teoria lineal

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



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



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



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



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



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


Tubería (4-5)

Ks/dNúmero de


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



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


Tubería (5-6)

Ks/dNúmero de


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:


(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



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



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



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


Tubería (1-2)

Ks/dNúmero de


Tubería (2-3)

Ks/dNúmero de


𝑸𝒊 +𝑸𝒊+𝟏

𝟐

𝑓 =1


3.7 ∗ 𝑑+

2.51

𝑅𝑒 ∗ 𝑓))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



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



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



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


(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


Tubería (2-5)

Ks/dNúmero de


Tubería (4-5)

Ks/dNúmero de


Tubería (5-6)

Ks/dNúmero de



-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


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:


(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



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


𝑿 = 𝑨 −𝟏 ∗ 𝑩


𝑴𝒂𝒕𝒓𝒊𝒛 𝒊𝒏𝒗𝒆𝒓𝒔𝒂 ( 𝑨−𝟏 )𝑨−𝟏 ∗ 𝑩

𝑸𝒊+𝟏 +𝑸𝒊+𝟐

𝟐

𝑵𝒖𝒆𝒗𝒐𝒔 𝒄𝒂𝒖𝒅𝒂𝒍𝒆𝒔(𝟏) − 𝑵𝒖𝒆𝒗𝒐𝒔 𝒄𝒂𝒖𝒅𝒂𝒍𝒆𝒔

𝑵𝒖𝒆𝒗𝒐𝒔 𝒄𝒂𝒖𝒅𝒂𝒍𝒆𝒔(𝟏)∗ 𝟏𝟎𝟎

𝑓 =1


3.7 ∗ 𝑑+

2.51

𝑅𝑒 ∗ 𝑓))2



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



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



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



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



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


Tubería (1-6)

Ks/dNúmero de


Tubería (4-5)

Ks/dNúmero de


Tubería (3-4)

Ks/dNúmero de


Tubería (2-5)

Ks/dNúmero de


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



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


(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


-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


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


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


𝑿 = 𝑨 −𝟏 ∗ 𝑩



𝑨−𝟏 ∗ 𝑩

𝑸𝒊+𝟐 +𝑸𝒊+𝟑

𝟐𝑵𝒖𝒆𝒗𝒐𝒔 𝒄𝒂𝒖𝒅𝒂𝒍𝒆𝒔(𝟐) − 𝑵𝒖𝒆𝒗𝒐𝒔 𝒄𝒂𝒖𝒅𝒂𝒍𝒆𝒔

𝑵𝒖𝒆𝒗𝒐𝒔 𝒄𝒂𝒖𝒅𝒂𝒍𝒆𝒔(𝟐)∗ 𝟏𝟎𝟎

CUARTA ITERACIÓN

Formula a utilizar:

DATOS DE INGRESO:


(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



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



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



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



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


Tubería (1-2)

Ks/dNúmero de


Tubería (3-4)

Ks/dNúmero de


Tubería (2-3)

Ks/dNúmero de


𝑓 =1


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



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



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



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


(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


-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


Tubería (4-5)

Ks/dNúmero de


Tubería (5-6)

Ks/dNúmero de


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


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


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:


(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



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


𝑿 = 𝑨 −𝟏 ∗ 𝑩



𝑨−𝟏 ∗ 𝑩

𝑸𝒊+𝟑 +𝑸𝒊+𝟒

𝟐𝑵𝒖𝒆𝒗𝒐𝒔 𝒄𝒂𝒖𝒅𝒂𝒍𝒆𝒔(𝟑) − 𝑵𝒖𝒆𝒗𝒐𝒔 𝒄𝒂𝒖𝒅𝒂𝒍𝒆𝒔

𝑵𝒖𝒆𝒗𝒐𝒔 𝒄𝒂𝒖𝒅𝒂𝒍𝒆𝒔(𝟑)∗ 𝟏𝟎𝟎

𝑓 =1


3.7 ∗ 𝑑+

2.51

𝑅𝑒 ∗ 𝑓))2



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



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



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



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



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


Tubería (1-6)

Ks/dNúmero de


Tubería (4-5)

Ks/dNúmero de


Tubería (3-4)

Ks/dNúmero de


Tubería (2-5)

Ks/dNúmero de


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



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


(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


-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


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


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


𝑿 = 𝑨 −𝟏 ∗ 𝑩

𝑴𝒂𝒕𝒓𝒊𝒛 𝑨 𝑴𝒂𝒕𝒓𝒊𝒛 𝑩


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:


(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



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



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



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



Ks= 0.000100 Velocidad= 3.213887079

Tubería (1-6)

Ks/dNúmero de


Tubería (1-2)

Ks/dNúmero de


Tubería (3-4)

Tubería (2-3)

Ks/dNúmero de


𝑓 =1


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



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



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



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


(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


Tubería (2-5)

Ks/dNúmero de


Tubería (4-5)

Ks/dNúmero de


Tubería (5-6)

Ks/dNúmero de



-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


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


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:


(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



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


𝑿 = 𝑨 −𝟏 ∗ 𝑩



𝑨−𝟏 ∗ 𝑩

𝑸𝒊+𝟓 +𝑸𝒊+𝟔

𝟐

𝑵𝒖𝒆𝒗𝒐𝒔 𝒄𝒂𝒖𝒅𝒂𝒍𝒆𝒔(𝟓) − 𝑵𝒖𝒆𝒗𝒐𝒔 𝒄𝒂𝒖𝒅𝒂𝒍𝒆𝒔

𝑵𝒖𝒆𝒗𝒐𝒔 𝒄𝒂𝒖𝒅𝒂𝒍𝒆𝒔(𝟓)∗ 𝟏𝟎𝟎

𝑓 =1


3.7 ∗ 𝑑+

2.51

𝑅𝑒 ∗ 𝑓))2



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



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



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



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



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


Tubería (1-6)

Ks/dNúmero de


Tubería (4-5)

Ks/dNúmero de


Tubería (3-4)

Ks/dNúmero de


Tubería (2-5)

Ks/dNúmero de


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



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


(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


-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


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


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


𝑿 = 𝑨 −𝟏 ∗ 𝑩



𝑨−𝟏 ∗ 𝑩

𝑸𝒊+𝟔 +𝑸𝒊+𝟕

𝟐𝑵𝒖𝒆𝒗𝒐𝒔 𝒄𝒂𝒖𝒅𝒂𝒍𝒆𝒔(𝟔) − 𝑵𝒖𝒆𝒗𝒐𝒔 𝒄𝒂𝒖𝒅𝒂𝒍𝒆𝒔

𝑵𝒖𝒆𝒗𝒐𝒔 𝒄𝒂𝒖𝒅𝒂𝒍𝒆𝒔(𝟔)∗ 𝟏𝟎𝟎

OCTAVA ITERACIÓN

Formula a utilizar:

DATOS DE INGRESO:


(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



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



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



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



Ks= 0.000100 Velocidad= 3.092713347

f G(f)

DATO CALCULADO

Tubería (1-6)

Ks/dNúmero de


Tubería (1-2)

Ks/dNúmero de


Tubería (3-4)

Ks/dNúmero de


Tubería (2-3)

Ks/dNúmero de


𝑓 =1


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



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



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



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


(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


-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


Tubería (4-5)

Ks/dNúmero de


Tubería (5-6)

Ks/dNúmero de


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


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


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:


(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



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


𝑿 = 𝑨 −𝟏 ∗ 𝑩



𝑨−𝟏 ∗ 𝑩

𝑸𝒊+𝟔 +𝑸𝒊+𝟕

𝟐𝑵𝒖𝒆𝒗𝒐𝒔 𝒄𝒂𝒖𝒅𝒂𝒍𝒆𝒔(𝟕) − 𝑵𝒖𝒆𝒗𝒐𝒔 𝒄𝒂𝒖𝒅𝒂𝒍𝒆𝒔

𝑵𝒖𝒆𝒗𝒐𝒔 𝒄𝒂𝒖𝒅𝒂𝒍𝒆𝒔(𝟕)∗ 𝟏𝟎𝟎

𝑓 =1


3.7 ∗ 𝑑+

2.51

𝑅𝑒 ∗ 𝑓))2



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



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



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



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



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


Tubería (1-6)

Ks/dNúmero de


Tubería (4-5)

Ks/dNúmero de


Tubería (3-4)

Ks/dNúmero de


Tubería (2-5)

Ks/dNúmero de


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



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


(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


-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


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


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


𝑿 = 𝑨 −𝟏 ∗ 𝑩



𝑨−𝟏 ∗ 𝑩

𝑸𝒊+𝟕 +𝑸𝒊+𝟖

𝟐𝑵𝒖𝒆𝒗𝒐𝒔 𝒄𝒂𝒖𝒅𝒂𝒍𝒆𝒔(𝟖) − 𝑵𝒖𝒆𝒗𝒐𝒔 𝒄𝒂𝒖𝒅𝒂𝒍𝒆𝒔

𝑵𝒖𝒆𝒗𝒐𝒔 𝒄𝒂𝒖𝒅𝒂𝒍𝒆𝒔(𝟖)∗ 𝟏𝟎𝟎

DÉCIMA ITERACIÓN

Formula a utilizar:

DATOS DE INGRESO:


(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



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



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



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



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


Tubería (1-2)

Ks/dNúmero de


Tubería (3-4)

Ks/dNúmero de


Tubería (2-3)

Ks/dNúmero de


𝑓 =1


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



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



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



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


(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


-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


Tubería (4-5)

Ks/dNúmero de


Tubería (5-6)

Ks/dNúmero de


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


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


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:


(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



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


𝑿 = 𝑨 −𝟏 ∗ 𝑩



𝑨−𝟏 ∗ 𝑩

𝑸𝒊+𝟖 +𝑸𝒊+𝟗

𝟐𝑵𝒖𝒆𝒗𝒐𝒔 𝒄𝒂𝒖𝒅𝒂𝒍𝒆𝒔(𝟗) − 𝑵𝒖𝒆𝒗𝒐𝒔 𝒄𝒂𝒖𝒅𝒂𝒍𝒆𝒔

𝑵𝒖𝒆𝒗𝒐𝒔 𝒄𝒂𝒖𝒅𝒂𝒍𝒆𝒔(𝟗)∗ 𝟏𝟎𝟎

𝑓 =1


3.7 ∗ 𝑑+

2.51

𝑅𝑒 ∗ 𝑓))2



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



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



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



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



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


Tubería (1-6)

Ks/dNúmero de


Tubería (4-5)

Ks/dNúmero de


Tubería (3-4)

Ks/dNúmero de


Tubería (2-5)

Ks/dNúmero de


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



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


(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


-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


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


(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


𝑿 = 𝑨 −𝟏 ∗ 𝑩


𝑴𝒂𝒕𝒓𝒊𝒛 𝒊𝒏𝒗𝒆𝒓𝒔𝒂 ( 𝑨−𝟏 )𝑨−𝟏 ∗ 𝑩

teoria lineal

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