teoria lineal
DESCRIPTION
Diseño de tuberías método de la teoría linealTRANSCRIPT
Hallar los Qij y las presiones en cada nudo, para la red mostrada en la figura:
Ecuación de continuidad en cada nudo (+ caudales que llegan, - caudales que llegan)
NUDO 1
Ecuación n° 1 500-Q12-+Q16=0 → -Q12-Q16=-500
NUDO 2
Ecuación n° 2 Q12-Q23-Q25-50=0 → Q12-Q23-Q25=50
NUDO 3
Ecuación n° 3 Q23-Q34-30=0 → Q23-Q34=30
NUDO 4
Ecuación n° 4 Q34-Q45-40=0 → Q34-Q45=40
NUDO 5
Ecuación n° 5 Q25+Q45+Q56-340=0 → Q25+Q45+Q56=340
NUDO 6
Ecuación n° 6 -Q56+Q16-40=0 → -Q56+Q16=40
Ecuaciones de conservación de la energía en los circuitos.
♠Se asume: Kij*Qij ---► + en sentido horario y - en sentido antihorario.
CIRCUITO I
Ecuación n° 7 K'12*Q12+K'25*Q25-K'56*Q56-K'16*Q16=0
CIRCUITO II
Ecuación n° 8 K'23*Q23+K'34*Q34+K'45*Q45-K'25*Q25=0
☼ se tiene 7 incógnitas (Qij) y hay 8 ecuaciones, entonces el sistema si se puede desarrolllar.
☼ podemos eliminar una ecuación (cualquiera) que no es indispensable (redundante).ORDENANDO: Las ecuaciones en forma ordenada serán:
-Q12 -Q16 0 0 0 0 0 =-500
Q12 0 -Q23 0 0 -Q25 0 =50
0 0 Q23 -Q34 0 0 0 =30
0 0 0 Q34 -Q45 0 0 =40
0 0 0 0 Q45 Q25 Q56 =340
K'12*Q12 -K'16*Q16 0 0 0 K'25*Q25 -K'56*Q56 =0
0 0 K'23*Q23 K'34*Q34 K'45*Q45 -K'25*Q25 0 =0
Formula a utilizar:
DATOS DE INGRESO:
Tramo Longitud (m) Diámetro (m) Caudal (m3/S)
(1-2) 600 0.2 0.242
(1-6) 300 0.25 0.242
(2-3) 500 0.3 0.242
(3-4) 250 0.2 0.242
(4-5) 450 0.2 0.242
(2-5) 250 0.15 0.242
(5-6) 700 0.2 0.242
Longitud= 600 Caudal= 0.242
Viscosidad= 0.00000114 Diámetro= 0.2
Ks= 0.000100 Velocidad= 7.703081232
f G(f)
DATO CALCULADO
Tubería (1-2)
1/fDato asumido
Ks/dNúmero de
Reynolds Denominador Denominador
MÉTODO DE LA TEORÍA LINEAL
𝑓 =1
(−2 ∗ 𝐿𝑜𝑔(𝐾𝑠
3.7 ∗ 𝑑+
2.51
𝑅𝑒 ∗ 𝑓))2
L = 600 m L = 500 m
L = 250 m
L = 450 m
L = 250 mL = 300 m
L = 700 m
Ø= 200 mm
Ø= 200 mm
Ø= 150 mm
Ø= 300 cmØ= 200 mm
Ø= 250 mm
Ø= 200 mm
Qe = 500 Lt/s
50 Lt/s 30 Lt/s
40 Lt/s340 Lt/s
40 Lt/s
Km=10m
III
++
1 23
45
6
0.001 0.000500 1,351,418 7.424985974 7.424985974 0.018138807
0.01813881 0.000500 1,351,418 7.654061129 7.654061129 0.017069317
0.01706932 0.000500 1,351,418 7.651583209 7.651583209 0.017080375
0.01708037 0.000500 1,351,418 7.651609975 7.651609975 0.017080255
0.01708026 0.000500 1,351,418 7.651609686 7.651609686 0.017080
Longitud= 300 Caudal= 0.242
Viscosidad= 0.00000114 Diámetro= 0.25
Ks= 0.000100 Velocidad= 4.929971989
f G(f)
DATO CALCULADO
0.001 0.000400 1,081,134 7.482128632 7.482128632 0.017862805
0.01786281 0.000400 1,081,134 7.802858687 7.802858687 0.016424514
0.01642451 0.000400 1,081,134 7.797719529 7.797719529 0.01644617
0.01644617 0.000400 1,081,134 7.797801636 7.797801636 0.016445824
0.01644582 0.000400 1,081,134 7.797800324 7.797800324 0.016445829
Longitud= 500 Caudal= 0.242
Viscosidad= 0.00000114 Diámetro= 0.3
Ks= 0.000100 Velocidad= 3.423591659
f G(f)
DATO CALCULADO
0.001 0.000333 900,945 7.498233449 7.498233449 0.017786155
0.01778616 0.000333 900,945 7.909511406 7.909511406 0.01598456
0.01598456 0.000333 900,945 7.900589689 7.900589689 0.016020681
0.01602068 0.000333 900,945 7.900782256 7.900782256 0.0160199
0.0160199 0.000333 900,945 7.900778099 7.900778099 0.016019917
Longitud= 250 Caudal= 0.242
Viscosidad= 0.00000114 Diámetro= 0.2
Ks= 0.000100 Velocidad= 7.703081232
f G(f)
DATO CALCULADO
0.001 0.000500 1,351,418 7.424985974 7.424985974 0.018138807
0.01813881 0.000500 1,351,418 7.654061129 7.654061129 0.017069317
0.01706932 0.000500 1,351,418 7.651583209 7.651583209 0.017080375
0.01708037 0.000500 1,351,418 7.651609975 7.651609975 0.017080255
0.01708026 0.000500 1,351,418 7.651609686 7.651609686 0.017080256
Longitud= 450 Caudal= 0.242
Viscosidad= 0.00000114 Diámetro= 0.2
Ks= 0.000100 Velocidad= 7.703081232
f G(f)
DATO CALCULADO
0.001 0.000500 1,351,418 7.424985974 7.424985974 0.018138807
0.01813881 0.000500 1,351,418 7.654061129 7.654061129 0.017069317
0.01706932 0.000500 1,351,418 7.651583209 7.651583209 0.017080375
0.01708037 0.000500 1,351,418 7.651609975 7.651609975 0.017080255
0.01708026 0.000500 1,351,418 7.651609686 7.651609686 0.017080256
Longitud= 250 Caudal= 0.242
Viscosidad= 0.00000114 Diámetro= 0.15
Ks= 0.000100 Velocidad= 13.69436664
Dato asumido 1/f
Tubería (1-6)
Ks/dNúmero de
Reynolds Denominador Denominador
Tubería (3-4)
Ks/dNúmero de
Reynolds Denominador DenominadorDato asumido 1/f
Tubería (2-3)
Ks/dNúmero de
Reynolds Denominador DenominadorDato asumido 1/f
Tubería (4-5)
Ks/dNúmero de
Reynolds Denominador DenominadorDato asumido 1/f
Tubería (2-5)
f G(f)
DATO CALCULADO
0.001 0.000667 1,801,890 7.298612084 7.298612084 0.018772384
0.01877238 0.000667 1,801,890 7.440907872 7.440907872 0.018061264
0.01806126 0.000667 1,801,890 7.440003849 7.440003849 0.018065654
0.01806565 0.000667 1,801,890 7.440009589 7.440009589 0.018065626
0.01806563 0.000667 1,801,890 7.440009552 7.440009552 0.018065626
Longitud= 700 Caudal= 0.242
Viscosidad= 0.00000114 Diámetro= 0.2
Ks= 0.000100 Velocidad= 7.703081232
f G(f)
DATO CALCULADO
0.001 0.000500 1,351,418 7.424985974 7.424985974 0.018138807
0.01813881 0.000500 1,351,418 7.654061129 7.654061129 0.017069317
0.01706932 0.000500 1,351,418 7.651583209 7.651583209 0.017080375
0.01708037 0.000500 1,351,418 7.651609975 7.651609975 0.017080255
0.01708026 0.000500 1,351,418 7.651609686 7.651609686 0.017080256
Tramo Longitud Diámetro Caudal Velocidad f hfi Kmi HFI+km
(1-2) 600 0.2 0.242 7.703081232 0.017080256 154.969271 0 640.368889
(1-6) 300 0.25 0.242 4.929971989 0.016445829 24.4470762 0 101.020976
(2-3) 500 0.3 0.242 3.423591659 0.016019917 15.9504866 10 71.8850976
(3-4) 250 0.2 0.242 7.703081232 0.017080256 64.5705297 0 266.820371
(4-5) 450 0.2 0.242 7.703081232 0.017080256 116.226953 0 480.276667
(2-5) 250 0.15 0.242 13.69436664 0.018065626 287.797265 0 1189.2449
(5-6) 700 0.2 0.242 7.703081232 0.017080256 180.797483 0 747.097038
ELABORACIÓN DE LA MATRIZ
-1.00 -1.00 0.00 0.00 0.00 0.00 0.00 Q1-2 -0.5
1.00 0.00 -1.00 0.00 0.00 -1.00 0.00 Q1-6 0.05
0.00 0.00 1.00 -1.00 0.00 0.00 0.00 Q2-3 0.03
0.00 0.00 0.00 1.00 -1.00 0.00 0.00 Q3-4 0.04
0.00 0.00 0.00 0.00 1.00 1.00 1.00 Q5-4 0.34
640.37 -101.02 0.00 0.00 0.00 1189.24 -747.10 Q2-5 0.00
0 0 71.89 266.82 480.277 -1189.2449 0 Q6-5 0.00
Tenemos que encontrar
Qi+1
-0.0511893 0.62432304 0.60275229 0.522686791 0.378568901 0.00050672 0.00030007 Q1-2 0.22451429
-0.9488107 -0.624323 -0.6027523 -0.52268679 -0.378568901 -0.00050672 -0.0003001 Q1-6 0.27548571
-0.0303136 -0.2224708 0.72895997 0.548682618 0.224183385 0.000300073 0.00067565 Q2-3 0.12407173
-0.0303136 -0.2224708 -0.27104 0.548682618 0.224183385 0.000300073 0.00067565 Q3-4 0.09407173
-0.0303136 -0.2224708 -0.27104 -0.45131738 0.224183385 0.000300073 0.00067565 Q5-4 0.05407173
-0.0208757 -0.1532061 -0.1262077 -0.02599583 0.154385516 0.000206647 -0.0003756 Q2-5 0.05044256
0.05118933 0.37567696 0.39724771 0.477313209 0.621431099 -0.00050672 -0.0003001 Q6-5 0.23548571
Número de
Reynolds Denominador DenominadorDato asumido 1/f
Tubería (5-6)
Ks/dNúmero de
Reynolds Denominador DenominadorDato asumido 1/f
Ks/d
𝑿 = 𝑨 −𝟏 ∗ 𝑩
𝑴𝒂𝒕𝒓𝒊𝒛 𝑨𝑴𝒂𝒕𝒓𝒊𝒛 𝑩
𝑴𝒂𝒕𝒓𝒊𝒛 𝒊𝒏𝒗𝒆𝒓𝒔𝒂 ( 𝑨−𝟏 )
𝑷𝒓𝒐𝒅𝒖𝒄𝒕𝒐 𝒅𝒆𝒎𝒂𝒕𝒓𝒊𝒄𝒆𝒔 ( 𝑨−𝟏 ∗ 𝑩 )
NUEVOS CAUDALES =
Q1-2 0.23325714
Q1-6 0.25874286
Q2-3 0.18303586
Q3-4 0.16803586
Q5-4 0.14803586
Q2-5 0.14622128
Q6-5 0.23874286
SEGUNDA ITERACIÓN
Formula a utilizar:
DATOS DE INGRESO:
Tramo Longitud (m) Diámetro (m) Caudal (m3/S)
(1-2) 600 0.2 0.233257143
(1-6) 300 0.25 0.258742857
(2-3) 500 0.3 0.183035865
(3-4) 250 0.2 0.168035865
(4-5) 450 0.2 0.148035865
(2-5) 250 0.15 0.146221278
(5-6) 700 0.2 0.238742857
Longitud= 600 Caudal= 0.233257143
Viscosidad= 0.00000114 Diámetro= 0.2
Ks= 0.000100 Velocidad= 7.424788091
f G(f)
DATO CALCULADO
0.001 0.000500 1,302,594 7.415178534 7.415178534 0.01818682
0.01818682 0.000500 1,302,594 7.651161503 7.651161503 0.017082257
0.01708226 0.000500 1,302,594 7.648522255 7.648522255 0.017094048
0.01709405 0.000500 1,302,594 7.648551728 7.648551728 0.017093917
0.01709392 0.000500 1,302,594 7.648551399 7.648551399 0.017094
Longitud= 300 Caudal= 0.258742857
Viscosidad= 0.00000114 Diámetro= 0.25
Ks= 0.000100 Velocidad= 5.27105388
f G(f)
DATO CALCULADO
0.001 0.000400 1,155,933 7.505163188 7.505163188 0.017753326
0.01775333 0.000400 1,155,933 7.810325255 7.810325255 0.016393125
0.01639313 0.000400 1,155,933 7.805711075 7.805711075 0.016412512
0.01641251 0.000400 1,155,933 7.805780661 7.805780661 0.016412219
0.01641222 0.000400 1,155,933 7.805779612 7.805779612 0.016412224
Longitud= 500 Caudal= 0.183035865
Viscosidad= 0.00000114 Diámetro= 0.3
Ks= 0.000100 Velocidad= 2.589421735
f G(f)
DATO CALCULADO
0.001 0.000333 681,427 7.36986155 7.36986155 0.018411168
0.01841117 0.000333 681,427 7.861873637 7.861873637 0.016178859
0.01617886 0.000333 681,427 7.848549285 7.848549285 0.016233838
0.01623384 0.000333 681,427 7.848907447 7.848907447 0.016232357
0.01623236 0.000333 681,427 7.848897818 7.848897818 0.016232397
Tubería (1-6)
Ks/dNúmero de
Reynolds Denominador DenominadorDato asumido 1/f
Tubería (1-2)
Ks/dNúmero de
Reynolds Denominador DenominadorDato asumido 1/f
Tubería (2-3)
Ks/dNúmero de
Reynolds Denominador DenominadorDato asumido 1/f
𝑸𝒊 +𝑸𝒊+𝟏
𝟐
𝑓 =1
(−2 ∗ 𝐿𝑜𝑔(𝐾𝑠
3.7 ∗ 𝑑+
2.51
𝑅𝑒 ∗ 𝑓))2
Longitud= 250 Caudal= 0.168035865
Viscosidad= 0.00000114 Diámetro= 0.2
Ks= 0.000100 Velocidad= 5.34873519
f G(f)
DATO CALCULADO
0.001 0.000500 938,375 7.316257108 7.316257108 0.018681945
0.01868194 0.000500 938,375 7.620991651 7.620991651 0.017217775
0.01721778 0.000500 938,375 7.616427209 7.616427209 0.017238418
0.01723842 0.000500 938,375 7.6164954 7.6164954 0.017238109
0.01723811 0.000500 938,375 7.616494381 7.616494381 0.017238114
0.01723811 0.000500 938,375 7.616494397 7.616494397 0.017238114
Longitud= 450 Caudal= 0.148035865
Viscosidad= 0.00000114 Diámetro= 0.2
Ks= 0.000100 Velocidad= 4.712116906
f G(f)
DATO CALCULADO
0.001 0.000500 826,687 7.272217151 7.272217151 0.018908903
0.0189089 0.000500 826,687 7.607011212 7.607011212 0.01728112
0.01728112 0.000500 826,687 7.60141325 7.60141325 0.017306582
0.01730658 0.000500 826,687 7.601506555 7.601506555 0.017306157
0.01730616 0.000500 826,687 7.601505 7.601505 0.017306165
Longitud= 250 Caudal= 0.146221278
Viscosidad= 0.00000114 Diámetro= 0.15
Ks= 0.000100 Velocidad= 8.274412355
f G(f)
DATO CALCULADO
0.001 0.000667 1,088,738 7.193470695 7.193470695 0.019325158
0.01932516 0.000667 1,088,738 7.41210803 7.41210803 0.018201891
0.01820189 0.000667 1,088,738 7.40988581 7.40988581 0.018212811
0.01821281 0.000667 1,088,738 7.409908367 7.409908367 0.0182127
0.0182127 0.000667 1,088,738 7.409908138 7.409908138 0.018212701
Longitud= 700 Caudal= 0.238742857
Viscosidad= 0.00000114 Diámetro= 0.2
Ks= 0.000100 Velocidad= 7.599403404
f G(f)
DATO CALCULADO
0.001 0.000500 1,333,229 7.421403345 7.421403345 0.018156324
0.01815632 0.000500 1,333,229 7.653003797 7.653003797 0.017074034
0.01707403 0.000500 1,333,229 7.650467556 7.650467556 0.017085356
0.01708536 0.000500 1,333,229 7.65049529 7.65049529 0.017085233
0.01708523 0.000500 1,333,229 7.650494987 7.650494987 0.017085234
Tramo Longitud Diámetro Caudal Velocidad f hfi Kmi HFI+km
(1-2) 600 0.2 0.233257143 7.424788091 0.017093918 144.089389 0 617.727659
(1-6) 300 0.25 0.258742857 5.27105388 0.016412224 27.8897476 0 107.78944
(2-3) 500 0.3 0.183035865 2.589421735 0.016232397 9.24566118 10 53.9303238
(3-4) 250 0.2 0.168035865 5.34873519 0.017238114 31.4197664 0 186.982502
(4-5) 450 0.2 0.148035865 4.712116906 0.017306165 44.0673015 0 297.679901
(2-5) 250 0.15 0.146221278 8.274412355 0.018212701 105.924987 0 724.415683
(5-6) 700 0.2 0.238742857 7.599403404 0.017085234 176.014712 0 737.256453
Tubería (3-4)
Ks/dNúmero de
Reynolds Denominador DenominadorDato asumido 1/f
Tubería (2-5)
Ks/dNúmero de
Reynolds Denominador DenominadorDato asumido 1/f
Tubería (4-5)
Ks/dNúmero de
Reynolds Denominador DenominadorDato asumido 1/f
Tubería (5-6)
Ks/dNúmero de
Reynolds Denominador DenominadorDato asumido 1/f
ELABORACIÓN DE LA MATRIZ
-1.00 -1.00 0.00 0.00 0.00 0.00 0.00 Q1-2 -0.5
1.00 0.00 -1.00 0.00 0.00 -1.00 0.00 Q1-6 0.05
0.00 0.00 1.00 -1.00 0.00 0.00 0.00 Q2-3 0.03
0.00 0.00 0.00 1.00 -1.00 0.00 0.00 Q3-4 0.04
0.00 0.00 0.00 0.00 1.00 1.00 1.00 Q5-4 0.34
617.73 -107.79 0.00 0.00 0.00 724.42 -737.26 Q2-5 0
0 0 53.93 186.98 297.680 -724.415683 0 Q6-5 0
Tenemos que encontrar
Qi+2
-0.0608399 0.5904945 0.57303521 0.512501867 0.41613157 0.000564433 0.00032374 Q1-2 0.23912053
-0.9391601 -0.5904945 -0.5730352 -0.51250187 -0.41613157 -0.00056443 -0.0003237 Q1-6 0.26087947
-0.0348955 -0.2348775 0.71240863 0.529643576 0.238677932 0.000323738 0.00097744 Q2-3 0.1294124
-0.0348955 -0.2348775 -0.2875914 0.529643576 0.238677932 0.000323738 0.00097744 Q3-4 0.0994124
-0.0348955 -0.2348775 -0.2875914 -0.47035642 0.238677932 0.000323738 0.00097744 Q5-4 0.0594124
-0.0259443 -0.174628 -0.1393734 -0.01714171 0.177453638 0.000240695 -0.0006537 Q2-5 0.05970813
0.06083987 0.4095055 0.42696479 0.487498133 0.58386843 -0.00056443 -0.0003237 Q6-5 0.22087947
NUEVOS CAUDALES (1) %
Q1-2 0.23618883 1.24124911
Q1-6 0.25981117 0.4111864
Q2-3 0.15622413 17.1623518
Q3-4 0.13372413 25.6585964
Q5-4 0.10372413 42.7207583
Q2-5 0.1029647 42.0110693
Q6-5 0.22981117 3.88653519
TERCERA ITERACIÓN
Formula a utilizar:
DATOS DE INGRESO:
Tramo Longitud (m) Diámetro (m) Caudal (m3/S)
(1-2) 600 0.2 0.236188834
(1-6) 300 0.25 0.259811166
(2-3) 500 0.3 0.15622413
(3-4) 250 0.2 0.13372413
(4-5) 450 0.2 0.10372413
(2-5) 250 0.15 0.102964705
(5-6) 700 0.2 0.229811166
Longitud= 600 Caudal= 0.236188834
Viscosidad= 0.00000114 Diámetro= 0.2
Ks= 0.000100 Velocidad= 7.518106521
f G(f)
DATO CALCULADO
0.001 0.000500 1,318,966 7.418535648 7.418535648 0.018170364
0.01817036 0.000500 1,318,966 7.652155891 7.652155891 0.017077818
0.01707782 0.000500 1,318,966 7.649572461 7.649572461 0.017089355
0.01708936 0.000500 1,318,966 7.649600987 7.649600987 0.017089228
0.01708923 0.000500 1,318,966 7.649600672 7.649600672 0.017089
Tubería (1-2)
Ks/dNúmero de
Reynolds Denominador DenominadorDato asumido 1/f
𝑿 = 𝑨 −𝟏 ∗ 𝑩
𝑴𝒂𝒕𝒓𝒊𝒛 𝑨𝑴𝒂𝒕𝒓𝒊𝒛 𝑩
𝑴𝒂𝒕𝒓𝒊𝒛 𝒊𝒏𝒗𝒆𝒓𝒔𝒂 ( 𝑨−𝟏 )𝑨−𝟏 ∗ 𝑩
𝑸𝒊+𝟏 +𝑸𝒊+𝟐
𝟐
𝑵𝒖𝒆𝒗𝒐𝒔 𝒄𝒂𝒖𝒅𝒂𝒍𝒆𝒔(𝟏) − 𝑵𝒖𝒆𝒗𝒐𝒔 𝒄𝒂𝒖𝒅𝒂𝒍𝒆𝒔
𝑵𝒖𝒆𝒗𝒐𝒔 𝒄𝒂𝒖𝒅𝒂𝒍𝒆𝒔(𝟏)∗ 𝟏𝟎𝟎
𝑓 =1
(−2 ∗ 𝐿𝑜𝑔(𝐾𝑠
3.7 ∗ 𝑑+
2.51
𝑅𝑒 ∗ 𝑓))2
Longitud= 300 Caudal= 0.259811166
Viscosidad= 0.00000114 Diámetro= 0.25
Ks= 0.000100 Velocidad= 5.292817225
f G(f)
DATO CALCULADO
0.001 0.000400 1,160,706 7.506551614 7.506551614 0.017746759
0.01774676 0.000400 1,160,706 7.810772269 7.810772269 0.016391249
0.01639125 0.000400 1,160,706 7.806188798 7.806188798 0.016410503
0.0164105 0.000400 1,160,706 7.806257675 7.806257675 0.016410214
0.01641021 0.000400 1,160,706 7.80625664 7.80625664 0.016410218
Longitud= 500 Caudal= 0.15622413
Viscosidad= 0.00000114 Diámetro= 0.3
Ks= 0.000100 Velocidad= 2.210114166
f G(f)
DATO CALCULADO
0.001 0.000333 581,609 7.289626655 7.289626655 0.018818692
0.01881869 0.000333 581,609 7.830495032 7.830495032 0.016308783
0.01630878 0.000333 581,609 7.813973169 7.813973169 0.016377823
0.01637782 0.000333 581,609 7.814473235 7.814473235 0.016375727
0.01637573 0.000333 581,609 7.814458096 7.814458096 0.01637579
Longitud= 250 Caudal= 0.13372413
Viscosidad= 0.00000114 Diámetro= 0.2
Ks= 0.000100 Velocidad= 4.256561304
f G(f)
DATO CALCULADO
0.001 0.000500 746,765 7.234437431 7.234437431 0.019106911
0.01910691 0.000500 746,765 7.594744063 7.594744063 0.017336991
0.01733699 0.000500 746,765 7.588171962 7.588171962 0.017367035
0.01736703 0.000500 746,765 7.588291395 7.588291395 0.017366488
0.01736649 0.000500 746,765 7.588289225 7.588289225 0.017366498
0.0173665 0.000500 746,765 7.588289264 7.588289264 0.017366498
Longitud= 450 Caudal= 0.10372413
Viscosidad= 0.00000114 Diámetro= 0.2
Ks= 0.000100 Velocidad= 3.301633878
f G(f)
DATO CALCULADO
0.001 0.000500 579,234 7.130330984 7.130330984 0.019668925
0.01966892 0.000500 579,234 7.55961084 7.55961084 0.017498512
0.01749851 0.000500 579,234 7.549933449 7.549933449 0.017543399
0.0175434 0.000500 579,234 7.550150426 7.550150426 0.017542391
0.01754239 0.000500 579,234 7.55014556 7.55014556 0.017542414
Longitud= 250 Caudal= 0.102964705
Viscosidad= 0.00000114 Diámetro= 0.15
Ks= 0.000100 Velocidad= 5.826596755
f G(f)
DATO CALCULADO
0.001 0.000667 766,657 7.094245682 7.094245682 0.019869528
Tubería (2-3)
Ks/dNúmero de
Reynolds Denominador DenominadorDato asumido 1/f
Tubería (1-6)
Ks/dNúmero de
Reynolds Denominador DenominadorDato asumido 1/f
Tubería (4-5)
Ks/dNúmero de
Reynolds Denominador DenominadorDato asumido 1/f
Tubería (3-4)
Ks/dNúmero de
Reynolds Denominador DenominadorDato asumido 1/f
Tubería (2-5)
Ks/dNúmero de
Reynolds Denominador DenominadorDato asumido 1/f
0.01986953 0.000667 766,657 7.383270763 7.383270763 0.018344353
0.01834435 0.000667 766,657 7.379239424 7.379239424 0.018364402
0.0183644 0.000667 766,657 7.379295525 7.379295525 0.018364123
0.01836412 0.000667 766,657 7.379294744 7.379294744 0.018364127
Longitud= 700 Caudal= 0.229811166
Viscosidad= 0.00000114 Diámetro= 0.2
Ks= 0.000100 Velocidad= 7.315099489
f G(f)
DATO CALCULADO
0.001 0.000500 1,283,351 7.411140227 7.411140227 0.018206646
0.01820665 0.000500 1,283,351 7.649962803 7.649962803 0.017087611
0.01708761 0.000500 1,283,351 7.64725559 7.64725559 0.017099712
0.01709971 0.000500 1,283,351 7.647286231 7.647286231 0.017099575
0.01709957 0.000500 1,283,351 7.647285884 7.647285884 0.017099576
Tramo Longitud Diámetro Caudal Velocidad f hfi Kmi HFI+km
(1-2) 600 0.2 0.236188834 7.518106521 0.017089229 147.693599 0 625.319986
(1-6) 300 0.25 0.259811166 5.292817225 0.016410218 28.117091 0 108.221257
(2-3) 500 0.3 0.15622413 2.210114166 0.01637579 6.79487434 10 45.9840019
(3-4) 250 0.2 0.13372413 4.256561304 0.017366498 20.0466147 0 149.910227
(4-5) 450 0.2 0.10372413 3.301633878 0.017542414 21.929599 0 211.422347
(2-5) 250 0.15 0.102964705 5.826596755 0.018364127 52.9602415 0 514.353358
(5-6) 700 0.2 0.229811166 7.315099489 0.017099576 163.228077 0 710.270436
ELABORACIÓN DE LA MATRIZ
-1.00 -1.00 0.00 0.00 0.00 0.00 0.00 Q1-2 -0.5
1.00 0.00 -1.00 0.00 0.00 -1.00 0.00 Q1-6 0.05
0.00 0.00 1.00 -1.00 0.00 0.00 0.00 Q2-3 0.03
0.00 0.00 0.00 1.00 -1.00 0.00 0.00 Q3-4 0.04
0.00 0.00 0.00 0.00 1.00 1.00 1.00 Q5-4 0.34
625.32 -108.22 0.00 0.00 0.00 514.35 -710.27 Q2-5 0
0 0 45.98 149.91 211.422 -514.353358 0 Q6-5 0
Tenemos que encontrar
Qi+3
-0.0647597 0.56104853 0.54569229 0.495630156 0.425026203 0.000598401 0.00033395 Q1-2 0.24113714
-0.9352403 -0.5610485 -0.5456923 -0.49563016 -0.425026203 -0.0005984 -0.0003339 Q1-6 0.25886286
-0.0361402 -0.2449642 0.69657392 0.505985239 0.237192998 0.000333947 0.00127135 Q2-3 0.12760414
-0.0361402 -0.2449642 -0.3034261 0.505985239 0.237192998 0.000333947 0.00127135 Q3-4 0.09760414
-0.0361402 -0.2449642 -0.3034261 -0.49401476 0.237192998 0.000333947 0.00127135 Q5-4 0.05760414
-0.0286194 -0.1939872 -0.1508816 -0.01035508 0.187833205 0.000264453 -0.0009374 Q2-5 0.063533
0.06475966 0.43895147 0.45430771 0.504369844 0.574973797 -0.0005984 -0.0003339 Q6-5 0.21886286
NUEVOS CAUDALES (2) %
Q1-2 0.23866299 1.03667207
Q1-6 0.25933701 0.18283257
Q2-3 0.14191414 10.083558
Q3-4 0.11566414 15.6141695
Q5-4 0.08066414 28.5876667
Q2-5 0.08324885 23.6830334
Q6-5 0.22433701 2.44014684
Tubería (5-6)
Ks/dNúmero de
Reynolds Denominador DenominadorDato asumido 1/f
𝑿 = 𝑨 −𝟏 ∗ 𝑩
𝑴𝒂𝒕𝒓𝒊𝒛 𝑨𝑴𝒂𝒕𝒓𝒊𝒛 𝑩
𝑴𝒂𝒕𝒓𝒊𝒛 𝒊𝒏𝒗𝒆𝒓𝒔𝒂 ( 𝑨−𝟏 )
𝑨−𝟏 ∗ 𝑩
𝑸𝒊+𝟐 +𝑸𝒊+𝟑
𝟐𝑵𝒖𝒆𝒗𝒐𝒔 𝒄𝒂𝒖𝒅𝒂𝒍𝒆𝒔(𝟐) − 𝑵𝒖𝒆𝒗𝒐𝒔 𝒄𝒂𝒖𝒅𝒂𝒍𝒆𝒔
𝑵𝒖𝒆𝒗𝒐𝒔 𝒄𝒂𝒖𝒅𝒂𝒍𝒆𝒔(𝟐)∗ 𝟏𝟎𝟎
CUARTA ITERACIÓN
Formula a utilizar:
DATOS DE INGRESO:
Tramo Longitud (m) Diámetro (m) Caudal (m3/S)
(1-2) 600 0.2 0.238662987
(1-6) 300 0.25 0.259337013
(2-3) 500 0.3 0.141914136
(3-4) 250 0.2 0.115664136
(4-5) 450 0.2 0.080664136
(2-5) 250 0.15 0.083248851
(5-6) 700 0.2 0.224337013
Longitud= 600 Caudal= 0.238662987
Viscosidad= 0.00000114 Diámetro= 0.2
Ks= 0.000100 Velocidad= 7.596861058
f G(f)
DATO CALCULADO
0.001 0.000500 1,332,783 7.421314453 7.421314453 0.018156759
0.01815676 0.000500 1,332,783 7.652977535 7.652977535 0.017074151
0.01707415 0.000500 1,332,783 7.650439838 7.650439838 0.01708548
0.01708548 0.000500 1,332,783 7.650467597 7.650467597 0.017085356
0.01708536 0.000500 1,332,783 7.650467293 7.650467293 0.017085
Longitud= 300 Caudal= 0.259337013
Viscosidad= 0.00000114 Diámetro= 0.25
Ks= 0.000100 Velocidad= 5.283157891
f G(f)
DATO CALCULADO
0.001 0.000400 1,158,587 7.50593652 7.50593652 0.017749668
0.01774967 0.000400 1,158,587 7.810574277 7.810574277 0.01639208
0.01639208 0.000400 1,158,587 7.805977215 7.805977215 0.016411393
0.01641139 0.000400 1,158,587 7.806046406 7.806046406 0.016411102
0.0164111 0.000400 1,158,587 7.806045364 7.806045364 0.016411106
Longitud= 500 Caudal= 0.141914136
Viscosidad= 0.00000114 Diámetro= 0.3
Ks= 0.000100 Velocidad= 2.007669633
f G(f)
DATO CALCULADO
0.001 0.000333 528,334 7.238409341 7.238409341 0.019085947
0.01908595 0.000333 528,334 7.809813455 7.809813455 0.016395274
0.01639527 0.000333 528,334 7.791074887 7.791074887 0.016474234
0.01647423 0.000333 528,334 7.79168303 7.79168303 0.016471663
0.01647166 0.000333 528,334 7.791663286 7.791663286 0.016471746
Longitud= 250 Caudal= 0.115664136
Viscosidad= 0.00000114 Diámetro= 0.2
Ks= 0.000100 Velocidad= 3.681695177
f G(f)
DATO CALCULADO
0.001 0.000500 645,911 7.176691018 7.176691018 0.019415631
0.01941563 0.000500 645,911 7.575498909 7.575498909 0.01742519
0.01742519 0.000500 645,911 7.567280796 7.567280796 0.017463058
Tubería (1-6)
Ks/dNúmero de
Reynolds Denominador DenominadorDato asumido 1/f
Tubería (1-2)
Ks/dNúmero de
Reynolds Denominador DenominadorDato asumido 1/f
Tubería (3-4)
Ks/dNúmero de
Reynolds Denominador DenominadorDato asumido 1/f
Tubería (2-3)
Ks/dNúmero de
Reynolds Denominador DenominadorDato asumido 1/f
𝑓 =1
(−2 ∗ 𝐿𝑜𝑔(𝐾𝑠
3.7 ∗ 𝑑+
2.51
𝑅𝑒 ∗ 𝑓))2
0.01746306 0.000500 645,911 7.567449362 7.567449362 0.01746228
0.01746228 0.000500 645,911 7.567445904 7.567445904 0.017462296
0.0174623 0.000500 645,911 7.567445975 7.567445975 0.017462296
Longitud= 450 Caudal= 0.080664136
Viscosidad= 0.00000114 Diámetro= 0.2
Ks= 0.000100 Velocidad= 2.56761318
f G(f)
DATO CALCULADO
0.001 0.000500 450,458 7.013528929 7.013528929 0.020329505
0.02032951 0.000500 450,458 7.517827779 7.517827779 0.017693561
0.01769356 0.000500 450,458 7.503929661 7.503929661 0.017759163
0.01775916 0.000500 450,458 7.504309718 7.504309718 0.017757364
0.01775736 0.000500 450,458 7.504299323 7.504299323 0.017757413
Longitud= 250 Caudal= 0.083248851
Viscosidad= 0.00000114 Diámetro= 0.15
Ks= 0.000100 Velocidad= 4.710910298
f G(f)
DATO CALCULADO
0.001 0.000667 619,857 7.022247273 7.022247273 0.020279057
0.02027906 0.000667 619,857 7.361306723 7.361306723 0.018453985
0.01845399 0.000667 619,857 7.355609007 7.355609007 0.018482586
0.01848259 0.000667 619,857 7.355704446 7.355704446 0.018482106
0.01848211 0.000667 619,857 7.355702847 7.355702847 0.018482114
Longitud= 700 Caudal= 0.224337013
Viscosidad= 0.00000114 Diámetro= 0.2
Ks= 0.000100 Velocidad= 7.140852209
f G(f)
DATO CALCULADO
0.001 0.000500 1,252,781 7.404510886 7.404510886 0.018239261
0.01823926 0.000500 1,252,781 7.647988979 7.647988979 0.017096432
0.01709643 0.000500 1,252,781 7.645168247 7.645168247 0.01710905
0.01710905 0.000500 1,252,781 7.645200873 7.645200873 0.017108904
0.0171089 0.000500 1,252,781 7.645200495 7.645200495 0.017108906
Tramo Longitud Diámetro Caudal Velocidad f hfi Kmi HFI+km
(1-2) 600 0.2 0.238662987 7.596861058 0.017085358 150.769916 0 631.727265
(1-6) 300 0.25 0.259337013 5.283157891 0.016411106 28.0160744 0 108.029602
(2-3) 500 0.3 0.141914136 2.007669633 0.016471746 5.63993234 10 41.7962668
(3-4) 250 0.2 0.115664136 3.681695177 0.017462296 15.0802318 0 130.379497
(4-5) 450 0.2 0.080664136 2.56761318 0.017757413 13.4252509 0 166.433952
(2-5) 250 0.15 0.083248851 4.710910298 0.018482114 34.8426408 0 418.535994
(5-6) 700 0.2 0.224337013 7.140852209 0.017108906 155.629303 0 693.729942
ELABORACIÓN DE LA MATRIZ
-1.00 -1.00 0.00 0.00 0.00 0.00 0.00 Q1-2 -0.5
1.00 0.00 -1.00 0.00 0.00 -1.00 0.00 Q1-6 0.05
0.00 0.00 1.00 -1.00 0.00 0.00 0.00 Q2-3 0.03
0.00 0.00 0.00 1.00 -1.00 0.00 0.00 Q3-4 0.04
Tubería (2-5)
Ks/dNúmero de
Reynolds Denominador DenominadorDato asumido 1/f
Tubería (4-5)
Ks/dNúmero de
Reynolds Denominador DenominadorDato asumido 1/f
Tubería (5-6)
Ks/dNúmero de
Reynolds Denominador DenominadorDato asumido 1/f
0.00 0.00 0.00 0.00 1.00 1.00 1.00 Q5-4 0.34
631.73 -108.03 0.00 0.00 0.00 418.54 -693.73 Q2-5 0
0 0 41.80 130.38 166.434 -418.535994 0 Q6-5 0
Tenemos que encontrar
Qi+4
-0.0666576 0.54354703 0.52929102 0.484820761 0.428052929 0.000617031 0.00034108 Q1-2 0.24131572
-0.9333424 -0.543547 -0.529291 -0.48482076 -0.428052929 -0.00061703 -0.0003411 Q1-6 0.25868428
-0.0368471 -0.2523187 0.68459847 0.487817452 0.236619657 0.000341083 0.00150929 Q2-3 0.12630895
-0.0368471 -0.2523187 -0.3154015 0.487817452 0.236619657 0.000341083 0.00150929 Q3-4 0.09630895
-0.0368471 -0.2523187 -0.3154015 -0.51218255 0.236619657 0.000341083 0.00150929 Q5-4 0.05630895
-0.0298105 -0.2041343 -0.1553074 -0.00299669 0.191433272 0.000275948 -0.0011682 Q2-5 0.06500677
0.06665762 0.45645297 0.47070898 0.515179239 0.571947071 -0.00061703 -0.0003411 Q6-5 0.21868428
NUEVOS CAUDALES (3) %
Q1-2 0.23998935 0.55267698
Q1-6 0.25901065 0.12600483
Q2-3 0.13411154 5.81798934
Q3-4 0.10598654 9.13096614
Q5-4 0.06848654 17.7810049
Q2-5 0.07412781 12.3044761
Q6-5 0.22151065 1.27595037
QUINTA ITERACIÓN
Formula a utilizar:
DATOS DE INGRESO:
Tramo Longitud (m) Diámetro (m) Caudal (m3/S)
(1-2) 600 0.2 0.239989353
(1-6) 300 0.25 0.259010647
(2-3) 500 0.3 0.134111541
(3-4) 250 0.2 0.105986541
(4-5) 450 0.2 0.068486541
(2-5) 250 0.15 0.074127812
(5-6) 700 0.2 0.221510647
Longitud= 600 Caudal= 0.239989353
Viscosidad= 0.00000114 Diámetro= 0.2
Ks= 0.000100 Velocidad= 7.639080498
f G(f)
DATO CALCULADO
0.001 0.000500 1,340,190 7.42278414 7.42278414 0.01814957
0.01814957 0.000500 1,340,190 7.653411565 7.653411565 0.017072215
0.01707221 0.000500 1,340,190 7.650897885 7.650897885 0.017083435
0.01708343 0.000500 1,340,190 7.650925244 7.650925244 0.017083312
0.01708331 0.000500 1,340,190 7.650924946 7.650924946 0.017083
Tubería (1-2)
Ks/dNúmero de
Reynolds Denominador DenominadorDato asumido 1/f
𝑿 = 𝑨 −𝟏 ∗ 𝑩
𝑴𝒂𝒕𝒓𝒊𝒛 𝑨𝑴𝒂𝒕𝒓𝒊𝒛 𝑩
𝑴𝒂𝒕𝒓𝒊𝒛 𝒊𝒏𝒗𝒆𝒓𝒔𝒂 ( 𝑨−𝟏 )
𝑨−𝟏 ∗ 𝑩
𝑸𝒊+𝟑 +𝑸𝒊+𝟒
𝟐𝑵𝒖𝒆𝒗𝒐𝒔 𝒄𝒂𝒖𝒅𝒂𝒍𝒆𝒔(𝟑) − 𝑵𝒖𝒆𝒗𝒐𝒔 𝒄𝒂𝒖𝒅𝒂𝒍𝒆𝒔
𝑵𝒖𝒆𝒗𝒐𝒔 𝒄𝒂𝒖𝒅𝒂𝒍𝒆𝒔(𝟑)∗ 𝟏𝟎𝟎
𝑓 =1
(−2 ∗ 𝐿𝑜𝑔(𝐾𝑠
3.7 ∗ 𝑑+
2.51
𝑅𝑒 ∗ 𝑓))2
Longitud= 300 Caudal= 0.259010647
Viscosidad= 0.00000114 Diámetro= 0.25
Ks= 0.000100 Velocidad= 5.276509235
f G(f)
DATO CALCULADO
0.001 0.000400 1,157,129 7.505512088 7.505512088 0.017751675
0.01775168 0.000400 1,157,129 7.810437618 7.810437618 0.016392654
0.01639265 0.000400 1,157,129 7.805831165 7.805831165 0.016412007
0.01641201 0.000400 1,157,129 7.805900573 7.805900573 0.016411715
0.01641172 0.000400 1,157,129 7.805899527 7.805899527 0.01641172
Longitud= 500 Caudal= 0.134111541
Viscosidad= 0.00000114 Diámetro= 0.3
Ks= 0.000100 Velocidad= 1.89728575
f G(f)
DATO CALCULADO
0.001 0.000333 499,286 7.20737972 7.20737972 0.019250641
0.01925064 0.000333 499,286 7.797035848 7.797035848 0.016449054
0.01644905 0.000333 499,286 7.776888905 7.776888905 0.016534391
0.01653439 0.000333 499,286 7.777569616 7.777569616 0.016531497
0.0165315 0.000333 499,286 7.777546608 7.777546608 0.016531595
Longitud= 250 Caudal= 0.105986541
Viscosidad= 0.00000114 Diámetro= 0.2
Ks= 0.000100 Velocidad= 3.373648477
f G(f)
DATO CALCULADO
0.001 0.000500 591,868 7.139716637 7.139716637 0.019617246
0.01961725 0.000500 591,868 7.562859084 7.562859084 0.017483484
0.01748348 0.000500 591,868 7.553487045 7.553487045 0.017526897
0.0175269 0.000500 591,868 7.553693532 7.553693532 0.017525938
0.01752594 0.000500 591,868 7.553688982 7.553688982 0.017525959
0.01752596 0.000500 591,868 7.553689083 7.553689083 0.017525959
Longitud= 450 Caudal= 0.068486541
Viscosidad= 0.00000114 Diámetro= 0.2
Ks= 0.000100 Velocidad= 2.179989195
f G(f)
DATO CALCULADO
0.001 0.000500 382,454 6.930243992 6.930243992 0.020821065
0.02082107 0.000500 382,454 7.486480486 7.486480486 0.017842044
0.01784204 0.000500 382,454 7.469100238 7.469100238 0.017925176
0.01792518 0.000500 382,454 7.469638073 7.469638073 0.017922595
0.01792259 0.000500 382,454 7.469621425 7.469621425 0.017922674
Longitud= 250 Caudal= 0.074127812
Viscosidad= 0.00000114 Diámetro= 0.15
Ks= 0.000100 Velocidad= 4.194766283
f G(f)
DATO CALCULADO
0.001 0.000667 551,943 6.978944775 6.978944775 0.02053149
Tubería (2-3)
Ks/dNúmero de
Reynolds Denominador DenominadorDato asumido 1/f
Tubería (1-6)
Ks/dNúmero de
Reynolds Denominador DenominadorDato asumido 1/f
Tubería (4-5)
Ks/dNúmero de
Reynolds Denominador DenominadorDato asumido 1/f
Tubería (3-4)
Ks/dNúmero de
Reynolds Denominador DenominadorDato asumido 1/f
Tubería (2-5)
Ks/dNúmero de
Reynolds Denominador DenominadorDato asumido 1/f
0.02053149 0.000667 551,943 7.347666638 7.347666638 0.018522564
0.01852256 0.000667 551,943 7.340821006 7.340821006 0.018557127
0.01855713 0.000667 551,943 7.340947611 7.340947611 0.018556487
0.01855649 0.000667 551,943 7.340945269 7.340945269 0.018556498
Longitud= 700 Caudal= 0.221510647
Viscosidad= 0.00000114 Diámetro= 0.2
Ks= 0.000100 Velocidad= 7.050886398
f G(f)
DATO CALCULADO
0.001 0.000500 1,236,998 7.400980525 7.400980525 0.018256666
0.01825667 0.000500 1,236,998 7.646934787 7.646934787 0.017101146
0.01710115 0.000500 1,236,998 7.644052613 7.644052613 0.017114045
0.01711404 0.000500 1,236,998 7.644086332 7.644086332 0.017113894
0.01711389 0.000500 1,236,998 7.644085938 7.644085938 0.017113896
Tramo Longitud Diámetro Caudal Velocidad f hfi Kmi HFI+km
(1-2) 600 0.2 0.239989353 7.639080498 0.017083314 152.432138 0 635.162086
(1-6) 300 0.25 0.259010647 5.276509235 0.01641172 27.9466486 0 107.897683
(2-3) 500 0.3 0.134111541 1.89728575 0.016531595 5.0551028 10 39.5279782
(3-4) 250 0.2 0.105986541 3.373648477 0.017525959 12.7084466 0 119.906231
(4-5) 450 0.2 0.068486541 2.179989195 0.017922674 9.76776076 0 142.623071
(2-5) 250 0.15 0.074127812 4.194766283 0.018556498 27.7371165 0 374.179618
(5-6) 700 0.2 0.221510647 7.050886398 0.017113896 151.776787 0 685.189578
ELABORACIÓN DE LA MATRIZ
-1.00 -1.00 0.00 0.00 0.00 0.00 0.00 Q1-2 -0.5
1.00 0.00 -1.00 0.00 0.00 -1.00 0.00 Q1-6 0.05
0.00 0.00 1.00 -1.00 0.00 0.00 0.00 Q2-3 0.03
0.00 0.00 0.00 1.00 -1.00 0.00 0.00 Q3-4 0.04
0.00 0.00 0.00 0.00 1.00 1.00 1.00 Q5-4 0.34
635.16 -107.90 0.00 0.00 0.00 374.18 -685.19 Q2-5 0
0 0 39.53 119.91 142.623 -374.179618 0 Q6-5 0
Tenemos que encontrar
Qi+5
-0.0676311 0.5342444 0.52053494 0.478947962 0.429482122 0.000626808 0.00034683 Q1-2 0.24132566
-0.9323689 -0.5342444 -0.5205349 -0.47894796 -0.429482122 -0.00062681 -0.0003468 Q1-6 0.25867434
-0.0374221 -0.2577148 0.67624655 0.475921438 0.237643726 0.000346829 0.00167068 Q2-3 0.12594841
-0.0374221 -0.2577148 -0.3237535 0.475921438 0.237643726 0.000346829 0.00167068 Q3-4 0.09594841
-0.0374221 -0.2577148 -0.3237535 -0.52407856 0.237643726 0.000346829 0.00167068 Q5-4 0.05594841
-0.030209 -0.2080408 -0.1557116 0.003026525 0.191838396 0.000279979 -0.0013239 Q2-5 0.06537725
0.0676311 0.4657556 0.47946506 0.521052038 0.570517878 -0.00062681 -0.0003468 Q6-5 0.21867434
NUEVOS CAUDALES (4) %
Q1-2 0.24065751 0.27763639
Q1-6 0.25884249 0.06496337
Q2-3 0.13002998 3.13894087
Q3-4 0.10096748 4.9709711
Q5-4 0.06221748 10.0760501
Q2-5 0.06975253 6.27257987
Q6-5 0.22009249 0.64434401
Tubería (5-6)
Ks/dNúmero de
Reynolds Denominador DenominadorDato asumido 1/f
𝑿 = 𝑨 −𝟏 ∗ 𝑩
𝑴𝒂𝒕𝒓𝒊𝒛 𝑨 𝑴𝒂𝒕𝒓𝒊𝒛 𝑩
𝑴𝒂𝒕𝒓𝒊𝒛 𝒊𝒏𝒗𝒆𝒓𝒔𝒂 ( 𝑨−𝟏 )
𝑨−𝟏 ∗ 𝑩
𝑸𝒊+𝟒 +𝑸𝒊+𝟓
𝟐
𝑵𝒖𝒆𝒗𝒐𝒔 𝒄𝒂𝒖𝒅𝒂𝒍𝒆𝒔(𝟒) − 𝑵𝒖𝒆𝒗𝒐𝒔 𝒄𝒂𝒖𝒅𝒂𝒍𝒆𝒔
𝑵𝒖𝒆𝒗𝒐𝒔 𝒄𝒂𝒖𝒅𝒂𝒍𝒆𝒔(𝟒)∗ 𝟏𝟎𝟎
SEXTA ITERACIÓN
Formula a utilizar:
DATOS DE INGRESO:
Tramo Longitud (m) Diámetro (m) Caudal (m3/S)
(1-2) 600 0.2 0.240657506
(1-6) 300 0.25 0.258842494
(2-3) 500 0.3 0.130029976
(3-4) 250 0.2 0.100967476
(4-5) 450 0.2 0.062217476
(2-5) 250 0.15 0.069752529
(5-6) 700 0.2 0.220092494
Longitud= 600 Caudal= 0.240657506
Viscosidad= 0.00000114 Diámetro= 0.2
Ks= 0.000100 Velocidad= 7.660348413
f G(f)
DATO CALCULADO
0.001 0.000500 1,343,921 7.423519286 7.423519286 0.018145975
0.01814598 0.000500 1,343,921 7.653628532 7.653628532 0.017071247
0.01707125 0.000500 1,343,921 7.651126822 7.651126822 0.017082412
0.01708241 0.000500 1,343,921 7.651153981 7.651153981 0.017082291
0.01708229 0.000500 1,343,921 7.651153686 7.651153686 0.017082
Longitud= 300 Caudal= 0.258842494
Viscosidad= 0.00000114 Diámetro= 0.25
Ks= 0.000100 Velocidad= 5.273083662
f G(f)
DATO CALCULADO
0.001 0.000400 1,156,378 7.505293072 7.505293072 0.017752711
0.01775271 0.000400 1,156,378 7.810367087 7.810367087 0.01639295
0.01639295 0.000400 1,156,378 7.805755784 7.805755784 0.016412324
0.01641232 0.000400 1,156,378 7.805825304 7.805825304 0.016412032
0.01641203 0.000400 1,156,378 7.805824256 7.805824256 0.016412036
Longitud= 500 Caudal= 0.130029976
Viscosidad= 0.00000114 Diámetro= 0.3
Ks= 0.000100 Velocidad= 1.839543565
f G(f)
DATO CALCULADO
0.001 0.000333 484,090 7.190149249 7.190149249 0.019343016
0.01934302 0.000333 484,090 7.789859678 7.789859678 0.016479375
0.01647937 0.000333 484,090 7.768909633 7.768909633 0.016568373
0.01656837 0.000333 484,090 7.769633039 7.769633039 0.016565288
0.01656529 0.000333 484,090 7.76960805 7.76960805 0.016565394
Longitud= 250 Caudal= 0.100967476
Viscosidad= 0.00000114 Diámetro= 0.2
Ks= 0.000100 Velocidad= 3.213887079
Tubería (1-6)
Ks/dNúmero de
Reynolds Denominador DenominadorDato asumido 1/f
Tubería (1-2)
Ks/dNúmero de
Reynolds Denominador DenominadorDato asumido 1/f
Tubería (3-4)
Tubería (2-3)
Ks/dNúmero de
Reynolds Denominador DenominadorDato asumido 1/f
𝑓 =1
(−2 ∗ 𝐿𝑜𝑔(𝐾𝑠
3.7 ∗ 𝑑+
2.51
𝑅𝑒 ∗ 𝑓))2
f G(f)
DATO CALCULADO
0.001 0.000500 563,840 7.118472419 7.118472419 0.019734512
0.01973451 0.000500 563,840 7.555483666 7.555483666 0.017517634
0.01751763 0.000500 563,840 7.545413267 7.545413267 0.017564425
0.01756443 0.000500 563,840 7.545644018 7.545644018 0.017563351
0.01756335 0.000500 563,840 7.54563873 7.54563873 0.017563375
0.01756338 0.000500 563,840 7.545638851 7.545638851 0.017563375
Longitud= 450 Caudal= 0.062217476
Viscosidad= 0.00000114 Diámetro= 0.2
Ks= 0.000100 Velocidad= 1.980439154
f G(f)
DATO CALCULADO
0.001 0.000500 347,445 6.8787929 6.8787929 0.0211337
0.0211337 0.000500 347,445 7.466461637 7.466461637 0.017937847
0.01793785 0.000500 347,445 7.446736314 7.446736314 0.018033003
0.018033 0.000500 347,445 7.447391187 7.447391187 0.018029831
0.01802983 0.000500 347,445 7.447369438 7.447369438 0.018029937
Longitud= 250 Caudal= 0.069752529
Viscosidad= 0.00000114 Diámetro= 0.15
Ks= 0.000100 Velocidad= 3.947176485
f G(f)
DATO CALCULADO
0.001 0.000667 519,365 6.95509218 6.95509218 0.020672558
0.02067256 0.000667 519,365 7.340013442 7.340013442 0.01856121
0.01856121 0.000667 519,365 7.332488363 7.332488363 0.018599327
0.01859933 0.000667 519,365 7.332634853 7.332634853 0.018598584
0.01859858 0.000667 519,365 7.332632001 7.332632001 0.018598599
Longitud= 700 Caudal= 0.220092494
Viscosidad= 0.00000114 Diámetro= 0.2
Ks= 0.000100 Velocidad= 7.005745298
f G(f)
DATO CALCULADO
0.001 0.000500 1,229,078 7.399180505 7.399180505 0.01826555
0.01826555 0.000500 1,229,078 7.646396469 7.646396469 0.017103554
0.01710355 0.000500 1,229,078 7.643482703 7.643482703 0.017116597
0.0171166 0.000500 1,229,078 7.643516989 7.643516989 0.017116443
0.01711644 0.000500 1,229,078 7.643516586 7.643516586 0.017116445
Tramo Longitud Diámetro Caudal Velocidad f hfi Kmi HFI+km
(1-2) 600 0.2 0.240657506 7.660348413 0.017082292 153.272925 0 636.892354
(1-6) 300 0.25 0.258842494 5.273083662 0.016412036 27.9109121 0 107.829714
(2-3) 500 0.3 0.130029976 1.839543565 0.016565394 4.76180581 10 38.3455612
(3-4) 250 0.2 0.100967476 3.213887079 0.017563375 11.5579343 0 114.471855
(4-5) 450 0.2 0.062217476 1.980439154 0.018029937 8.10962415 0 130.343187
(2-5) 250 0.15 0.069752529 3.947176485 0.018598599 24.6151823 0 352.893043
(5-6) 700 0.2 0.220092494 7.005745298 0.017116445 149.861924 0 680.904293
Ks/dNúmero de
Reynolds Denominador DenominadorDato asumido 1/f
Tubería (2-5)
Ks/dNúmero de
Reynolds Denominador DenominadorDato asumido 1/f
Tubería (4-5)
Ks/dNúmero de
Reynolds Denominador DenominadorDato asumido 1/f
Tubería (5-6)
Ks/dNúmero de
Reynolds Denominador DenominadorDato asumido 1/f
ELABORACIÓN DE LA MATRIZ
-1.00 -1.00 0.00 0.00 0.00 0.00 0.00 Q1-2 -0.5
1.00 0.00 -1.00 0.00 0.00 -1.00 0.00 Q1-6 0.05
0.00 0.00 1.00 -1.00 0.00 0.00 0.00 Q2-3 0.03
0.00 0.00 0.00 1.00 -1.00 0.00 0.00 Q3-4 0.04
0.00 0.00 0.00 0.00 1.00 1.00 1.00 Q5-4 0.34
636.89 -107.83 0.00 0.00 0.00 352.89 -680.90 Q2-5 0
0 0 38.35 114.47 130.343 -352.893043 0 Q6-5 0
Tenemos que encontrar
Qi+6
-0.068129 0.52946949 0.51602767 0.475900211 0.430209149 0.00063182 0.00035054 Q1-2 0.24132592
-0.931871 -0.5294695 -0.5160277 -0.47590021 -0.430209149 -0.00063182 -0.0003505 Q1-6 0.25867408
-0.0377991 -0.2610581 0.6711975 0.468962111 0.238687124 0.000350544 0.00176668 Q2-3 0.12589467
-0.0377991 -0.2610581 -0.3288025 0.468962111 0.238687124 0.000350544 0.00176668 Q3-4 0.09589467
-0.0377991 -0.2610581 -0.3288025 -0.53103789 0.238687124 0.000350544 0.00176668 Q5-4 0.05589467
-0.0303299 -0.2094724 -0.1551698 0.0069381 0.191522024 0.000281276 -0.0014161 Q2-5 0.06543125
0.068129 0.47053051 0.48397233 0.524099789 0.569790851 -0.00063182 -0.0003505 Q6-5 0.21867408
NUEVOS CAUDALES (5) %
Q1-2 0.24099171 0.13868074
Q1-6 0.25875829 0.03254354
Q2-3 0.12796233 1.6158282
Q3-4 0.09843108 2.57682986
Q5-4 0.05905608 5.35321951
Q2-5 0.06759189 3.19659588
Q6-5 0.21938329 0.32327399
SÉTIMA ITERACIÓN
Formula a utilizar:
DATOS DE INGRESO:
Tramo Longitud (m) Diámetro (m) Caudal (m3/S)
(1-2) 600 0.2 0.240991715
(1-6) 300 0.25 0.258758285
(2-3) 500 0.3 0.127962325
(3-4) 250 0.2 0.098431075
(4-5) 450 0.2 0.059056075
(2-5) 250 0.15 0.06759189
(5-6) 700 0.2 0.219383285
Longitud= 600 Caudal= 0.240991715
Viscosidad= 0.00000114 Diámetro= 0.2
Ks= 0.000100 Velocidad= 7.670986594
f G(f)
DATO CALCULADO
0.001 0.000500 1,345,787 7.423885709 7.423885709 0.018144184
0.01814418 0.000500 1,345,787 7.653736642 7.653736642 0.017070764
0.01707076 0.000500 1,345,787 7.651240886 7.651240886 0.017081903
0.0170819 0.000500 1,345,787 7.651267947 7.651267947 0.017081782
0.01708178 0.000500 1,345,787 7.651267653 7.651267653 0.017082
Tubería (1-2)
Ks/dNúmero de
Reynolds Denominador DenominadorDato asumido 1/f
𝑿 = 𝑨 −𝟏 ∗ 𝑩
𝑴𝒂𝒕𝒓𝒊𝒛 𝑨𝑴𝒂𝒕𝒓𝒊𝒛 𝑩
𝑴𝒂𝒕𝒓𝒊𝒛 𝒊𝒏𝒗𝒆𝒓𝒔𝒂 ( 𝑨−𝟏 )
𝑨−𝟏 ∗ 𝑩
𝑸𝒊+𝟓 +𝑸𝒊+𝟔
𝟐
𝑵𝒖𝒆𝒗𝒐𝒔 𝒄𝒂𝒖𝒅𝒂𝒍𝒆𝒔(𝟓) − 𝑵𝒖𝒆𝒗𝒐𝒔 𝒄𝒂𝒖𝒅𝒂𝒍𝒆𝒔
𝑵𝒖𝒆𝒗𝒐𝒔 𝒄𝒂𝒖𝒅𝒂𝒍𝒆𝒔(𝟓)∗ 𝟏𝟎𝟎
𝑓 =1
(−2 ∗ 𝐿𝑜𝑔(𝐾𝑠
3.7 ∗ 𝑑+
2.51
𝑅𝑒 ∗ 𝑓))2
Longitud= 300 Caudal= 0.258758285
Viscosidad= 0.00000114 Diámetro= 0.25
Ks= 0.000100 Velocidad= 5.271368172
f G(f)
DATO CALCULADO
0.001 0.000400 1,156,002 7.505183305 7.505183305 0.017753231
0.01775323 0.000400 1,156,002 7.810331734 7.810331734 0.016393098
0.0163931 0.000400 1,156,002 7.805718 7.805718 0.016412483
0.01641248 0.000400 1,156,002 7.805787576 7.805787576 0.01641219
0.01641219 0.000400 1,156,002 7.805786527 7.805786527 0.016412195
Longitud= 500 Caudal= 0.127962325
Viscosidad= 0.00000114 Diámetro= 0.3
Ks= 0.000100 Velocidad= 1.810292351
f G(f)
DATO CALCULADO
0.001 0.000333 476,393 7.181138174 7.181138174 0.019391591
0.01939159 0.000333 476,393 7.786083718 7.786083718 0.016495362
0.01649536 0.000333 476,393 7.764707735 7.764707735 0.01658631
0.01658631 0.000333 476,393 7.765454166 7.765454166 0.016583121
0.01658312 0.000333 476,393 7.76542809 7.76542809 0.016583233
Longitud= 250 Caudal= 0.098431075
Viscosidad= 0.00000114 Diámetro= 0.2
Ks= 0.000100 Velocidad= 3.133151106
f G(f)
DATO CALCULADO
0.001 0.000500 549,676 7.10712715 7.10712715 0.019797567
0.01979757 0.000500 549,676 7.551510957 7.551510957 0.017536071
0.01753607 0.000500 549,676 7.541057037 7.541057037 0.017584724
0.01758472 0.000500 549,676 7.541301521 7.541301521 0.017583584
0.01758358 0.000500 549,676 7.541295803 7.541295803 0.01758361
0.01758361 0.000500 549,676 7.541295937 7.541295937 0.01758361
Longitud= 450 Caudal= 0.059056075
Viscosidad= 0.00000114 Diámetro= 0.2
Ks= 0.000100 Velocidad= 1.87980886
f G(f)
DATO CALCULADO
0.001 0.000500 329,791 6.850058022 6.850058022 0.021311376
0.02131138 0.000500 329,791 7.455063087 7.455063087 0.017992742
0.01799274 0.000500 329,791 7.43396445 7.43396445 0.018095019
0.01809502 0.000500 329,791 7.434691673 7.434691673 0.018091479
0.01809148 0.000500 329,791 7.434666597 7.434666597 0.018091601
Longitud= 250 Caudal= 0.06759189
Viscosidad= 0.00000114 Diámetro= 0.15
Ks= 0.000100 Velocidad= 3.824909583
f G(f)
DATO CALCULADO
0.001 0.000667 503,278 6.94244241 6.94244241 0.020747961
Tubería (2-3)
Ks/dNúmero de
Reynolds Denominador DenominadorDato asumido 1/f
Tubería (1-6)
Ks/dNúmero de
Reynolds Denominador DenominadorDato asumido 1/f
Tubería (4-5)
Ks/dNúmero de
Reynolds Denominador DenominadorDato asumido 1/f
Tubería (3-4)
Ks/dNúmero de
Reynolds Denominador DenominadorDato asumido 1/f
Tubería (2-5)
Ks/dNúmero de
Reynolds Denominador DenominadorDato asumido 1/f
0.02074796 0.000667 503,278 7.33591416 7.33591416 0.01858196
0.01858196 0.000667 503,278 7.328015111 7.328015111 0.018622041
0.01862204 0.000667 503,278 7.328172982 7.328172982 0.018621239
0.01862124 0.000667 503,278 7.328169826 7.328169826 0.018621255
Longitud= 700 Caudal= 0.219383285
Viscosidad= 0.00000114 Diámetro= 0.2
Ks= 0.000100 Velocidad= 6.983170524
f G(f)
DATO CALCULADO
0.001 0.000500 1,225,118 7.398273014 7.398273014 0.018270031
0.01827003 0.000500 1,225,118 7.646124863 7.646124863 0.01710477
0.01710477 0.000500 1,225,118 7.643195102 7.643195102 0.017117885
0.01711789 0.000500 1,225,118 7.643229676 7.643229676 0.01711773
0.01711773 0.000500 1,225,118 7.643229268 7.643229268 0.017117732
Tramo Longitud Diámetro Caudal Velocidad f hfi Kmi HFI+km
(1-2) 600 0.2 0.240991715 7.670986594 0.017081783 153.694353 0 637.757828
(1-6) 300 0.25 0.258758285 5.271368172 0.016412195 27.8930242 0 107.795676
(2-3) 500 0.3 0.127962325 1.810292351 0.016583233 4.61653757 10 37.7476338
(3-4) 250 0.2 0.098431075 3.133151106 0.01758361 10.9971903 0 111.724781
(4-5) 450 0.2 0.059056075 1.87980886 0.018091601 7.33141669 0 124.143311
(2-5) 250 0.15 0.06759189 3.824909583 0.018621255 23.1420082 0 342.378476
(5-6) 700 0.2 0.219383285 6.983170524 0.017117732 148.908868 0 678.761228
ELABORACIÓN DE LA MATRIZ
-1.00 -1.00 0.00 0.00 0.00 0.00 0.00 Q1-2 -0.5
1.00 0.00 -1.00 0.00 0.00 -1.00 0.00 Q1-6 0.05
0.00 0.00 1.00 -1.00 0.00 0.00 0.00 Q2-3 0.03
0.00 0.00 0.00 1.00 -1.00 0.00 0.00 Q3-4 0.04
0.00 0.00 0.00 0.00 1.00 1.00 1.00 Q5-4 0.34
637.76 -107.80 0.00 0.00 0.00 342.38 -678.76 Q2-5 0
0 0 37.75 111.72 124.143 -342.378476 0 Q6-5 0
Tenemos que encontrar
Qi+7
-0.0683812 0.52705138 0.5137421 0.474349515 0.43057833 0.000634359 0.00035259 Q1-2 0.24132603
-0.9316188 -0.5270514 -0.5137421 -0.47434951 -0.43057833 -0.00063436 -0.0003526 Q1-6 0.25867397
-0.0380072 -0.2628717 0.66845163 0.465183559 0.239321656 0.000352586 0.00181936 Q2-3 0.12589029
-0.0380072 -0.2628717 -0.3315484 0.465183559 0.239321656 0.000352586 0.00181936 Q3-4 0.09589029
-0.0380072 -0.2628717 -0.3315484 -0.53481644 0.239321656 0.000352586 0.00181936 Q5-4 0.05589029
-0.0303739 -0.2100769 -0.1547095 0.009165956 0.191256674 0.000281773 -0.0014668 Q2-5 0.06543574
0.06838116 0.47294862 0.4862579 0.525650485 0.56942167 -0.00063436 -0.0003526 Q6-5 0.21867397
NUEVOS CAUDALES (6) %
Q1-2 0.24115887 0.06931359
Q1-6 0.25871613 0.01629425
Q2-3 0.12692631 0.81623553
Q3-4 0.09716068 1.30751718
Q5-4 0.05747318 2.75414123
Q2-5 0.06651381 1.62083102
Q6-5 0.21902863 0.16192215
Tubería (5-6)
Ks/dNúmero de
Reynolds Denominador DenominadorDato asumido 1/f
𝑿 = 𝑨 −𝟏 ∗ 𝑩
𝑴𝒂𝒕𝒓𝒊𝒛 𝑨𝑴𝒂𝒕𝒓𝒊𝒛 𝑩
𝑴𝒂𝒕𝒓𝒊𝒛 𝒊𝒏𝒗𝒆𝒓𝒔𝒂 ( 𝑨−𝟏 )
𝑨−𝟏 ∗ 𝑩
𝑸𝒊+𝟔 +𝑸𝒊+𝟕
𝟐𝑵𝒖𝒆𝒗𝒐𝒔 𝒄𝒂𝒖𝒅𝒂𝒍𝒆𝒔(𝟔) − 𝑵𝒖𝒆𝒗𝒐𝒔 𝒄𝒂𝒖𝒅𝒂𝒍𝒆𝒔
𝑵𝒖𝒆𝒗𝒐𝒔 𝒄𝒂𝒖𝒅𝒂𝒍𝒆𝒔(𝟔)∗ 𝟏𝟎𝟎
OCTAVA ITERACIÓN
Formula a utilizar:
DATOS DE INGRESO:
Tramo Longitud (m) Diámetro (m) Caudal (m3/S)
(1-2) 600 0.2 0.241158871
(1-6) 300 0.25 0.258716129
(2-3) 500 0.3 0.126926308
(3-4) 250 0.2 0.097160683
(4-5) 450 0.2 0.057473183
(2-5) 250 0.15 0.066513813
(5-6) 700 0.2 0.219028629
Longitud= 600 Caudal= 0.241158871
Viscosidad= 0.00000114 Diámetro= 0.2
Ks= 0.000100 Velocidad= 7.676307318
f G(f)
DATO CALCULADO
0.001 0.000500 1,346,721 7.424068653 7.424068653 0.01814329
0.01814329 0.000500 1,346,721 7.65379061 7.65379061 0.017070524
0.01707052 0.000500 1,346,721 7.651297824 7.651297824 0.017081649
0.01708165 0.000500 1,346,721 7.651324835 7.651324835 0.017081528
0.01708153 0.000500 1,346,721 7.651324543 7.651324543 0.017082
Longitud= 300 Caudal= 0.258716129
Viscosidad= 0.00000114 Diámetro= 0.25
Ks= 0.000100 Velocidad= 5.270509382
f G(f)
DATO CALCULADO
0.001 0.000400 1,155,813 7.505128333 7.505128333 0.017753491
0.01775349 0.000400 1,155,813 7.810314029 7.810314029 0.016393172
0.01639317 0.000400 1,155,813 7.805699077 7.805699077 0.016412562
0.01641256 0.000400 1,155,813 7.805768681 7.805768681 0.01641227
0.01641227 0.000400 1,155,813 7.805767631 7.805767631 0.016412274
Longitud= 500 Caudal= 0.126926308
Viscosidad= 0.00000114 Diámetro= 0.3
Ks= 0.000100 Velocidad= 1.795635734
f G(f)
DATO CALCULADO
0.001 0.000333 472,536 7.176548734 7.176548734 0.019416401
0.0194164 0.000333 472,536 7.784154504 7.784154504 0.01650354
0.01650354 0.000333 472,536 7.762560025 7.762560025 0.016595489
0.01659549 0.000333 472,536 7.763318368 7.763318368 0.016592247
0.01659225 0.000333 472,536 7.763291726 7.763291726 0.016592361
Longitud= 250 Caudal= 0.097160683
Viscosidad= 0.00000114 Diámetro= 0.2
Ks= 0.000100 Velocidad= 3.092713347
f G(f)
DATO CALCULADO
Tubería (1-6)
Ks/dNúmero de
Reynolds Denominador DenominadorDato asumido 1/f
Tubería (1-2)
Ks/dNúmero de
Reynolds Denominador DenominadorDato asumido 1/f
Tubería (3-4)
Ks/dNúmero de
Reynolds Denominador DenominadorDato asumido 1/f
Tubería (2-3)
Ks/dNúmero de
Reynolds Denominador DenominadorDato asumido 1/f
𝑓 =1
(−2 ∗ 𝐿𝑜𝑔(𝐾𝑠
3.7 ∗ 𝑑+
2.51
𝑅𝑒 ∗ 𝑓))2
0.001 0.000500 542,581 7.101280192 7.101280192 0.019830182
0.01983018 0.000500 542,581 7.549454311 7.549454311 0.017545626
0.01754563 0.000500 542,581 7.538799867 7.538799867 0.017595255
0.01759526 0.000500 542,581 7.539051644 7.539051644 0.01759408
0.01759408 0.000500 542,581 7.539045693 7.539045693 0.017594108
0.01759411 0.000500 542,581 7.539045834 7.539045834 0.017594107
Longitud= 450 Caudal= 0.057473183
Viscosidad= 0.00000114 Diámetro= 0.2
Ks= 0.000100 Velocidad= 1.829423941
f G(f)
DATO CALCULADO
0.001 0.000500 320,952 6.834871364 6.834871364 0.021406187
0.02140619 0.000500 320,952 7.448975531 7.448975531 0.018022163
0.01802216 0.000500 320,952 7.427132836 7.427132836 0.018128322
0.01812832 0.000500 320,952 7.427900397 7.427900397 0.018124576
0.01812458 0.000500 320,952 7.427873414 7.427873414 0.018124708
Longitud= 250 Caudal= 0.066513813
Viscosidad= 0.00000114 Diámetro= 0.15
Ks= 0.000100 Velocidad= 3.763903075
f G(f)
DATO CALCULADO
0.001 0.000667 495,250 6.935896022 6.935896022 0.020787145
0.02078715 0.000667 495,250 7.333781662 7.333781662 0.018592768
0.01859277 0.000667 495,250 7.325685361 7.325685361 0.018633888
0.01863389 0.000667 495,250 7.325849358 7.325849358 0.018633054
0.01863305 0.000667 495,250 7.325846035 7.325846035 0.01863307
Longitud= 700 Caudal= 0.219028629
Viscosidad= 0.00000114 Diámetro= 0.2
Ks= 0.000100 Velocidad= 6.971881503
f G(f)
DATO CALCULADO
0.001 0.000500 1,223,137 7.397817356 7.397817356 0.018272282
0.01827228 0.000500 1,223,137 7.645988434 7.645988434 0.01710538
0.01710538 0.000500 1,223,137 7.643050624 7.643050624 0.017118532
0.01711853 0.000500 1,223,137 7.643085344 7.643085344 0.017118377
0.01711838 0.000500 1,223,137 7.643084933 7.643084933 0.017118379
Tramo Longitud Diámetro Caudal Velocidad f hfi Kmi HFI+km
(1-2) 600 0.2 0.241158871 7.676307318 0.017081529 153.905348 0 638.190697
(1-6) 300 0.25 0.258716129 5.270509382 0.016412274 27.8840715 0 107.778636
(2-3) 500 0.3 0.126926308 1.795635734 0.016592361 4.54458691 10 37.4483029
(3-4) 250 0.2 0.097160683 3.092713347 0.017594108 10.7215505 0 110.348654
(4-5) 450 0.2 0.057473183 1.829423941 0.018124708 6.95637913 0 121.036957
(2-5) 250 0.15 0.066513813 3.763903075 0.01863307 22.4238942 0 337.131388
(5-6) 700 0.2 0.219028629 6.971881503 0.017118379 148.43341 0 677.689534
ELABORACIÓN DE LA MATRIZ
-1.00 -1.00 0.00 0.00 0.00 0.00 0.00 Q1-2 -0.5
1.00 0.00 -1.00 0.00 0.00 -1.00 0.00 Q1-6 0.05
0.00 0.00 1.00 -1.00 0.00 0.00 0.00 Q2-3 0.03
Tubería (2-5)
Ks/dNúmero de
Reynolds Denominador DenominadorDato asumido 1/f
Tubería (4-5)
Ks/dNúmero de
Reynolds Denominador DenominadorDato asumido 1/f
Tubería (5-6)
Ks/dNúmero de
Reynolds Denominador DenominadorDato asumido 1/f
0.00 0.00 0.00 1.00 -1.00 0.00 0.00 Q3-4 0.04
0.00 0.00 0.00 0.00 1.00 1.00 1.00 Q5-4 0.34
638.19 -107.78 0.00 0.00 0.00 337.13 -677.69 Q2-5 0
0 0 37.45 110.35 121.037 -337.131388 0 Q6-5 0
Tenemos que encontrar
Qi+8
-0.0685081 0.52583453 0.51259134 0.473567735 0.430764325 0.000635637 0.00035364 Q1-2 0.24132607
-0.9314919 -0.5258345 -0.5125913 -0.47356774 -0.430764325 -0.00063564 -0.0003536 Q1-6 0.25867393
-0.0381147 -0.263804 0.66702869 0.463213825 0.239657575 0.000353639 0.00184701 Q2-3 0.12589016
-0.0381147 -0.263804 -0.3329713 0.463213825 0.239657575 0.000353639 0.00184701 Q3-4 0.09589016
-0.0381147 -0.263804 -0.3329713 -0.53678618 0.239657575 0.000353639 0.00184701 Q5-4 0.05589016
-0.0303933 -0.2103615 -0.1544373 0.010353911 0.19110675 0.000281997 -0.0014934 Q2-5 0.06543591
0.06850805 0.47416547 0.48740866 0.526432265 0.569235675 -0.00063564 -0.0003536 Q6-5 0.21867393
NUEVOS CAUDALES (7) %
Q1-2 0.24124247 0.03465454
Q1-6 0.25869503 0.00815689
Q2-3 0.12640824 0.40984009
Q3-4 0.09652542 0.65812623
Q5-4 0.05668167 1.39641102
Q2-5 0.06597486 0.81690494
Q6-5 0.21885128 0.08103744
NOVENA ITERACIÓN
Formula a utilizar:
DATOS DE INGRESO:
Tramo Longitud (m) Diámetro (m) Caudal (m3/S)
(1-2) 600 0.2 0.241242472
(1-6) 300 0.25 0.258695028
(2-3) 500 0.3 0.126408236
(3-4) 250 0.2 0.096525423
(4-5) 450 0.2 0.056681673
(2-5) 250 0.15 0.065974861
(5-6) 700 0.2 0.218851278
Longitud= 600 Caudal= 0.241242472
Viscosidad= 0.00000114 Diámetro= 0.2
Ks= 0.000100 Velocidad= 7.678968429
f G(f)
DATO CALCULADO
0.001 0.000500 1,347,187 7.42416007 7.42416007 0.018142843
0.01814284 0.000500 1,347,187 7.653817575 7.653817575 0.017070403
0.0170704 0.000500 1,347,187 7.651326273 7.651326273 0.017081522
0.01708152 0.000500 1,347,187 7.65135326 7.65135326 0.017081401
0.0170814 0.000500 1,347,187 7.651352967 7.651352967 0.017081
Tubería (1-2)
Ks/dNúmero de
Reynolds Denominador DenominadorDato asumido 1/f
𝑿 = 𝑨 −𝟏 ∗ 𝑩
𝑴𝒂𝒕𝒓𝒊𝒛 𝑨𝑴𝒂𝒕𝒓𝒊𝒛 𝑩
𝑴𝒂𝒕𝒓𝒊𝒛 𝒊𝒏𝒗𝒆𝒓𝒔𝒂 ( 𝑨−𝟏 )
𝑨−𝟏 ∗ 𝑩
𝑸𝒊+𝟔 +𝑸𝒊+𝟕
𝟐𝑵𝒖𝒆𝒗𝒐𝒔 𝒄𝒂𝒖𝒅𝒂𝒍𝒆𝒔(𝟕) − 𝑵𝒖𝒆𝒗𝒐𝒔 𝒄𝒂𝒖𝒅𝒂𝒍𝒆𝒔
𝑵𝒖𝒆𝒗𝒐𝒔 𝒄𝒂𝒖𝒅𝒂𝒍𝒆𝒔(𝟕)∗ 𝟏𝟎𝟎
𝑓 =1
(−2 ∗ 𝐿𝑜𝑔(𝐾𝑠
3.7 ∗ 𝑑+
2.51
𝑅𝑒 ∗ 𝑓))2
Longitud= 300 Caudal= 0.258695028
Viscosidad= 0.00000114 Diámetro= 0.25
Ks= 0.000100 Velocidad= 5.270079508
f G(f)
DATO CALCULADO
0.001 0.000400 1,155,719 7.50510081 7.50510081 0.017753621
0.01775362 0.000400 1,155,719 7.810305164 7.810305164 0.01639321
0.01639321 0.000400 1,155,719 7.805689602 7.805689602 0.016412602
0.0164126 0.000400 1,155,719 7.80575922 7.80575922 0.01641231
0.01641231 0.000400 1,155,719 7.80575817 7.80575817 0.016412314
Longitud= 500 Caudal= 0.126408236
Viscosidad= 0.00000114 Diámetro= 0.3
Ks= 0.000100 Velocidad= 1.788306537
f G(f)
DATO CALCULADO
0.001 0.000333 470,607 7.174234733 7.174234733 0.019428928
0.01942893 0.000333 470,607 7.783180237 7.783180237 0.016507672
0.01650767 0.000333 470,607 7.761475194 7.761475194 0.016600129
0.01660013 0.000333 470,607 7.762239591 7.762239591 0.016596859
0.01659686 0.000333 470,607 7.762212659 7.762212659 0.016596974
Longitud= 250 Caudal= 0.096525423
Viscosidad= 0.00000114 Diámetro= 0.2
Ks= 0.000100 Velocidad= 3.072492468
f G(f)
DATO CALCULADO
0.001 0.000500 539,034 7.098313785 7.098313785 0.01984676
0.01984676 0.000500 539,034 7.54840848 7.54840848 0.017550489
0.01755049 0.000500 539,034 7.537651554 7.537651554 0.017600617
0.01760062 0.000500 539,034 7.537907089 7.537907089 0.017599423
0.01759942 0.000500 539,034 7.537901017 7.537901017 0.017599452
0.01759945 0.000500 539,034 7.537901162 7.537901162 0.017599451
Longitud= 450 Caudal= 0.056681673
Viscosidad= 0.00000114 Diámetro= 0.2
Ks= 0.000100 Velocidad= 1.804229481
f G(f)
DATO CALCULADO
0.001 0.000500 316,531 6.827063289 6.827063289 0.021455179
0.02145518 0.000500 316,531 7.445828614 7.445828614 0.0180374
0.0180374 0.000500 316,531 7.423598484 7.423598484 0.018145588
0.01814559 0.000500 316,531 7.424387361 7.424387361 0.018141732
0.01814173 0.000500 316,531 7.424359354 7.424359354 0.018141869
Longitud= 250 Caudal= 0.065974861
Viscosidad= 0.00000114 Diámetro= 0.15
Ks= 0.000100 Velocidad= 3.733404707
f G(f)
DATO CALCULADO
0.001 0.000667 491,237 6.932562149 6.932562149 0.020807143
Tubería (2-3)
Ks/dNúmero de
Reynolds Denominador DenominadorDato asumido 1/f
Tubería (1-6)
Ks/dNúmero de
Reynolds Denominador DenominadorDato asumido 1/f
Tubería (4-5)
Ks/dNúmero de
Reynolds Denominador DenominadorDato asumido 1/f
Tubería (3-4)
Ks/dNúmero de
Reynolds Denominador DenominadorDato asumido 1/f
Tubería (2-5)
Ks/dNúmero de
Reynolds Denominador DenominadorDato asumido 1/f
0.02080714 0.000667 491,237 7.332692739 7.332692739 0.01859829
0.01859829 0.000667 491,237 7.324495009 7.324495009 0.018639945
0.01863994 0.000667 491,237 7.324662187 7.324662187 0.018639094
0.01863909 0.000667 491,237 7.324658777 7.324658777 0.018639111
Longitud= 700 Caudal= 0.218851278
Viscosidad= 0.00000114 Diámetro= 0.2
Ks= 0.000100 Velocidad= 6.966236244
f G(f)
DATO CALCULADO
0.001 0.000500 1,222,147 7.397589032 7.397589032 0.01827341
0.01827341 0.000500 1,222,147 7.645920058 7.645920058 0.017105686
0.01710569 0.000500 1,222,147 7.642978211 7.642978211 0.017118857
0.01711886 0.000500 1,222,147 7.643013004 7.643013004 0.017118701
0.0171187 0.000500 1,222,147 7.643012592 7.643012592 0.017118703
Tramo Longitud Diámetro Caudal Velocidad f hfi Kmi HFI+km
(1-2) 600 0.2 0.241242472 7.678968429 0.017081402 154.010929 0 638.407193
(1-6) 300 0.25 0.258695028 5.270079508 0.016412314 27.8795907 0 107.770106
(2-3) 500 0.3 0.126408236 1.788306537 0.016596974 4.50881692 10 37.2986858
(3-4) 250 0.2 0.096525423 3.072492468 0.017599452 10.5850229 0 109.660466
(4-5) 450 0.2 0.056681673 1.804229481 0.018141869 6.77250128 0 119.483087
(2-5) 250 0.15 0.065974861 3.733404707 0.018639111 22.0691239 0 334.508076
(5-6) 700 0.2 0.218851278 6.966236244 0.017118703 148.195934 0 677.153615
ELABORACIÓN DE LA MATRIZ
-1.00 -1.00 0.00 0.00 0.00 0.00 0.00 Q1-2 -0.5
1.00 0.00 -1.00 0.00 0.00 -1.00 0.00 Q1-6 0.05
0.00 0.00 1.00 -1.00 0.00 0.00 0.00 Q2-3 0.03
0.00 0.00 0.00 1.00 -1.00 0.00 0.00 Q3-4 0.04
0.00 0.00 0.00 0.00 1.00 1.00 1.00 Q5-4 0.34
638.41 -107.77 0.00 0.00 0.00 334.51 -677.15 Q2-5 0
0 0 37.30 109.66 119.483 -334.508076 0 Q6-5 0
Tenemos que encontrar
Qi+9
-0.0685717 0.52522413 0.51201396 0.473175258 0.430857653 0.000636278 0.00035417 Q1-2 0.24132609
-0.9314283 -0.5252241 -0.512014 -0.47317526 -0.430857653 -0.00063628 -0.0003542 Q1-6 0.25867391
-0.0381692 -0.2642754 0.66630526 0.462207981 0.239829085 0.000354172 0.00186117 Q2-3 0.12589019
-0.0381692 -0.2642754 -0.3336947 0.462207981 0.239829085 0.000354172 0.00186117 Q3-4 0.09589019
-0.0381692 -0.2642754 -0.3336947 -0.53779202 0.239829085 0.000354172 0.00186117 Q5-4 0.05589019
-0.0304025 -0.2105005 -0.1542913 0.010967277 0.191028567 0.000282105 -0.001507 Q2-5 0.06543589
0.0685717 0.47477587 0.48798604 0.526824742 0.569142347 -0.00063628 -0.0003542 Q6-5 0.21867391
NUEVOS CAUDALES (8) %
Q1-2 0.24128428 0.0173272
Q1-6 0.25868447 0.00408134
Q2-3 0.12614921 0.20532912
Q3-4 0.09620781 0.33013414
Q5-4 0.05628593 0.70308832
Q2-5 0.06570538 0.41013938
Q6-5 0.2187626 0.04053837
Tubería (5-6)
Ks/dNúmero de
Reynolds Denominador DenominadorDato asumido 1/f
𝑿 = 𝑨 −𝟏 ∗ 𝑩
𝑴𝒂𝒕𝒓𝒊𝒛 𝑨𝑴𝒂𝒕𝒓𝒊𝒛 𝑩
𝑴𝒂𝒕𝒓𝒊𝒛 𝒊𝒏𝒗𝒆𝒓𝒔𝒂 ( 𝑨−𝟏 )
𝑨−𝟏 ∗ 𝑩
𝑸𝒊+𝟕 +𝑸𝒊+𝟖
𝟐𝑵𝒖𝒆𝒗𝒐𝒔 𝒄𝒂𝒖𝒅𝒂𝒍𝒆𝒔(𝟖) − 𝑵𝒖𝒆𝒗𝒐𝒔 𝒄𝒂𝒖𝒅𝒂𝒍𝒆𝒔
𝑵𝒖𝒆𝒗𝒐𝒔 𝒄𝒂𝒖𝒅𝒂𝒍𝒆𝒔(𝟖)∗ 𝟏𝟎𝟎
DÉCIMA ITERACIÓN
Formula a utilizar:
DATOS DE INGRESO:
Tramo Longitud (m) Diámetro (m) Caudal (m3/S)
(1-2) 600 0.2 0.24128428
(1-6) 300 0.25 0.25868447
(2-3) 500 0.3 0.126149215
(3-4) 250 0.2 0.096207809
(4-5) 450 0.2 0.056285934
(2-5) 250 0.15 0.065705378
(5-6) 700 0.2 0.218762595
Longitud= 600 Caudal= 0.24128428
Viscosidad= 0.00000114 Diámetro= 0.2
Ks= 0.000100 Velocidad= 7.68029921
f G(f)
DATO CALCULADO
0.001 0.000500 1,347,421 7.424205766 7.424205766 0.01814262
0.01814262 0.000500 1,347,421 7.653831054 7.653831054 0.017070343
0.01707034 0.000500 1,347,421 7.651340493 7.651340493 0.017081458
0.01708146 0.000500 1,347,421 7.651367467 7.651367467 0.017081338
0.01708134 0.000500 1,347,421 7.651367175 7.651367175 0.017081
Longitud= 300 Caudal= 0.25868447
Viscosidad= 0.00000114 Diámetro= 0.25
Ks= 0.000100 Velocidad= 5.269864426
f G(f)
DATO CALCULADO
0.001 0.000400 1,155,672 7.505087039 7.505087039 0.017753686
0.01775369 0.000400 1,155,672 7.810300729 7.810300729 0.016393228
0.01639323 0.000400 1,155,672 7.805684861 7.805684861 0.016412622
0.01641262 0.000400 1,155,672 7.805754486 7.805754486 0.016412329
0.01641233 0.000400 1,155,672 7.805753436 7.805753436 0.016412334
Longitud= 500 Caudal= 0.126149215
Viscosidad= 0.00000114 Diámetro= 0.3
Ks= 0.000100 Velocidad= 1.784642147
f G(f)
DATO CALCULADO
0.001 0.000333 469,643 7.173072998 7.173072998 0.019435222
0.01943522 0.000333 469,643 7.782690716 7.782690716 0.016509748
0.01650975 0.000333 469,643 7.760930064 7.760930064 0.016602461
0.01660246 0.000333 469,643 7.761697513 7.761697513 0.016599178
0.01659918 0.000333 469,643 7.761670435 7.761670435 0.016599293
Longitud= 250 Caudal= 0.096207809
Viscosidad= 0.00000114 Diámetro= 0.2
Ks= 0.000100 Velocidad= 3.062382498
f G(f)
DATO CALCULADO
0.001 0.000500 537,260 7.096819802 7.096819802 0.019855117
Tubería (1-6)
Ks/dNúmero de
Reynolds Denominador DenominadorDato asumido 1/f
Tubería (1-2)
Ks/dNúmero de
Reynolds Denominador DenominadorDato asumido 1/f
Tubería (3-4)
Ks/dNúmero de
Reynolds Denominador DenominadorDato asumido 1/f
Tubería (2-3)
Ks/dNúmero de
Reynolds Denominador DenominadorDato asumido 1/f
𝑓 =1
(−2 ∗ 𝐿𝑜𝑔(𝐾𝑠
3.7 ∗ 𝑑+
2.51
𝑅𝑒 ∗ 𝑓))2
0.01985512 0.000500 537,260 7.547881149 7.547881149 0.017552941
0.01755294 0.000500 537,260 7.53707242 7.53707242 0.017603322
0.01760332 0.000500 537,260 7.537329861 7.537329861 0.017602119
0.01760212 0.000500 537,260 7.537323729 7.537323729 0.017602148
0.01760215 0.000500 537,260 7.537323875 7.537323875 0.017602147
Longitud= 450 Caudal= 0.056285934
Viscosidad= 0.00000114 Diámetro= 0.2
Ks= 0.000100 Velocidad= 1.791632721
f G(f)
DATO CALCULADO
0.001 0.000500 314,322 6.823103952 6.823103952 0.021480086
0.02148009 0.000500 314,322 7.444228439 7.444228439 0.018045155
0.01804515 0.000500 314,322 7.421800584 7.421800584 0.018154381
0.01815438 0.000500 314,322 7.422600422 7.422600422 0.018150468
0.01815047 0.000500 314,322 7.422571885 7.422571885 0.018150608
Longitud= 250 Caudal= 0.065705378
Viscosidad= 0.00000114 Diámetro= 0.15
Ks= 0.000100 Velocidad= 3.718155089
f G(f)
DATO CALCULADO
0.001 0.000667 489,231 6.93087952 6.93087952 0.020817247
0.02081725 0.000667 489,231 7.332142406 7.332142406 0.018601082
0.01860108 0.000667 489,231 7.323893233 7.323893233 0.018643008
0.01864301 0.000667 489,231 7.324062033 7.324062033 0.018642149
0.01864215 0.000667 489,231 7.324058579 7.324058579 0.018642166
Longitud= 700 Caudal= 0.218762595
Viscosidad= 0.00000114 Diámetro= 0.2
Ks= 0.000100 Velocidad= 6.963413389
f G(f)
DATO CALCULADO
0.001 0.000500 1,221,651 7.397474745 7.397474745 0.018273975
0.01827397 0.000500 1,221,651 7.645885829 7.645885829 0.017105839
0.01710584 0.000500 1,221,651 7.642941961 7.642941961 0.017119019
0.01711902 0.000500 1,221,651 7.64297679 7.64297679 0.017118863
0.01711886 0.000500 1,221,651 7.642976378 7.642976378 0.017118865
Tramo Longitud Diámetro Caudal Velocidad f hfi Kmi HFI+km
(1-2) 600 0.2 0.24128428 7.68029921 0.017081339 154.063743 0 638.515459
(1-6) 300 0.25 0.25868447 5.269864426 0.016412334 27.8773489 0 107.765839
(2-3) 500 0.3 0.126149215 1.784642147 0.016599293 4.49098537 10 37.2238981
(3-4) 250 0.2 0.096207809 3.062382498 0.017602148 10.5170888 0 109.316374
(4-5) 450 0.2 0.056285934 1.791632721 0.018150608 6.68147983 0 118.706032
(2-5) 250 0.15 0.065705378 3.718155089 0.018642166 21.8927909 0 333.196334
(5-6) 700 0.2 0.218762595 6.963413389 0.017118865 148.077258 0 676.885634
ELABORACIÓN DE LA MATRIZ
-1.00 -1.00 0.00 0.00 0.00 0.00 0.00 Q1-2 -0.5
1.00 0.00 -1.00 0.00 0.00 -1.00 0.00 Q1-6 0.05
0.00 0.00 1.00 -1.00 0.00 0.00 0.00 Q2-3 0.03
0.00 0.00 0.00 1.00 -1.00 0.00 0.00 Q3-4 0.04
Tubería (2-5)
Ks/dNúmero de
Reynolds Denominador DenominadorDato asumido 1/f
Tubería (4-5)
Ks/dNúmero de
Reynolds Denominador DenominadorDato asumido 1/f
Tubería (5-6)
Ks/dNúmero de
Reynolds Denominador DenominadorDato asumido 1/f
0.00 0.00 0.00 0.00 1.00 1.00 1.00 Q5-4 0.34
638.52 -107.77 0.00 0.00 0.00 333.20 -676.89 Q2-5 0
0 0 37.22 109.32 118.706 -333.196334 0 Q6-5 0
Tenemos que encontrar
Qi+10
-0.0686036 0.52491842 0.51172477 0.472978621 0.430904398 0.000636599 0.00035444 Q1-2 0.24132609
-0.9313964 -0.5249184 -0.5117248 -0.47297862 -0.430904398 -0.0006366 -0.0003544 Q1-6 0.25867391
-0.0381966 -0.2645123 0.66594056 0.46169968 0.239915668 0.00035444 0.00186835 Q2-3 0.1258902
-0.0381966 -0.2645123 -0.3340594 0.46169968 0.239915668 0.00035444 0.00186835 Q3-4 0.0958902
-0.0381966 -0.2645123 -0.3340594 -0.53830032 0.239915668 0.00035444 0.00186835 Q5-4 0.0558902
-0.030407 -0.2105693 -0.1542158 0.011278941 0.190988729 0.000282158 -0.0015139 Q2-5 0.06543589
0.06860357 0.47508158 0.48827523 0.527021379 0.569095602 -0.0006366 -0.0003544 Q6-5 0.21867391
NUEVOS CAUDALES (9) %
Q1-2 0.24130519 0.00866362
Q1-6 0.25867919 0.00204144
Q2-3 0.12601971 0.10276604
Q3-4 0.09604901 0.16533471
Q5-4 0.05608807 0.35277528
Q2-5 0.06557063 0.20549598
Q6-5 0.21871825 0.02027415
DÉCIMA PRIMERA ITERACIÓN
Formula a utilizar:
DATOS DE INGRESO:
Tramo Longitud (m) Diámetro (m) Caudal (m3/S)
(1-2) 600 0.2 0.241305186
(1-6) 300 0.25 0.258679189
(2-3) 500 0.3 0.126019709
(3-4) 250 0.2 0.096049006
(4-5) 450 0.2 0.056088069
(2-5) 250 0.15 0.065570633
(5-6) 700 0.2 0.218718252
Longitud= 600 Caudal= 0.241305186
Viscosidad= 0.00000114 Diámetro= 0.2
Ks= 0.000100 Velocidad= 7.680964659
f G(f)
DATO CALCULADO
0.001 0.000500 1,347,538 7.424228611 7.424228611 0.018142508
0.01814251 0.000500 1,347,538 7.653837792 7.653837792 0.017070313
0.01707031 0.000500 1,347,538 7.651347601 7.651347601 0.017081426
0.01708143 0.000500 1,347,538 7.65137457 7.65137457 0.017081306
0.01708131 0.000500 1,347,538 7.651374278 7.651374278 0.017081
Tubería (1-2)
Ks/dNúmero de
Reynolds Denominador DenominadorDato asumido 1/f
𝑿 = 𝑨 −𝟏 ∗ 𝑩
𝑴𝒂𝒕𝒓𝒊𝒛 𝑨𝑴𝒂𝒕𝒓𝒊𝒛 𝑩
𝑴𝒂𝒕𝒓𝒊𝒛 𝒊𝒏𝒗𝒆𝒓𝒔𝒂 ( 𝑨−𝟏 )
𝑨−𝟏 ∗ 𝑩
𝑸𝒊+𝟖 +𝑸𝒊+𝟗
𝟐𝑵𝒖𝒆𝒗𝒐𝒔 𝒄𝒂𝒖𝒅𝒂𝒍𝒆𝒔(𝟗) − 𝑵𝒖𝒆𝒗𝒐𝒔 𝒄𝒂𝒖𝒅𝒂𝒍𝒆𝒔
𝑵𝒖𝒆𝒗𝒐𝒔 𝒄𝒂𝒖𝒅𝒂𝒍𝒆𝒔(𝟗)∗ 𝟏𝟎𝟎
𝑓 =1
(−2 ∗ 𝐿𝑜𝑔(𝐾𝑠
3.7 ∗ 𝑑+
2.51
𝑅𝑒 ∗ 𝑓))2
Longitud= 300 Caudal= 0.258679189
Viscosidad= 0.00000114 Diámetro= 0.25
Ks= 0.000100 Velocidad= 5.269756848
f G(f)
DATO CALCULADO
0.001 0.000400 1,155,648 7.50508015 7.50508015 0.017753719
0.01775372 0.000400 1,155,648 7.81029851 7.81029851 0.016393238
0.01639324 0.000400 1,155,648 7.80568249 7.80568249 0.016412632
0.01641263 0.000400 1,155,648 7.805752118 7.805752118 0.016412339
0.01641234 0.000400 1,155,648 7.805751068 7.805751068 0.016412344
Longitud= 500 Caudal= 0.126019709
Viscosidad= 0.00000114 Diámetro= 0.3
Ks= 0.000100 Velocidad= 1.782810024
f G(f)
DATO CALCULADO
0.001 0.000333 469,161 7.172490947 7.172490947 0.019438376
0.01943838 0.000333 469,161 7.782445358 7.782445358 0.016510789
0.01651079 0.000333 469,161 7.76065682 7.76065682 0.01660363
0.01660363 0.000333 469,161 7.761425801 7.761425801 0.01660034
0.01660034 0.000333 469,161 7.76139865 7.76139865 0.016600456
Longitud= 250 Caudal= 0.096049006
Viscosidad= 0.00000114 Diámetro= 0.2
Ks= 0.000100 Velocidad= 3.057327674
f G(f)
DATO CALCULADO
0.001 0.000500 536,373 7.096070097 7.096070097 0.019859312
0.01985931 0.000500 536,373 7.547616372 7.547616372 0.017554173
0.01755417 0.000500 536,373 7.536781598 7.536781598 0.01760468
0.01760468 0.000500 536,373 7.53704 7.53704 0.017603473
0.01760347 0.000500 536,373 7.537033837 7.537033837 0.017603502
0.0176035 0.000500 536,373 7.537033984 7.537033984 0.017603501
Longitud= 450 Caudal= 0.056088069
Viscosidad= 0.00000114 Diámetro= 0.2
Ks= 0.000100 Velocidad= 1.785334502
f G(f)
DATO CALCULADO
0.001 0.000500 313,217 6.821110226 6.821110226 0.021492645
0.02149264 0.000500 313,217 7.443421542 7.443421542 0.018049068
0.01804907 0.000500 313,217 7.420893801 7.420893801 0.018158818
0.01815882 0.000500 313,217 7.421699196 7.421699196 0.018154877
0.01815488 0.000500 313,217 7.421670389 7.421670389 0.018155018
Longitud= 250 Caudal= 0.065570633
Viscosidad= 0.00000114 Diámetro= 0.15
Ks= 0.000100 Velocidad= 3.710530099
f G(f)
DATO CALCULADO
0.001 0.000667 488,228 6.93003423 6.93003423 0.020822326
Tubería (2-3)
Ks/dNúmero de
Reynolds Denominador DenominadorDato asumido 1/f
Tubería (1-6)
Ks/dNúmero de
Reynolds Denominador DenominadorDato asumido 1/f
Tubería (4-5)
Ks/dNúmero de
Reynolds Denominador DenominadorDato asumido 1/f
Tubería (3-4)
Ks/dNúmero de
Reynolds Denominador DenominadorDato asumido 1/f
Tubería (2-5)
Ks/dNúmero de
Reynolds Denominador DenominadorDato asumido 1/f
0.02082233 0.000667 488,228 7.33186575 7.33186575 0.018602486
0.01860249 0.000667 488,228 7.323590671 7.323590671 0.018644549
0.01864455 0.000667 488,228 7.323760291 7.323760291 0.018643685
0.01864369 0.000667 488,228 7.323756813 7.323756813 0.018643703
Longitud= 700 Caudal= 0.218718252
Viscosidad= 0.00000114 Diámetro= 0.2
Ks= 0.000100 Velocidad= 6.962001902
f G(f)
DATO CALCULADO
0.001 0.000500 1,221,404 7.39741757 7.39741757 0.018274257
0.01827426 0.000500 1,221,404 7.645868705 7.645868705 0.017105916
0.01710592 0.000500 1,221,404 7.642923824 7.642923824 0.0171191
0.0171191 0.000500 1,221,404 7.642958671 7.642958671 0.017118944
0.01711894 0.000500 1,221,404 7.642958259 7.642958259 0.017118946
Tramo Longitud Diámetro Caudal Velocidad f hfi Kmi HFI+km
(1-2) 600 0.2 0.241305186 7.680964659 0.017081307 154.090155 0 638.569596
(1-6) 300 0.25 0.258679189 5.269756848 0.016412344 27.8762276 0 107.763704
(2-3) 500 0.3 0.126019709 1.782810024 0.016600456 4.48208305 10 37.1865098
(3-4) 250 0.2 0.096049006 3.057327674 0.017603502 10.4832044 0 109.14433
(4-5) 450 0.2 0.056088069 1.785334502 0.018155018 6.63619877 0 118.317477
(2-5) 250 0.15 0.065570633 3.710530099 0.018643703 21.8048867 0 332.540435
(5-6) 700 0.2 0.218718252 6.962001902 0.017118946 148.017935 0 676.751637
ELABORACIÓN DE LA MATRIZ
-1.00 -1.00 0.00 0.00 0.00 0.00 0.00 Q1-2 -0.5
1.00 0.00 -1.00 0.00 0.00 -1.00 0.00 Q1-6 0.05
0.00 0.00 1.00 -1.00 0.00 0.00 0.00 Q2-3 0.03
0.00 0.00 0.00 1.00 -1.00 0.00 0.00 Q3-4 0.04
0.00 0.00 0.00 0.00 1.00 1.00 1.00 Q5-4 0.34
638.57 -107.76 0.00 0.00 0.00 332.54 -676.75 Q2-5 0
0 0 37.19 109.14 118.317 -332.540435 0 Q6-5 0
Tenemos que encontrar
Qi+11
-0.0686195 0.52476545 0.51158005 0.472880202 0.43092779 0.000636759 0.00035457 Q1-2 0.24132609
-0.9313805 -0.5247654 -0.51158 -0.4728802 -0.43092779 -0.00063676 -0.0003546 Q1-6 0.25867391
-0.0382103 -0.2646311 0.66575745 0.461444165 0.239959166 0.000354575 0.00187196 Q2-3 0.12589021
-0.0382103 -0.2646311 -0.3342426 0.461444165 0.239959166 0.000354575 0.00187196 Q3-4 0.09589021
-0.0382103 -0.2646311 -0.3342426 -0.53855583 0.239959166 0.000354575 0.00187196 Q5-4 0.05589021
-0.0304092 -0.2106035 -0.1541774 0.011436037 0.190968624 0.000282184 -0.0015174 Q2-5 0.06543589
0.06861952 0.47523455 0.48841995 0.527119798 0.56907221 -0.00063676 -0.0003546 Q6-5 0.21867391
Tramo Longitud Diámetro Caudal Velocidad f hfi Kmi HFI+km
(1-2) 600 0.2 0.241305186 7.680964659 0.017081307 154.090155 0 638.569596
(1-6) 300 0.25 0.258679189 5.269756848 0.016412344 27.8762276 0 107.763704
(2-3) 500 0.3 0.126019709 1.782810024 0.016600456 4.48208305 10 37.1865098
(3-4) 250 0.2 0.096049006 3.057327674 0.017603502 10.4832044 0 109.14433
(4-5) 450 0.2 0.056088069 1.785334502 0.018155018 6.63619877 0 118.317477
(2-5) 250 0.15 0.065570633 3.710530099 0.018643703 21.8048867 0 332.540435
(5-6) 700 0.2 0.218718252 6.962001902 0.017118946 148.017935 0 676.751637
MÉTODO DE LA TEORÍA LINEAL
Tubería (5-6)
Ks/dNúmero de
Reynolds Denominador DenominadorDato asumido 1/f
𝑿 = 𝑨 −𝟏 ∗ 𝑩
𝑴𝒂𝒕𝒓𝒊𝒛 𝑨𝑴𝒂𝒕𝒓𝒊𝒛 𝑩
𝑴𝒂𝒕𝒓𝒊𝒛 𝒊𝒏𝒗𝒆𝒓𝒔𝒂 ( 𝑨−𝟏 )𝑨−𝟏 ∗ 𝑩