Primer ciclo

EJEMPLO: La red mostrada en la siguiente figura tiene una válvula en la tubería 2-3, la cual se encuentra parcialmente cerrada y produce una pérdida menor local de 10.0 V2/2g, la presión en el punto 1 es 100 mca. Analizar los caudales y presiones en la red. Los diámetros (en milímetros) y las longitudes (en metros) para cada una de las tuberías son los indicados. Los caudales están dados en l/s. ( = 1.141x10-6 m2/s).



=

1.1410E-06 m2/s

Primer ciclo

T u ber ía de 6 6 1 2

Circuito

1

5 2 3 4

2

a 5 1 2 5

Cau d da al D iá i ám e ett r o l /s m3 m3 / s mm m -40.00 -0.04000 200 0.200 -80.00 -0.08000 250 0.250 120.00 0.12000 25 250 0.250 10.00 0. 0.01000 100 0.100

2 3 4 5

-10.00 50.00 10.00 -20.00

-0.01000 0. 0.05000 0. 0.01000 -0.02000

100 150 100 150

0.100 0.150 0.100 0.150

L on gi t u d m 600 300 500 200

A m2 0.031415927 0.049087385 0.049087385 0.007853982

V m /s - 1. 1.273239545 - 1. 1.629746617 2.444619926 1.273239545

e m 0.002 0.002 0.002 0.002

200 400 200 400

0.007853982 0.017671459 0.007853982 0.017671459

- 1. 1.273239545 2.829421211 1.273239545 - 1. 1.131768484

0.002 0.002 0.002 0.002

L on gi t u d m 600 300 500 200

A m2 0.031415927 0.049087385 0.049087385 0.007853982

V m /s - 1. 1.449959954 - 1. 1.742847679 2.331518864 1.472493607

e m 0.002 0.002 0.002 0.002

200 400 200 400

0.007853982 0.017671459 0.007853982 0.017671459

- 1. 1.472493607 2.426694232 0.367103844 - 1. 1.534495463

0.002 0.002 0.002 0.002

L on gi t u d m 600 300 500 200

A m2 0.031415927 0.049087385 0.049087385 0.007853982

V m /s - 1. 1.576659252 -1.82393523 2.250431313 1.294434027

e m 0.002 0.002 0.002 0.002

200 400 200 400

0.007853982 0.017671459 0.007853982 0.017671459

- 1. 1.294434027 2.280588627 0.038366233 - 1. 1.680601067

0.002 0.002 0.002 0.002

L on gi t u d m 600

A m2 0.031415927

V m /s - 1. 1.634217237

e m 0.002

Segundo ciclo

Circuito

1

Tu T u ber ía de a 5 6 6 1 1 2 2 5 5 2 3 4

2

2 3 4 5

Cau dal D i ám et r o l /s m3 m3 / s mm m -45.55 -0.04555 200 0.200 -85.55 -0.08555 250 0.250 114.45 0.11445 25 250 0.250 11.56 0. 0.01156 100 0.100 -11.56 42.88 2.88 -27.12

-0.01156 0. 0.04288 0.00288 -0.02712

100 150 100 150

0.100 0.150 0.100 0.150

Tercer ciclo

Circuito

1

2

Tu T u ber ía de a 5 6 6 1 1 2 2 5 5 2 3 4

2 3 4 5

Cau dal D i ám et r o l /s m3 m3 / s mm m -49.53 -0.04953 200 0.200 -89.53 -0.08953 250 0.250 110.47 0.11047 25 250 0.250 10.17 0. 0.01017 100 0.100 -10.17 40.30 0.30 -29.70

-0.01017 0. 0.04030 0.00030 -0.02970

100 150 100 150

0.100 0.150 0.100 0.150

Cuarto ciclo

Circuito

T u ber ía de a 5 6

Cau dal D i ám et r o l /s m3 m3 / s mm m -51.34 -0.05134 200 0.200

1

2

6 1 2

1 2 5

-91.34 -0.09134 108.66 0.10866 10.14 0.01014

250 250 100

0.250 0.250 0.100

300 500 200

0.049087385 0.049087385 0.007853982

-1.86077234 2.213594203 1.291587676

0.002 0.002 0.002

5 2 3 4

2 3 4 5

-10.14 38.52 -1.48 -31.48

100 150 100 150

0.100 0.150 0.100 0.150

200 400 200 400

0.007853982 0.017671459 0.007853982 0.017671459

- 1.291587676 2.179528367 - 0.189019354 - 1.781661328

0.002 0.002 0.002 0.002

L ongitud m 600 300 500 200

A m2 0.031415927 0.049087385 0.049087385 0.007853982

V m/s - 1.668251009 - 1.882553955 2.191812588 1.23607596

e m 0.002 0.002 0.002 0.002

200 400 200 400

0.007853982 0.017671459 0.007853982 0.017671459

-1.23607596 2.143695755 - 0.269642729 - 1.817493939

0.002 0.002 0.002 0.002

L ongitud m 600 300 500 200

A m2 0.031415927 0.049087385 0.049087385 0.007853982

V m/s - 1.680781656 - 1.890573569 2.183792975 1.233266539

e m 0.002 0.002 0.002 0.002

200 400 200 400

0.007853982 0.017671459 0.007853982 0.017671459

- 1.233266539 2.122667682 - 0.316955895 - 1.838522013

0.002 0.002 0.002 0.002

L ongitud m 600 300 500 200

A m2 0.031415927 0.049087385 0.049087385 0.007853982

V m/s - 1.687726822 - 1.895018475 2.179348068 1.222185841

e m 0.002 0.002 0.002 0.002

200 400 200 400

0.007853982 0.017671459 0.007853982 0.017671459

- 1.222185841 2.115245475 - 0.333655861 -1.84594422

0.002 0.002 0.002 0.002

L ongitud m 600 300 500 200

A m2 0.031415927 0.049087385 0.049087385 0.007853982

V m/s - 1.690198988 - 1.896600661 2.177765882 1.221595595

e m 0.002 0.002 0.002 0.002

-0.01014 0.03852 -0.00148 -0.03148

Quinto ciclo

Circuito

1

Tubería de a 5 6 6 1 1 2 2 5 5 2 3 4

2

2 3 4 5

Caudal Diámetro l /s m3/s mm m -52.41 -0.05241 200 0.200 -92.41 -0.09241 250 0.250 107.59 0.10759 250 0.250 9.71 0.00971 100 0.100 -9.71 37.88 -2.12 -32.12

-0.00971 0.03788 -0.00212 -0.03212

100 150 100 150

0.100 0.150 0.100 0.150

Sexto ciclo

Circuito

1

Tubería de a 5 6 6 1 1 2 2 5 5 2 3 4

2

2 3 4 5


-0.00969 0.03751 -0.00249 -0.03249

100 150 100 150

0.100 0.150 0.100 0.150

Septimo ciclo

Circuito

1

Tubería de a 5 6 6 1 1 2 2 5 5 2 3 4

2

2 3 4 5


-0.00960 0.03738 -0.00262 -0.03262

100 150 100 150

0.100 0.150 0.100 0.150

Octavo ciclo

Circuito

1

Tubería de a 5 6 6 1 1 2 2 5

Caudal Diámetro l /s m3/s mm m -53.10 -0.05310 200 0.200 -93.10 -0.09310 250 0.250 106.90 0.10690 250 0.250 9.59 0.00959 100 0.100

5 2 3 4

2

2 3 4 5

-9.59 37.31 -2.69 -32.69

-0.00959 0.03731 -0.00269 -0.03269

100 150 100 150

0.100 0.150 0.100 0.150

200 400 200 400

0.007853982 0.017671459 0.007853982 0.017671459

- 1.221595595 2.111112844 - 0.342954279 -1.85007685

0.002 0.002 0.002 0.002

L ongitud m 600 300 500 200

A m2 0.031415927 0.049087385 0.049087385 0.007853982

V m/s - 1.691556073 - 1.897469196 2.176897348 1.219459751

e m 0.002 0.002 0.002 0.002

200 400 200 400

0.007853982 0.017671459 0.007853982 0.017671459

- 1.219459751 2.109649513 - 0.346246775 - 1.851540182

0.002 0.002 0.002 0.002

Noveno ciclo

Circuito

1

2

Tubería de a 5 6 6 1 1 2 2 5 5 2 3 4

2 3 4 5


-0.00958 0.03728 -0.00272 -0.03272

100 150 100 150

0.100 0.150 0.100 0.150

D/e

Re

f

f

hf

km

hm

hf+hm

(hf+hm)/Q

-9.454467149 -5.744926205 21.50351742 8.086981311 14.39110538 -8.086981311 49.75305711 8.086981311 -7.342811376 42.41024574

236.3616787 71.81157757 179.1959785 808.6981311 1296.067366 808.6981311 995.0611423 808.6981311 367.1405688 2979.597973

100 125 125 50

223179.5872 0.01 357087.3395 0.01 535631.0092 0.01 111589.7936 0.01

0.038141219 -9.454467149 0.035364053 -5.744926205 0.035298465 21.50351742 0.04893676 8.086981311

0 0 0 0

0 0 0 0

50 75 50 75

0.01 111589.7936 371965.9786 0.01 0.01 111589.7936 148786.3914 0.01

0.04893676 -8.086981311 0.041975118 45.67271849 0.04893676 8.086981311 0.042177171 -7.342811376

0 10 0 0

0 4.080338627 0 0

km

hm

D/e

Re

f

f

hf

100 125 125 50

254155.9955 0.01 381868.4661 0.01 510849.8825 0.01 0.01 129052.9016

0.038108311 -12.25050433 0.035351309 -6.567598613 0.035304842 19.56334572 0.04888977 10.8057725

0 0 0 0

0 0 0 0

50 75 50 75

0.01 129052.9016 319022.0288 0.01 32173.86884 0.01 201730.3413 0.01

0.04888977 0.041997583 0.049777929 0.042089064

-10.8057725 33.61430525 0.683826108 -13.4700813

0 10 0 0

0 3.001449998 0 0

hf

km

hm

D/e

Re

f

100 125 125 50

276364.4614 399635.2388 493083.1098 113447.3293

0.01 0.01 0.01 0.01

0.038089226 -14.47771728 0.035343138 -7.191279583 0.035309806 18.2287904 0.048931079 8.357485384

0 0 0 0

0 0 0 0

50 75 50 75

113447.3293 0.01 299814.4558 0.01 0.01 3362.509428 220937.9142 0.01

0.048931079 -8.357485384 0.042007685 29.69561939 0.05826373 0.008742338 0.042067474 -16.14899253

0 10 0 0

0 2.650909525 0 0

hf

km

hm

-15.5509235

0

0

D/e 100

Re

f

f

286453.5034 0.01

f 0.038081527

hf+hm -12.25050433 -6.567598613 19.56334572 10.8057725 11.55101527 -10.8057725 36.61575525 0.683826108 -13.4700813 13.02372755

hf+hm -14.47771728 -7.191279583 18.2287904 8.357485384 4.917278925 -8.357485384 32.34652892 0.008742338 -16.14899253 7.84879334

hf+hm -15.5509235

(hf+hm)/Q 268.9354715 76.76747766 170.9362993 934.3563046 1450.995553 934.3563046 853.847948 237.1738835 496.7435182 2522.121654

(hf+hm)/Q 292.2889351 80.320585 165.0145314 822.0643666 1359.688418 822.0643666 802.6169552 29.01272713 543.7614301 2197.455479

(hf+hm)/Q 302.8980834

125 125 50

0.01 407706.4724 485011.8762 0.01 113197.8682 0.01

0.03533966 -7.483953721 0.035312181 17.63808994 0.048931831 8.320898891

0 0 0

0 0 0

50 75 50 75

113197.8682 0.01 286528.7073 0.01 16566.11341 0.01 0.01 234223.6628

0.048931831 -8.320898891 0.042015462 27.12713444 0.050848622 -0.185192217 0.0420546 -18.14402098

0 10 0 0

0 2.421174262 0 0

km

hm

D/e

Re

f

f

hf

100 125 125 50

292419.1077 412478.9559 480239.3927 108332.6871

0.01 0.01 0.01 0.01

0.038077223 -16.2035553 0.035337667 -7.659756825 0.035313623 17.2933885 0.048947187 7.623406089

0 0 0 0

0 0 0 0

50 75 50 75

108332.6871 281818.0222 23632.14106 238934.3479

0.01 0.01 0.01 0.01

0.048947187 -7.623406089 0.042018394 26.24432907 0.050194168 -0.372016055 0.042050377 -18.87928589

0 10 0 0

0 2.342217886 0 0

km

hm

D/e

Re

f

f

hf

100 125 125 50

294615.5401 414236.1018 478482.2468 108086.4627

0.01 0.01 0.01 0.01

0.038075682 -16.44722164 0.035336945 -7.724998528 0.035314161 17.16733212 0.048948001 7.588917835

0 0 0 0

0 0 0 0

50 75 50 75

108086.4627 279053.5953 27778.78137 241698.7747

0.01 0.01 0.01 0.01

0.048948001 -7.588917835 0.042020161 25.7330613 0.049961002 -0.51163448 0.042047975 -19.31756936

0 10 0 0

0 2.296492399 0 0

km

hm

D/e

Re

f

hf

100 125 125 50

295832.9224 415210.0076 477508.341 107115.3234

0.01 0.01 0.01 0.01

0.038074838 -16.58305801 0.035336547 -7.761278194 0.03531446 17.09766343 0.048951246 7.453654247

0 0 0 0

0 0 0 0

50 75 50 75

107115.3234 0.01 0.01 278077.845 29242.40674 0.01 242674.525 0.01

0.048951246 -7.453654247 0.042020793 25.55380167 0.049894084 -0.566210037 0.04204714 -19.47346958

0 10 0 0

0 2.280460458 0 0

km

hm

0 0 0 0

0 0 0 0

D/e 100 125 125 50

f

Re 296266.2556 415556.6742 477161.6745 107063.5929

f

0.01 0.01 0.01 0.01

f

hf

0.038074539 -16.63154443 0.035336406 -7.774212628 0.035314567 17.0728987 0.048951421 7.446483164

-7.483953721 17.63808994 8.320898891 2.924111611 -8.320898891 29.5483087 -0.185192217 -18.14402098 2.898196606

hf+hm -16.2035553 -7.659756825 17.2933885 7.623406089 1.053482455 -7.623406089 28.58654696 -0.372016055 -18.87928589 1.71183893

hf+hm -16.44722164 -7.724998528 17.16733212 7.588917835 0.584029784 -7.588917835 28.0295537 -0.51163448 -19.31756936 0.611432021

hf+hm -16.58305801 -7.761278194 17.09766343 7.453654247 0.206981473 -7.453654247 27.83426213 -0.566210037 -19.47346958 0.34092827

hf+hm -16.63154443 -7.774212628 17.0728987 7.446483164

81.93471602 162.3243398 820.2693254 1367.426465 820.2693254 767.1807593 124.7459846 576.2832364 2288.479306

(hf+hm)/Q 309.1712108 82.88914338 160.7336409 785.260972 1338.054967 785.260972 754.6162472 175.6641292 587.814361 2303.355709

(hf+hm)/Q 311.4808655 83.24054687 160.1479729 783.4892119 1338.358597 783.4892119 747.2428627 205.528044 594.5813006 2330.841419

(hf+hm)/Q 312.7610012 83.43531375 159.8233638 776.5011691 1332.520848 776.5011691 744.6403039 216.0672398 596.9698029 2334.178516

(hf+hm)/Q 313.2166717 83.50464197 159.7078176 776.1289308

50 75 50 75

D/e

107063.5929 0.01 277534.5545 0.01 0.01 30057.3426 0.01 243217.8156

Re

f

0.048951421 -7.446483164 0.042021147 25.45426278 0.049859577 -0.597794669 0.042046678 -19.56054522

f

hf

0 10 0 0

0 2.271558329 0 0

km

hm

100 125 125 50

0.01 296504.132 415746.9754 0.01 476971.3733 0.01 106876.4023 0.01

0.038074375 -16.65819094 0.035336329 -7.781317511 0.035314626 17.05931183 0.048952054 7.420562915

0 0 0 0

0 0 0 0

50 75 50 75

106876.4023 277342.1796 30345.90492 243410.1904

0.048952054 -7.420562915 0.042021272 25.41906341 0.049847792 -0.609183866 0.042046515 -19.59142458

0 10 0 0

0 2.26841033 0 0

0.01 0.01 0.01 0.01

0.113624803

1332.558062

-7.446483164 27.72582111 -0.597794669 -19.56054522 0.120998055

776.1289308 743.1912181 221.9350679 598.2997033 2339.55492

hf+hm -16.65819094 -7.781317511 17.05931183 7.420562915 0.040366291 -7.420562915 27.68747374 -0.609183866 -19.59142458 0.066302381

(hf+hm)/Q 313.4668101 83.54269941 159.644389 774.7819593 1331.435858 774.7819593 742.6781083 224.0127691 598.7706104 2340.243447

DQ

-0.005551835

-0.007116773

DQ

-0.003980376

-0.002581899

DQ

-0.001808237

-0.001785882

DQ

-0.001069203

-0.000633215

DQ

-0.000393662

-0.000371597

DQ

-0.000218189

-0.000131161

DQ

-7.76654E-05

-7.30296E-05

DQ

-4.26341E-05

-2.58592E-05

DQ

-1.51589E-05

-1.41657E-05

-3.78 3.78 1.52 -1.89



=

1.89 1.14 -1.14 -1.89

1.1410E-06 m2/s

Primer ciclo

Circuito

1

2

Tubería

Caudal

Diámetro

de F A B C

a A B C F

l/s -43.75 43.75 17.59 -21.88

m3/s -0.04375 0.04375 0.01759 -0.02188

mm 203 305 203 203

m 0.203 0.305 0.203 0.203

Longitud m 305 610 305 610

F C E D

C E D F

21.88 13.19 -13.19 -21.88

0.02188 0.01319 -0.01319 -0.02188

203 152 152 152

0.203 0.152 0.152 0.152

610 305 610 305

de 5 6 1 2

a 6 1 2 5

l/s -35.00 52.50 26.34 -16.12

m3/s -0.03500 0.05250 0.02634 -0.01612

mm 203 305 203 203

m 0.203 0.305 0.203 0.203

Longitud m 305 610 305 610

5 2 3 4

2 3 4 5

16.12 16.19 -10.19 -18.88

0.01612 0.01619 -0.01019 -0.01888

203 152 152 152

0.203 0.152 0.152 0.152

610 305 610 305

Segundo ciclo

Circuito

1

2

Tubería

Caudal

Diámetro

Tercer ciclo

Circuito

1

2

Tubería

Caudal

Diámetro

de 5 6 1 2

a 6 1 2 5

l/s -33.19 54.31 28.15 -15.78

m3/s -0.03319 0.05431 0.02815 -0.01578

mm 203 305 203 203

m 0.203 0.305 0.203 0.203

Longitud m 305 610 305 610

5 2 3 4

2 3 4 5

15.78 17.66 -8.73 -17.41

0.01578 0.01766 -0.00873 -0.01741

203 152 152 152

0.203 0.152 0.152 0.152

610 305 610 305

Cuarto ciclo

Circuito

1

Tubería de 5 6 1 2

Caudal a 6 1 2 5

l/s -32.67 54.83 28.67 -15.57

m3/s -0.03267 0.05483 0.02867 -0.01557

Diámetro mm 203 305 203 203

m 0.203 0.305 0.203 0.203

Longitud m 305 610 305 610

2

5 2 3 4

2 3 4 5

15.57 17.97 -8.42 -17.10

0.01557 0.01797 -0.00842 -0.01710

203 152 152 152

0.203 0.152 0.152 0.152

610 305 610 305

de 5 6 1 2

a 6 1 2 5

l/s -32.55 54.95 28.79 -15.53

m3/s -0.03255 0.05495 0.02879 -0.01553

mm 203 305 203 203

m 0.203 0.305 0.203 0.203

Longitud m 305 610 305 610

5 2 3 4

2 3 4 5

15.53 18.05 -8.34 -17.02

0.01553 0.01805 -0.00834 -0.01702

203 152 152 152

0.203 0.152 0.152 0.152

610 305 610 305

Quinto ciclo

Circuito

1

2

Tubería

Caudal

Diámetro

Sexto ciclo

Circuito

1

2

Tubería

Caudal

Diámetro

de 5 6 1 2

a 6 1 2 5

l/s -32.53 54.97 28.82 -15.52

m3/s -0.03253 0.05497 0.02882 -0.01552

mm 203 305 203 203

m 0.203 0.305 0.203 0.203

Longitud m 305 610 305 610

5 2 3 4

2 3 4 5

15.52 18.06 -8.32 -17.00

0.01552 0.01806 -0.00832 -0.01700

203 152 152 152

0.203 0.152 0.152 0.152

610 305 610 305

Septimo ciclo

Circuito

1

2

Tubería

Caudal

Diámetro

de 5 6 1 2

a 6 1 2 5

l/s -32.52 54.98 28.82 -15.52

m3/s -0.03252 0.05498 0.02882 -0.01552

mm 203 305 203 203

m 0.203 0.305 0.203 0.203

Longitud m 305 610 305 610

5 2 3 4

2 3 4 5

15.52 18.07 -8.32 -17.00

0.01552 0.01807 -0.00832 -0.01700

203 152 152 152

0.203 0.152 0.152 0.152

610 305 610 305

de 5 6 1 2

a 6 1 2 5

l/s -32.52 54.98 28.82 -15.52

m3/s -0.03252 0.05498 0.02882 -0.01552

mm 203 305 203 203

m 0.203 0.305 0.203 0.203

Longitud m 305 610 305 610

5 2

2 3

15.52 18.07

0.01552 0.01807

203 152

0.203 0.152

610 305

Octavo ciclo

Circuito

1

Tubería

Caudal

Diámetro

3 4

4 5

-8.32 -17.00

-0.00832 -0.01700

152 152

0.152 0.152

610 305

Noveno ciclo

Circuito

1

2

Tubería

Caudal

Diámetro

de 5 6 1 2

a 6 1 2 5

l/s -32.52 54.98 28.82 -15.52

m3/s -0.03252 0.05498 0.02882 -0.01552

mm 203 305 203 203

m 0.203 0.305 0.203 0.203

Longitud m 305 610 305 610

5 2 3 4

2 3 4 5

15.52 18.07 -8.32 -17.00

0.01552 0.01807 -0.00832 -0.01700

203 152 152 152

0.203 0.152 0.152 0.152

610 305 610 305

-2.809565 4.750435 2.490435 -1.34081521 1.34081521 1.56125021 -0.71874979 -1.46874979

A m2 0.032365473 0.073061664 0.032365473 0.032365473

V m/s -1.351749134 0.598809246 0.543560499 -0.675874567

e m 0.00015 0.00015 0.00015 0.00015

D/ e

Re

1353.333333 2033.333333 1353.333333 1353.333333

240495.2448 160067.3269 96707.08256 120247.6224

0.01 0.01 0.01 0.01

0.032365473 0.018145839 0.018145839 0.018145839

0.675874567 0.727133329 -0.727133329 -1.205510519

0.00015 0.00015 0.00015 0.00015

1353.333333 1013.333333 1013.333333 1013.333333

120247.6224 96866.14026 96866.14026 160593.8641

0.01 0.01 0.01 0.01

A m2 0.032365473 0.073061664 0.032365473 0.032365473

V m/s -1.081359865 0.718588567 0.813949768 -0.498170231

e m 0.00015 0.00015 0.00015 0.00015

1353.333333 2033.333333 1353.333333 1353.333333

192389.1784 192085.4628 144813.1489 88631.51348

0.01 0.01 0.01 0.01

0.020000601 -1.79097 0.018842293 0.9918029 0.020473197 1.0386893 0.021542743 -0.818825

0 0 0 0

0.032365473 0.018145839 0.018145839 0.018145839

0.498170231 0.892449006 -0.561817652 -1.040194842

0.00015 0.00015 0.00015 0.00015

1353.333333 1013.333333 1013.333333 1013.333333

88631.51348 118888.9123 74843.36818 138571.092

0.01 0.01 0.01 0.01

0.021542743 0.021777029 0.022797887 0.021506185

0.8188255 1.7738737 -1.471881 -2.379852

0 0 0 0

A m2 0.032365473 0.073061664 0.032365473 0.032365473

V m/s -1.025522456 0.743323894 0.869787177 -0.487483763

e m 0.00015 0.00015 0.00015 0.00015

hf

km

1353.333333 2033.333333 1353.333333 1353.333333

182454.9155 198697.4477 154747.4119 86730.24007

0.01 0.01 0.01 0.01

0.020081562 0.018782435 0.020354037 0.021598268

-1.617308 1.0578865 1.1791834 -0.786093

0 0 0 0

0.032365473 0.018145839 0.018145839 0.018145839

0.487483763 0.972981605 -0.481285054 -0.959662244

0.00015 0.00015 0.00015 0.00015

1353.333333 1013.333333 1013.333333 1013.333333

86730.24007 129617.1813 64115.09919 127842.823

0.01 0.01 0.01 0.01

0.021598268 0.021620545 0.02321562 0.021644853

0.7860932 2.093308 -1.099948 -2.038678

0 0 0 0

A m2 0.032365473 0.073061664 0.032365473 0.032365473

V m/s -1.009454258 0.75044192 0.885855375 -0.481149617

e m 0.00015 0.00015 0.00015 0.00015

hf

km

-1.568954 1.0772904 1.2212365 -0.766998

0 0 0 0

D/e

D/e

D/e 1353.333333 2033.333333 1353.333333 1353.333333

Re

Re

Re 179596.1563 200600.1628 157606.171 85603.30601

f

f

f

hf

km

0.019693088 0.019188864 0.021326932 0.020837778

-2.755566 0.7013862 0.4825351 -1.457869

0 0 0 0

0.020837778 0.022189174 0.022189174 0.021273069

1.4578687 1.1998487 -2.399697 -3.161764

0 0 0 0

hf

km

f

f

f

f

f 0.01 0.01 0.01 0.01

0.020106296 0.018765824 0.020322135 0.021632119

1353.333333 1013.333333 1013.333333 1013.333333

0.01 0.01 0.01 0.01

0.481149617 0.990343555 -0.463923103 -0.942300293

0.00015 0.00015 0.00015 0.00015

A m2 0.032365473 0.073061664 0.032365473 0.032365473

V m/s -1.005829849 0.752047492 0.889479784 -0.479902635

e m 0.00015 0.00015 0.00015 0.00015

1353.333333 2033.333333 1353.333333 1353.333333

178951.3228 201029.3471 158251.0045 85381.45033

0.01 0.01 0.01 0.01

0.032365473 0.018145839 0.018145839 0.018145839

0.479902635 0.994584007 -0.459682651 -0.938059841

0.00015 0.00015 0.00015 0.00015

1353.333333 1013.333333 1013.333333 1013.333333

85381.45033 132494.9773 61237.3032 124965.0271

0.01 0.01 0.01 0.01

A m2 0.032365473 0.073061664 0.032365473 0.032365473

V m/s -1.004967629 0.752429445 0.890342004 -0.479574602

e m 0.00015 0.00015 0.00015 0.00015

1353.333333 2033.333333 1353.333333 1353.333333

178797.9217 201131.4468 158404.4056 85323.08874

0.01 0.01 0.01 0.01

0.032365473 0.018145839 0.018145839 0.018145839

0.479574602 0.995536801 -0.458729858 -0.937107048

0.00015 0.00015 0.00015 0.00015

1353.333333 1013.333333 1013.333333 1013.333333

85323.08874 132621.9051 61110.37545 124838.0993

0.01 0.01 0.01 0.01

A m2 0.032365473 0.073061664 0.032365473 0.032365473

V m/s -1.004771972 0.752516119 0.89053766 -0.479503779

e m 0.00015 0.00015 0.00015 0.00015

1353.333333 2033.333333 1353.333333 1353.333333

178763.1117 201154.6155 158439.2157 85310.48821

0.01 0.01 0.01 0.01

0.020113633 -1.555 0.018761032 1.0829773 0.020313024 1.2336273 0.021641033 -0.762073

0 0 0 0

0.032365473 0.018145839 0.018145839 0.018145839

0.479503779 0.995759456 -0.458507202 -0.936884392

0.00015 0.00015 0.00015 0.00015

1353.333333 1013.333333 1013.333333 1013.333333

85310.48821 132651.5665 61080.71406 124808.4379

0.01 0.01 0.01 0.01

0.021641033 0.7620735 0.021580286 2.188383 0.023355171 -1.004298 0.021687808 -1.946906

0 0 0 0

A m2 0.032365473 0.073061664 0.032365473 0.032365473

V m/s -1.00472655 0.75253624 0.890583083 -0.479486828

e m 0.00015 0.00015 0.00015 0.00015

1353.333333 2033.333333 1353.333333 1353.333333

178755.0303 201159.9942 158447.297 85307.47254

0.01 0.01 0.01 0.01

0.020113704 0.018760986 0.020312936 0.021641125

0.032365473 0.018145839

0.479486828 0.995810241

0.00015 0.00015

1353.333333 1013.333333

85307.47254 132658.3318

0.01 0.01

D/e

D/e

D/e

D/e

85603.30601 131930.0793 61802.20126 125529.9251

0.021632119 0.021589712 0.023320983 0.021677431

0.032365473 0.018145839 0.018145839 0.018145839

Re

Re

Re

Re

f

0.7669979 2.1655882 -1.026659 -1.968538

0 0 0 0

hf

km

0.02011197 0.018762113 0.020315076 0.021638868

-1.558147 1.0816911 1.2308224 -0.763265

0 0 0 0

0.021638868 0.021582324 0.023347695 0.021685547

0.7632655 2.1834256 -1.009131 -1.951591

0 0 0 0

hf

km

0.020113325 0.018761232 0.020313403 0.021640649

-1.555582 1.0827393 1.2331083 -0.762285

0 0 0 0

0.021640649 0.021580672 0.023353753 0.021687379

0.7622851 2.1874435 -1.005213 -1.947793

0 0 0 0

hf

km

f

f

f

f

f

f

f

hf

km

-1.554865 1.0830325 1.2337478 -0.762023

0 0 0 0

0.021641125 0.7620229 0.021580198 2.1885973

0 0

1013.333333 1013.333333

0.01 0.01

0.018145839 0.018145839

-0.458456418 -0.936833608

0.00015 0.00015

A m2 0.032365473 0.073061664 0.032365473 0.032365473

V m/s -1.004716153 0.752540846 0.89059348 -0.479483014

e m 0.00015 0.00015 0.00015 0.00015

1353.333333 2033.333333 1353.333333 1353.333333

178753.1806 201161.2253 158449.1468 85306.79399

0.01 0.01 0.01 0.01

0.032365473 0.018145839 0.018145839 0.018145839

0.479483014 0.995821982 -0.458444676 -0.936821866

0.00015 0.00015 0.00015 0.00015

1353.333333 1013.333333 1013.333333 1013.333333

85306.79399 132659.896 61072.38457 124800.1084

0.01 0.01 0.01 0.01

D/e

61073.94873 124801.6726

Re

f

0.023355495 -1.00409 0.021687905 -1.946703

f

0 0

hf

km

0.020113721 0.018760975 0.020312916 0.021641146

-1.554834 1.0830451 1.2337754 -0.762011

0 0 0 0

0.021641146 0.021580178 0.023355569 0.021687928

0.7620115 2.1886468 -1.004041 -1.946657

0 0 0 0

hm

hf+hm

(hf+hm)/Q

0 0 0 0

-2.75556596 0.701386248 0.482535149 -1.457868669 -3.029513233 1.457868669 1.199848727 -2.399697454 -3.161763742 -2.9037438

62.98436481 16.03168566 27.42831373 66.64542489 173.0897891 66.64542489 90.93590351 181.871807 144.5377711 483.9909065

hm

hf+hm

(hf+hm)/Q

0 0 0 0

-1.790970104 0.991802856 1.038689316 -0.818825476 -0.579303407 0.818825476 1.77387368 -1.47188069 -2.379852417 -1.259033952

51.17244086 18.89102363 39.42812309 50.784551 160.2761386 50.784551 109.5373481 144.377717 126.0835048 430.7831209

hm

hf+hm

(hf+hm)/Q

0 0 0 0

-1.617307603 1.057886525 1.179183388 -0.786093178 -0.166330868 0.786093178 2.093308033 -1.099948326 -2.038678336 -0.259225452

48.72653131 19.47921413 41.8876884 49.82323411 159.916668 49.82323411 118.5636207 125.9484569 117.0720551 411.4073668

hm

hf+hm

(hf+hm)/Q

DQ

0 0 0 0

-1.56895382 1.077290407 1.221236501 -0.766997852

48.02214552 19.64835275 42.59464415 49.25292717

0.000117306

0 0 0 0

0 0 0 0

0 0 0 0

DQ

0.008751277

0.002999792

DQ

0.001807204

0.001461332

DQ

0.000520055

0.000315047

-0.037424764

159.5180696

0 0 0 0

0.766997852 2.165588153 -1.026658726 -1.968537633 -0.062610355

49.25292717 120.5071817 121.9559645 115.1270399 406.8431132

hm

hf+hm

(hf+hm)/Q

0 0 0 0

-1.558147075 1.081691138 1.230822434 -0.763265457 -0.00889896 0.763265457 2.183425644 -1.009130867 -1.951590578 -0.014030345

47.86322656 19.68649698 42.75406018 49.14060696 159.4443907 49.14060696 120.9817543 120.979649 114.6518618 405.7538721

hm

hf+hm

(hf+hm)/Q

0 0 0 0

-1.555581658 1.082739335 1.233108289 -0.762285076 -0.00201911 0.762285076 2.187443509 -1.005212625 -1.947792659 -0.003276699

47.82541902 19.6955708 42.79198152 49.11105736 159.4240287 49.11105736 121.0883804 120.7602126 114.5450861 405.5047364

hm

hf+hm

(hf+hm)/Q

0 0 0 0

-1.5549998 1.082977263 1.233627291 -0.762073487 -0.000468734 0.762073487 2.188382958 -1.004298046 -1.946905659 -0.00074726

47.81683956 19.69762983 42.80058656 49.10467733 159.4197333 49.10467733 121.1132972 120.7089295 114.5201336 405.4470377

hm

hf+hm

(hf+hm)/Q

0 0 0 0

-1.554864734 1.083032503 1.233747795 -0.762022852 -0.000107289 0.762022852 2.18859726

47.81484779 19.69810785 42.80258426 49.1031504 159.4186903 49.1031504 121.1189803

0 0 0 0

0 0 0 0

0 0 0 0

0 0

7.69466E-05

DQ

2.79062E-05

1.72892E-05

DQ

6.33251E-06

4.04027E-06

DQ

1.47012E-06

9.21526E-07

DQ

3.36501E-07

-

0 0

-1.0040895 -1.946703376 -0.000172764

120.6972324 114.5144423 405.4338055

hm

hf+hm

(hf+hm)/Q

0 0 0 0

-1.554833819 1.083045147 1.233775378 -0.762011459 -2.47536E-05 0.762011459 2.188646809 -1.004041287 -1.946656609 -3.96272E-05

47.81439189 19.69821726 42.80304151 49.10280682 159.4184575 49.10280682 121.1202943 120.694528 114.5131265 405.4307556

0 0 0 0

.

DQ

7.76371E-08

4.88704E-08

Primer ciclo

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