METODO DE LINEALIZACIÓN DE ECUACIONES DE FLUJO

60 l/s200 l/s 100 l/s 100 l/s 40 l/s

1 Tubo 1 2 Tubo 2 3

CIRCUITO I CIRCUITO II100 l/s Tubo 6 100 l/s Tubo 3 100 l/s

Tubo 7

6 Tubo 5 5 Tubo 4 440 l/s 100 l/s 100 l/s 30 l/s

30 l/s

FORMACIÓN DE ECUACIONES ITERACIÓN 1

Nodo Ecuación de la continuidad en el nodoTubo D(m) L(m) IQI(m3/s)

1 -Q1-Q6 = -0.2 1 0.254 500 0.12 Q1-Q2-Q7 = 0.06 2 0.152 400 0.13 Q2-Q3 = 0.04 3 0.102 200 0.14 Q4+Q3 = 0.03 4 0.212 400 0.15 Q7+Q5-Q4=0.03 5 0.203 600 0.16 -Q5+Q6 = 0.012 (Redundante) 6 0.254 300 0.1

7 0.102 200 0.1Circuito Ecuación de conservación de energíaI KQ1+KQ7-KQ5-KQ6 = 0II KQ2+KQ3-KQ4-KQ7 = 0 Q1 Q2 Q3 Q4

-1 0 0 01 -1 0 0

FORMULA : 0 1 -1 0

A= 0 0 1 10 0 0 -1

53.4245 0 0 00 490.835 1737.16 -99.0551

Q1 Q2 Q3 Q40.02614 0.98164 0.8069 0.188460.01117 -0.00785 0.79669 0.104930.01117 -0.00785 -0.20331 0.10493

-0.01117 0.00785 0.20331 0.89507-0.02614 0.01836 0.1931 0.811541.02614 0.98164 0.8069 0.188460.01497 -0.01051 0.01021 0.08353

A-1=

ITERACIÓN 1 ITERACIÓN 2

Re f k' (s2/m5) k(s/m2) Tubo

439715.27308 0.01367 534.245304 53.4245 1829651.45864 0.01221 4908.34551 490.835 2

1244477.188 0.01138 17371.5604 1737.16 3595286.63982 0.01296 990.551179 99.0551 4622238.59398 0.01285 1839.27883 183.928 5497790.87519 0.01339 313.86807 31.3868 6

1244477.188 0.01138 17371.5604 1737.16 7

Q5 Q6 Q7 Q10 1 0 Q1= -0.20 l/s -10 0 -1 Q2= 0.06 l/s 10 0 0 Q3= 0.04 l/s 0

0 0 0 Q4= 0.03 l/s =B A= 01 0 1 Q5= 0.03 l/s 0

-183.9278829 -31.3868 1737.15604 Q6= 0.00 l/s 52.58130 0 -1737.15604 Q7= 0.00 l/s 0

Q5 Q6 Q7 Q10.1531951726 0.00083 0.00035601 Q1= -0.20 l/s 0.041770.0654799972 0.00036 0.00039822 Q2= 0.06 l/s 0.016980.0654799972 0.00036 0.00039822 Q3= 0.04 l/s 0.01698

-0.065479997 -0.00036 -0.00039822 Q4= 0.03 l/s =B -0.016980.8468048274 -0.00083 -0.00035601 Q5= 0.03 l/s -0.041770.1531951726 0.00083 0.00035601 Q6= 0.00 l/s 1.041770.0877151753 0.00048 -4.221E-05 Q7= 0.00 l/s 0.02479

Q1= 0.09619597Q2= 0.03427442Q3= -0.00572558

Q4= 0.03572558Q5= 0.06380403Q6= -0.10380403Q7= 0.00192155

Q1= 0.09809799Q2= 0.06713721

A-1=

A-1xB=

Q3= 0.05286279CAUDALES PROMEDIOS= Q4= 0.06786279

Q5= 0.08190201Q6= 0.10190201Q7= 0.05096078

ITERACIÓN 2

D(m) L(m) IQI(m3/s) Re f k(s/m2)

0.254 500 0.09809799 431351.827 0.01372 536.008 52.58130.152 400 0.06713721 557004.835 0.01305 5244.74 352.1170.102 200 0.05286279 657865.373 0.01263 19283.5 1019.380.212 400 0.06786279 403978.127 0.01384 1058.26 71.81670.203 600 0.08190201 509625.941 0.01329 1901.92 155.7710.254 300 0.10190201 507258.928 0.01334 312.876 31.88270.102 200 0.05096078 634195.241 0.01271 19404.5 988.866

Q2 Q3 Q4 Q5 Q6 Q70 0 0 0 1 0 Q1= -0.20 l/s

-1 0 0 0 0 -1 Q2= 0.06 l/s1 -1 0 0 0 0 Q3= 0.04 l/s

0 1 1 0 0 0 Q4= 0.03 l/s =B A=0 0 -1 1 0 1 Q5= 0.03 l/s0 0 0 -155.771382 -31.8827 988.866 Q6= 0.00 l/s

352.117 1019.38 -71.816717 0 0 -988.866 Q7= 0.00 l/s

Q2 Q3 Q4 Q5 Q6 Q70.97288 0.78532 0.24233407 0.20407979 0.00131 0.00053 Q1= -0.20 l/s

-0.01103 0.76794 0.12805504 0.08297402 0.00053 0.00063 Q2= 0.06 l/s-0.01103 -0.23206 0.12805504 0.08297402 0.00053 0.00063 Q3= 0.04 l/s

0.01103 0.23206 0.87194496 -0.08297402 -0.00053 -0.00063 Q4= 0.03 l/s =B0.02712 0.21468 0.75766593 0.79592021 -0.00131 -0.00053 Q5= 0.03 l/s0.97288 0.78532 0.24233407 0.20407979 0.00131 0.00053 Q6= 0.00 l/s

-0.01609 0.01738 0.11427903 0.12110577 0.00078 -9.5E-05 Q7= 0.00 l/s

Q1= 0.09482415Q2= 0.03299048Q3= -0.00700952

Q4= 0.03700952Q5= 0.06517585Q6= -0.10517585Q7= 0.00183368

Q1= 0.09646107Q2= 0.05006384

k' (s2/m5)

A-1=

A-1xB=

Q3= 0.02993616CAUDALES PROMEDIOS= Q4= 0.05243616

Q5= 0.07353893Q6= 0.10353893Q7= 0.02639723

ITERACIÓN 3

Tubo D(m) L(m) IQI(m3/s) Re f k(s/m2)

1 0.254 500 0.09646107 424154.057 0.01376 537.561 51.85372 0.152 400 0.05006384 415355.401 0.01373 5519.41 276.3233 0.102 200 0.02993616 372548.648 0.01396 21311.9 637.9964 0.212 400 0.05243616 312145.439 0.01449 1107.98 58.09815 0.203 600 0.07353893 457587.605 0.01354 1937.36 142.4716 0.254 300 0.10353893 515407.346 0.01331 312.042 32.30857 0.102 200 0.02639723 328507.471 0.01429 21807.1 575.648

Q1 Q2 Q3 Q4 Q5 Q6 Q7-1 0 0 0 0 1 0 Q1= -0.20 l/s1 -1 0 0 0 0 -1 Q2= 0.06 l/s0 1 -1 0 0 0 0 Q3= 0.04 l/s

0 0 1 1 0 0 0 Q4= 0.03 l/s =B0 0 0 -1 1 0 1 Q5= 0.03 l/s

51.8537 0 0 0 -142.471188 -32.3085 575.648 Q6= 0.00 l/s0 276.323 637.996 -58.098087 0 0 -575.648 Q7= 0.00 l/s

Q1 Q2 Q3 Q4 Q5 Q6 Q70.0617 0.96267 0.76644 0.31335374 0.27209441 0.00191 0.00071 Q1= -0.20 l/s

0.02294 -0.01388 0.73465 0.15405008 0.10117829 0.00071 0.00091 Q2= 0.06 l/s0.02294 -0.01388 -0.26535 0.15405008 0.10117829 0.00071 0.00091 Q3= 0.04 l/s

-0.02294 0.01388 0.26535 0.84594992 -0.10117829 -0.00071 -0.00091 Q4= 0.03 l/s =B-0.0617 0.03733 0.23356 0.68664626 0.72790559 -0.00191 -0.00071 Q5= 0.03 l/s1.0617 0.96267 0.76644 0.31335374 0.27209441 0.00191 0.00071 Q6= 0.00 l/s

0.03876 -0.02345 0.03178 0.15930366 0.17091612 0.0012 -0.0002 Q7= 0.00 l/s

Q1= 0.09364Q2= 0.03162Q3= -0.00838

Q4= 0.03838Q5= 0.06636Q6= -0.10636Q7= 0.00202

Q1= 0.09505Q2= 0.04084

k' (s2/m5)

A-1xB=

Q3= 0.01916CAUDALES PROMEDIOS= Q4= 0.04541

Q5= 0.06995Q6= 0.10495Q7= 0.01421

ITERACIÓN 4

Tubo D(m) L(m) IQI(m3/s) Re f k(s/m2)

1 0.254 500 0.0950508 417952.956 0.01379 538.927 51.22552 0.152 400 0.0408426 338851.006 0.01424 5724.46 233.8023 0.102 200 0.0191574 238409.804 0.01517 23153.4 443.564 0.212 400 0.0454074 270304.344 0.01488 1137.46 51.64935 0.203 600 0.0699492 435250.818 0.01366 1954.22 136.6966 0.254 300 0.1049492 522427.461 0.01328 311.338 32.67467 0.102 200 0.0142082 176818.341 0.01607 24527.1 348.487

Q1 Q2 Q3 Q4 Q5 Q6 Q7-1 0 0 0 0 1 0 Q1= -0.20 l/s1 -1 0 0 0 0 -1 Q2= 0.06 l/s0 1 -1 0 0 0 0 Q3= 0.04 l/s

A= 0 0 1 1 0 0 0 Q4= 0.03 l/s =B0 0 0 -1 1 0 1 Q5= 0.03 l/s

51.2255 0 0 0 -136.696316 -32.6746 348.487 Q6= 0.00 l/s0 233.802 443.56 -51.649286 0 0 -348.487 Q7= 0.00 l/s

Q1 Q2 Q3 Q4 Q5 Q6 Q70.08356 0.95256 0.75918 0.3923039 0.34958409 0.00256 0.00083 Q1= -0.20 l/s0.02703 -0.01534 0.70513 0.1748144 0.11306336 0.00083 0.0012 Q2= 0.06 l/s0.02703 -0.01534 -0.29487 0.1748144 0.11306336 0.00083 0.0012 Q3= 0.04 l/s

-0.02703 0.01534 0.29487 0.8251856 -0.11306336 -0.00083 -0.0012 Q4= 0.03 l/s =B-0.08356 0.04744 0.24082 0.6076961 0.65041591 -0.00256 -0.00083 Q5= 0.03 l/s1.08356 0.95256 0.75918 0.3923039 0.34958409 0.00256 0.00083 Q6= 0.00 l/s0.05654 -0.0321 0.05405 0.2174895 0.23652073 0.00173 -0.00037 Q7= 0.00 l/s

Q1= 0.09307Q2= 0.03052Q3= -0.00948

Q4= 0.03948Q5= 0.06693Q6= -0.10693Q7= 0.00255

Q1= 0.09406Q2= 0.03568

k' (s2/m5)

A-1=

A-1xB=

Q3= 0.01432CAUDALES PROMEDIOS= Q4= 0.04245

Q5= 0.06844Q6= 0.10594Q7= 0.00838

ITERACIÓN 5

Tubo D(m) L(m) Re f k(s/m2)

1 0.254 500 0.09406 413586.993 0.01382 539.905 50.78232 0.152 400 0.03568 296012.34 0.01459 5867.58 209.353 0.102 200 0.01432 178220.084 0.01645 25109.8 359.5954 0.212 400 0.04245 252674.652 0.01604 1226.51 52.06015 0.203 600 0.06844 425873.103 0.01371 1961.64 134.2596 0.254 300 0.10594 527370.061 0.01326 310.849 32.9327 0.102 200 0.00838 104272.12 0.01787 27274.1 228.524

Q1 Q2 Q3 Q4 Q5 Q6 Q7-1 0 0 0 0 1 0 Q1= -0.20 l/s1 -1 0 0 0 0 -1 Q2= 0.06 l/s0 1 -1 0 0 0 0 Q3= 0.04 l/s

A= 0 0 1 1 0 0 0 Q4= 0.03 l/s0 0 0 -1 1 0 1 Q5= 0.03 l/s

50.7823 0 0 0 -134.259066 -32.932 228.524 Q6= 0.00 l/s0 209.35 359.595 -52.0601 0 0 -228.524 Q7= 0.00 l/s

Q1 Q2 Q3 Q4 Q5 Q6 Q70.10318 0.94407 0.76762 0.46454 0.42066363 0.00313 0.00084 Q1= -0.20 l/s0.02776 -0.01504 0.69106 0.18624 0.11315878 0.00084 0.0014 Q2= 0.06 l/s0.02776 -0.01504 -0.30894 0.18624 0.11315878 0.00084 0.0014 Q3= 0.04 l/s

-0.02776 0.01504 0.30894 0.81376 -0.11315878 -0.00084 -0.0014 Q4= 0.03 l/s-0.10318 0.05593 0.23238 0.53546 0.57933637 -0.00313 -0.00084 Q5= 0.03 l/s1.10318 0.94407 0.76762 0.46454 0.42066363 0.00313 0.00084 Q6= 0.00 l/s0.07543 -0.04088 0.07656 0.2783 0.30750484 0.00229 -0.00056 Q7= 0.00 l/s

Q1= 0.09327Q2= 0.03017Q3= -0.00983

Q4= 0.03983Q5= 0.06673Q6= -0.10673Q7= 0.0031

Q1= 0.09366Q2= 0.03292

IQI(m3/s)

k' (s2/m5)

A-1=

A-1xB=

Q3= 0.01208CAUDALES PROMEDIOS= Q4= 0.04114

Q5= 0.06759Q6= 0.10634Q7= 0.00574

=B

=B

60 l/s200 l/s 93.66 l/s 32.92 l/s

1 Tubo 1 2 Tubo 2

CIRCUITO I CIRCUITO II106.34 l/s Tubo 6 5.74 l/s

Tubo 7

6 Tubo 5 5 Tubo 440 l/s 67.59 l/s 41.14 l/s

30 l/s

40 l/s3

Tubo 3 12.08 l/s

430 l/s