 2 3 4 5 6 71 0.5 0 0 0 0 0 02 0 0.5 0 0 0 0 03 0 0 0.5 0 0 0 0
4 0 0 0 0.5 0 0 05 0 0 0 0 0.5 0 06 0 0 0 0 0 0.5 07 0 0 0 0 0 0 0.5
(1.14 - 0.031 (T-15) + 0.00068 (T - 15)2)
10-6 m2/s
(m3/s)
A11 = αij x Qij(nj-1)+βi+(gi/Qi)
H(next) [(A21 x Ndw-1 x A11
-1 x A12)] [A21 x Ndw-1 x (Qa x A11
-1 x A10 x Hn) + q - A21 x Qa]
Calculo de Matrices por Partes para el calculo del (H next)
Ndw-1
1 2 3 4 5 6 71 71.30821 0 0 0 0 0 02 0 347.6799 0 0 0 0 0
A11 ' 3 0 0 123.0516 0 0 0 04 0 0 0 257.327 0 0 05 0 0 0 0 328.1353 0 06 0 0 0 0 0 141.32748156 07 0 0 0 0 0 0 38.10056
1 2 3 4 5 6 71 142.6164 0 0 0 0 0 02 0 695.3598 0 0 0 0 03 0 0 246.1033 0 0 0 0
4 0 0 0 514.6541 0 0 05 0 0 0 0 656.2706 0 06 0 0 0 0 0 282.65496313 07 0 0 0 0 0 0 76.20112
1 2 3 4 5 6 71 0.0070 0 0 0 0 0 02 0 0.0014 0 0 0 0 03 0 0 0.0041 0 0 0 0
4 0 0 0 0.0019 0 0 05 0 0 0 0 0.0015 0 06 0 0 0 0 0 0.0035 07 0 0 0 0 0 0 0.0131
[A21] [([N] x [A11]')-1]1 2 3 4 5 6 7
1 0.007012 -0.00144 0 0 -0.00152 0 02 0 0.001438 0.004063 0 0 0 03 0 0 -0.00406 0.001943 0 0 04 0 0 0 -0.00194 0.001524 0.0035378823 05 0 0 0 0 0 -0.0035378823 0.013123
[A21] [([N] x [A11])-1][A12]1 2 3 4 5 6 7
1 0.009974 -0.00144 0 -0.00152 02 -0.00144 0.005501 -0.00406 0 03 0 -0.00406 0.006006 -0.00194 04 -0.00152 0 -0.00194 0.007005 -0.003545 0 0 0 -0.00354 0.016661
[N] x [A11']
[N] x [A11']
([N] x [A11])-1
([N] x [A11])-1
[A21] [([N] x [A11])-1]
.-([A12])([N][A11]')-1[A12])-11 2 3 4 5 6 7
1 -121.293 -88.9927 -77.561 -53.6547 -11.39332 -88.9927 -474.225 -364.463 -134.93 -28.65163 -77.561 -364.463 -466.005 -163.695 -34.75974 -53.6547 -134.93 -163.695 -223.848 -47.5335 -11.3933 -28.6516 -34.7597 -47.533 -70.1136
[A11][Q] [A10][Ho]1 1
1 7.614745 1 -100 12 12.60346 2 0 23 0.461422 3 0 34 8.684741 4 0 45 3.457295 5 0 56 7.520549 6 0 67 3.551492 7 -100 7
[A21][Q]
1 11 -0.671 1 0.06 12 0.020 2 0.04 23 0.015 3 0.03 34 0.015 4 0.03 45 -1.292 5 0.04 5
Hi+1=-([A12])([N][A11]')-1[A12])-1(([A21][N][A11'])-1([A11][Q]+[A10][Ho])-[A21][Q]-[q])
H2 92.38525H3 79.7818H4 = 80.24322H5 88.92796H6 96.44851
Cálculo de Qi+1Para el cálculo de Qi+1 se utilizará la Ecuación
de la resolución sistemática de esta ecuación resultan las siguientes matrices:
([A21][N][A11'])-1([A11][Q]+[A10][Ho])
([A21][N][A11'])-1([A11][Q]+[A10][Ho])-[A21][Q]-[q]
[A12][Hi+1] [A12][Hi+1]+[A10][Ho]92.38525 -7.61475-12.6035 -12.6035-0.46142 -0.46142-8.68474 -8.68474
-3.4573 -3.4573-7.52055 -7.5205596.44851 -3.55149
([N] x [A11])-1[A11]
0.5 0 0 0 0 0 00 0.5 0 0 0 0 00 0 0.5 0 0 0 00 0 0 0.5 0 0 00 0 0 0 0.5 0 00 0 0 0 0 0.5 00 0 0 0 0 0 0.5
[I]-(([N] x [A11])-1[A11])0.5 0 0 0 0 0 0
0 0.5 0 0 0 0 00 0 0.5 0 0 0 00 0 0 0.5 0 0 00 0 0 0 0.5 0 00 0 0 0 0 0.5 00 0 0 0 0 0 0.5
Luego
Tuberia No Q(m3/s)1 2 0.10682 3 0.03634 3 0.00375 4 0.03372 5 0.01056 5 0.05321 6 0.0932
x
V Re f hf hf+hm B=hl
(m/s) (m) (m) (m)2.17543 476692.70058 0.01579 6.678 6.678 0.0002.05134 269700.39861 0.01829 79.590 95.911 16.3210.47744 41847.86734 0.01986 328.153 328.153 0.0001.90985 251097.81085 0.01752 76.245 76.245 0.0001.34151 117583.45567 0.01885 311.436 311.436 0.0001.69384 296931.05477 0.01714 26.559 26.559 0.0001.89893 416104.22992 0.01610 4.087 4.087 0.000
Q(m3/s)1
1 0.10682 0.03633 0.00374 0.03375 0.01056 0.05327 0.0932
10-6 m2/s
[A21 x Ndw-1 x (Qa x A11
-1 x A10 x Hn) + q - A21 x Qa]
([A11][Q]+[A10][Ho])1
-92.38512.6030.46148.68473.45737.5205
-96.449
1-0.670.020.010.02-1.29
Hi+1=-([A12])([N][A11]')-1[A12])-1(([A21][N][A11'])-1([A11][Q]+[A10][Ho])-[A21][Q]-[q])
([A21][N][A11'])-1([A11][Q]+[A10][Ho])-[A21][Q]-[q]
([N] x [A11])-1([A12][Hi+1]+[A10][Ho])-0.0534-0.0181-0.0019-0.0169-0.0053-0.0266-0.0466
([I]-(([N] x [A11])-1)[A11])[Q]0.050.020.000.020.010.030.05
α = hf
(m) (m)667.765 0
9591.122 032815.327 07624.545 0
31143.645 02655.851 0408.744 0
g = hBomba
Re D K f X0 0.001 0.00253999 0.005688476692.701 0.25 0.00006 0.01584168 X1 0.00253999 0.005688 0.01041767269700.399 0.15 0.00006 0.01777309 F(X) 24.350745 12.2985565 5.516770741847.8673 0.10 0.00006 0.02355745 F'(X) -15812.2569 -3906.7725 -1166.41754251097.811 0.15 0.00006 0.0178864 ERROR 6062979316 5534473910 4540045721117583.456 0.10 0.00006 0.02033102 X0 0.001 0.00257039 0.00586748296931.055 0.20 0.00006 0.01698541 X1 0.00257039 0.00586748 0.01105523416104.23 0.25 0.00006 0.01602734 F(X) 24.8314836 12.6531593 5.77577863
F'(X) -15812.257 -3837.67869 -1113.34924ERROR 6109546818 5619253818 4692575280X0 0.001 0.0026601 0.00640003X1 0.0026601 0.00640003 0.01296775F(X) 26.2498499 13.6330244 6.41944519F'(X) -15812.257 -3645.25387 -977.423602ERROR 6240735862 5843623097 5064655509X0 0.001 0.0025733 0.00588332X1 0.0025733 0.00588332 0.0111058F(X) 24.8773471 12.6813449 5.79099544F'(X) -15812.257 -3831.1935 -1108.85991ERROR 6113931961 5626117157 4702478471X0 0.001 0.00261065 0.00610404X1 0.00261065 0.00610404 0.01189482F(X) 25.4679804 13.0977005 6.0763307F'(X) -15812.257 -3749.28247 -1049.31049ERROR 6169533414 5723079337 4868324070X0 0.001 0.00256248 0.0058158X1 0.00256248 0.0058158 0.01084861F(X) 24.7063701 12.5430435 5.67807131F'(X) -15812.257 -3855.46334 -1128.21128ERROR 6097533870 5593929193 4639128586X0 0.001 0.00254547 0.00571723X1 0.00254547 0.00571723 0.01050767F(X) 24.437365 12.3513823 5.54488638F'(X) -15812.2569 -3894.17062 -1157.49028ERROR 6071452060 5547723297 4558992216
0.01041767 0.01451122 0.01580574 0.01584303 0.01584162 0.01584168 0.01584168 0.015841680.01451122 0.01580574 0.01584303 0.01584162 0.01584168 0.01584168 0.01584168 0.015841681.92848271 0.37139674 0.00941536 -0.00035309 1.39126E-05 -5.4719E-07 2.15232E-08 -8.4658E-10
-471.102621 -286.900224 -252.490191 -251.602345 -251.635663 -251.634351 -251.634402 -251.63442820955376 819016043 23537177.3 885865.67 34900.6427 1372.68171 53.9926976 2.123729260.01105523 0.01591989 0.01769612 0.017776 0.01777297 0.0177731 0.01777309 0.017773090.01591989 0.01769612 0.017776 0.01777297 0.0177731 0.01777309 0.01777309 0.01777309
2.0967515 0.44368056 0.01703722 -0.00064264 2.65773E-05 -1.0955E-06 4.51581E-08 -1.8616E-09-431.016967 -249.788669 -213.267956 -211.837763 -211.89178 -211.889547 -211.889639 -211.8896353055712135 1003736408 44940614.8 1706898.15 70572.0738 2908.84401 119.912202 4.943151040.01296775 0.02020635 0.02344855 0.02356656 0.02355665 0.02355752 0.02355744 0.023557450.02020635 0.02344855 0.02356656 0.02355665 0.02355752 0.02355744 0.02355745 0.023557452.45719854 0.56720492 0.01653458 -0.00137816 0.00012101 -1.058E-05 9.25356E-07 -8.0932E-08
-339.457741 -174.944407 -140.118953 -139.07437 -139.161587 -139.15393 -139.154599 -139.1545413582338264 1382686929 50072612.5 4206669.66 369123.95 32274.5093 2822.81915 246.884929
0.0111058 0.01601766 0.01781185 0.01788938 0.01788627 0.01788641 0.0178864 0.01788640.01601766 0.01781185 0.01788938 0.01788627 0.01788641 0.0178864 0.0178864 0.01788642.10268476 0.44408432 0.0163755 -0.00065237 2.82867E-05 -1.2225E-06 5.28421E-08 -2.2841E-09
-428.082626 -247.513082 -211.201243 -209.835311 -209.889796 -209.887434 -209.887536 -209.8875323066531292 1007298730 43341373.1 1738182.31 75347.3102 3256.42399 140.757174 6.08412150.01189482 0.01778528 0.0202115 0.02033695 0.0203307 0.02033104 0.02033102 0.020331020.01778528 0.0202115 0.02033695 0.0203307 0.02033104 0.02033102 0.02033102 0.020331022.27541369 0.51356319 0.02193808 -0.00108264 5.89695E-05 -3.1969E-06 1.73355E-07 -9.4002E-09
-386.287753 -211.672709 -174.877954 -173.270382 -173.349865 -173.345536 -173.345771 -173.3457583311987041 1200412566 61684753.4 3073321.6 167318.704 9070.97317 491.884318 26.67267830.01084861 0.01540482 0.0169414 0.01698736 0.01698532 0.01698541 0.01698541 0.016985410.01540482 0.0169414 0.01698736 0.01698532 0.01698541 0.01698541 0.01698541 0.016985412.02006323 0.40316127 0.0104616 -0.00046281 2.14999E-05 -9.9667E-07 4.62069E-08 -2.1422E-09
-443.364315 -262.376641 -227.61807 -226.698449 -226.739164 -226.737273 -226.737361 -226.7373572957655082 906993988 27056128.9 1201926.82 55825.6954 2587.9237 119.979711 5.562402140.01050767 0.01467696 0.01599508 0.01602867 0.01602728 0.01602734 0.01602733 0.016027340.01467696 0.01599508 0.01602867 0.01602728 0.01602734 0.01602733 0.01602734 0.016027341.93902667 0.37180303 0.00833089 -0.00034428 1.48149E-05 -6.3646E-07 2.73447E-08 -1.1748E-09
-465.074199 -282.069124 -248.035527 -247.25904 -247.291149 -247.289767 -247.289827 -247.2898242840701303 824082885 20954628.2 868757.064 37379.0386 1605.84331 68.9932155 2.96420779
0.015841680.01584168
3.32996E-11-251.6344
0.083533860.017773090.01777309
7.67395E-11-211.8896350.203773580.023557450.02355745
7.07836E-09-139.15454621.5927085
0.01788640.0178864
9.87281E-11-209.8875320.262986130.020331020.02033102
5.09733E-10-173.345759
1.44633870.016985410.01698541
9.93152E-11-226.7373570.257878820.016027340.016027345.0477E-11
-247.2898240.12735832
Octavo Paso PROCESO DE ITERACIÓN: SEGUNDA ITERACIÓN
Calculo de la Viscocidad Cinematica
Ѵ = m =r
Ѵ = 1.1409 x
Ks = 0.00006
Tuberia Q L D V
(i) (j) (m) (m) (m/s)1 2 0.1068 500.00 0.25 2.175432 3 0.0363 400.00 0.15 2.051344 3 0.0037 200.00 0.10 0.477445 4 0.0337 400.00 0.15 1.909852 5 0.0105 200.00 0.10 1.341516 5 0.0532 600.00 0.20 1.693841 6 0.0932 300.00 0.25 1.89893
Calculo de la Matriz A11
1 2 3 4 5 6 71 71.30821 0 0 0 0 0 02 0 347.6799 0 0 0 0 0
A11 3 0 0 123.0516 0 0 0 04 0 0 0 257.327 0 0 05 0 0 0 0 328.1353 0 06 0 0 0 0 0 141.32748156 07 0 0 0 0 0 0 38.10056
Finalmente:
=
1 2 3 4 5 6 71 0.5 0 0 0 0 0 02 0 0.5 0 0 0 0 03 0 0 0.5 0 0 0 0
4 0 0 0 0.5 0 0 05 0 0 0 0 0.5 0 06 0 0 0 0 0 0.5 07 0 0 0 0 0 0 0.5
(1.14 - 0.031 (T-15) + 0.00068 (T - 15)2)
10-6 m2/s
(m3/s)
A11 = αij x Qij(nj-1)+βi+(gi/Qi)
H(next) [(A21 x Ndw-1 x A11
-1 x A12)] [A21 x Ndw-1 x (Qa x A11
-1 x A10 x Hn) + q - A21 x Qa]
Calculo de Matrices por Partes para el calculo del (H next)
Ndw-1
1 2 3 4 5 6 71 71.30821 0 0 0 0 0 02 0 347.6799 0 0 0 0 0
A11 ' 3 0 0 123.0516 0 0 0 04 0 0 0 257.327 0 0 05 0 0 0 0 328.1353 0 06 0 0 0 0 0 141.32748156 07 0 0 0 0 0 0 38.10056
1 2 3 4 5 6 71 142.6164 0 0 0 0 0 02 0 695.3598 0 0 0 0 03 0 0 246.1033 0 0 0 0
4 0 0 0 514.6541 0 0 05 0 0 0 0 656.2706 0 06 0 0 0 0 0 282.65496313 07 0 0 0 0 0 0 76.20112
1 2 3 4 5 6 71 0.0070 0 0 0 0 0 02 0 0.0014 0 0 0 0 03 0 0 0.0041 0 0 0 0
4 0 0 0 0.0019 0 0 05 0 0 0 0 0.0015 0 06 0 0 0 0 0 0.0035 07 0 0 0 0 0 0 0.0131
[A21] [([N] x [A11]')-1]1 2 3 4 5 6 7
1 0.007012 -0.00144 0 0 -0.00152 0 02 0 0.001438 0.004063 0 0 0 03 0 0 -0.00406 0.001943 0 0 04 0 0 0 -0.00194 0.001524 0.0035378823 05 0 0 0 0 0 -0.0035378823 0.013123
[A21] [([N] x [A11])-1][A12]1 2 3 4 5 6 7
1 0.009974 -0.00144 0 -0.00152 02 -0.00144 0.005501 -0.00406 0 03 0 -0.00406 0.006006 -0.00194 04 -0.00152 0 -0.00194 0.007005 -0.003545 0 0 0 -0.00354 0.016661
[N] x [A11']
[N] x [A11']
([N] x [A11])-1
([N] x [A11])-1
[A21] [([N] x [A11])-1]
.-([A12])([N][A11]')-1[A12])-11 2 3 4 5 6 7
1 -121.293 -88.9927 -77.561 -53.6547 -11.39332 -88.9927 -474.225 -364.463 -134.93 -28.65163 -77.561 -364.463 -466.005 -163.695 -34.75974 -53.6547 -134.93 -163.695 -223.848 -47.5335 -11.3933 -28.6516 -34.7597 -47.533 -70.1136
[A11][Q] [A10][Ho]1 1
1 7.614745 1 -100 12 12.60346 2 0 23 0.461422 3 0 34 8.684741 4 0 45 3.457295 5 0 56 7.520549 6 0 67 3.551492 7 -100 7
[A21][Q]
1 11 -0.671 1 0.06 12 0.020 2 0.04 23 0.015 3 0.03 34 0.015 4 0.03 45 -1.292 5 0.04 5
Hi+1=-([A12])([N][A11]')-1[A12])-1(([A21][N][A11'])-1([A11][Q]+[A10][Ho])-[A21][Q]-[q])
H2 92.38525H3 79.7818H4 = 80.24322H5 88.92796H6 96.44851
Cálculo de Qi+1Para el cálculo de Qi+1 se utilizará la Ecuación
de la resolución sistemática de esta ecuación resultan las siguientes matrices:
([A21][N][A11'])-1([A11][Q]+[A10][Ho])
([A21][N][A11'])-1([A11][Q]+[A10][Ho])-[A21][Q]-[q]
[A12][Hi+1] [A12][Hi+1]+[A10][Ho]92.38525 -7.61475-12.6035 -12.6035-0.46142 -0.46142-8.68474 -8.68474
-3.4573 -3.4573-7.52055 -7.5205596.44851 -3.55149
([N] x [A11])-1[A11]
0.5 0 0 0 0 0 00 0.5 0 0 0 0 00 0 0.5 0 0 0 00 0 0 0.5 0 0 00 0 0 0 0.5 0 00 0 0 0 0 0.5 00 0 0 0 0 0 0.5
[I]-(([N] x [A11])-1[A11])0.5 0 0 0 0 0 0
0 0.5 0 0 0 0 00 0 0.5 0 0 0 00 0 0 0.5 0 0 00 0 0 0 0.5 0 00 0 0 0 0 0.5 00 0 0 0 0 0 0.5
Luego
Tuberia No Q(m3/s)1 2 0.10682 3 0.03634 3 0.00375 4 0.03372 5 0.01056 5 0.05321 6 0.0932
x
V Re f hf hf+hm B=hl
(m/s) (m) (m) (m)2.17543 476692.70058 0.01579 6.678 6.678 0.0002.05134 269700.39861 0.01829 79.590 95.911 16.3210.47744 41847.86734 0.01986 328.153 328.153 0.0001.90985 251097.81085 0.01752 76.245 76.245 0.0001.34151 117583.45567 0.01885 311.436 311.436 0.0001.69384 296931.05477 0.01714 26.559 26.559 0.0001.89893 416104.22992 0.01610 4.087 4.087 0.000
Q(m3/s)1
1 0.10682 0.03633 0.00374 0.03375 0.01056 0.05327 0.0932
10-6 m2/s
[A21 x Ndw-1 x (Qa x A11
-1 x A10 x Hn) + q - A21 x Qa]
([A11][Q]+[A10][Ho])1
-92.38512.6030.46148.68473.45737.5205
-96.449
1-0.670.020.010.01-1.29
Hi+1=-([A12])([N][A11]')-1[A12])-1(([A21][N][A11'])-1([A11][Q]+[A10][Ho])-[A21][Q]-[q])
([A21][N][A11'])-1([A11][Q]+[A10][Ho])-[A21][Q]-[q]
([N] x [A11])-1([A12][Hi+1]+[A10][Ho])-0.0534-0.0181-0.0019-0.0169-0.0053-0.0266-0.0466
([I]-(([N] x [A11])-1)[A11])[Q]0.050.020.000.020.010.030.05
α = hf
(m) (m)667.765 0
9591.122 032815.327 07624.545 0
31143.645 02655.851 0408.744 0
g = hBomba
Re D K f X0 0.001 0.002539992476692.7006 0.25 0.00006 0.015841678 X1 0.002539992 0.005688001269700.3986 0.15 0.00006 0.01777309 F(X) 24.35074501 12.2985564641847.86734 0.10 0.00006 0.023557448 F'(X) -15812.2569 -3906.7725251097.8109 0.15 0.00006 0.017886404 ERROR 6062979316 5534473910117583.4557 0.10 0.00006 0.02033102 X0 0.001 0.002570395296931.0548 0.20 0.00006 0.016985408 X1 0.002570395 0.005867481416104.2299 0.25 0.00006 0.016027335 F(X) 24.83148359 12.6531593
F'(X) -15812.257 -3837.67869ERROR 6109546818 5619253818X0 0.001 0.002660095X1 0.002660095 0.006400033F(X) 26.24984995 13.63302439F'(X) -15812.257 -3645.25387ERROR 6240735862 5843623097X0 0.001 0.002573295X1 0.002573295 0.00588332F(X) 24.87734707 12.68134485F'(X) -15812.257 -3831.1935ERROR 6113931961 5626117157X0 0.001 0.002610648X1 0.002610648 0.006104037F(X) 25.46798045 13.09770051F'(X) -15812.257 -3749.28247ERROR 6169533414 5723079337X0 0.001 0.002562482X1 0.002562482 0.005815799F(X) 24.70637006 12.5430435F'(X) -15812.257 -3855.46334ERROR 6097533870 5593929193X0 0.001 0.00254547X1 0.00254547 0.005717232F(X) 24.43736502 12.35138227F'(X) -15812.2569 -3894.17062ERROR 6071452060 5547723297
0.005688001 0.010417672 0.014511223 0.015805738 0.015843028 0.015841625 0.015841680.010417672 0.014511223 0.015805738 0.015843028 0.015841625 0.01584168 0.0158416785.516770703 1.928482712 0.371396735 0.009415363 -0.00035309 1.39126E-05 -5.47194E-07-1166.41754 -471.102621 -286.900224 -252.490191 -251.602345 -251.635663 -251.6343514540045721 2820955376 819016043 23537177.3 885865.6704 34900.64273 1372.681708
0.005867481 0.011055232 0.015919893 0.017696117 0.017776004 0.01777297 0.0177730950.011055232 0.015919893 0.017696117 0.017776004 0.01777297 0.017773095 0.01777309
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