mecanica de fluidos punto 2 parcial.xlsx

HARDY-CROSS

Ley de continuidad de masa en los nodos : "La suma algebraíca de los caudales en un nuedo debe ser igual a cero

Ley de conservación de la energía en los circuitos : " La suma algebraica de las perdidas de energía en los tramos que conforman un anillo cerrado debe ser igual a cero"

ECUACIONES BÁSICAS

Continuidad:

La ecuación de Hazen & Williams originalmente expresa :

La ecuación de Darcy & Weisbach

El metodo de Hardy Cross corrige sucesivamente, iteración tras iteración , los caudales en los tramos con la siguiente ecuacion general

http://fluidos.eia.edu.co/hidraulica/articuloses/flujoentuberias/metodohardycross/elmetododehardycross.html

ECUACIONES UTILIZADAS

Numero tubería Nodos Longitud (pies) Longitud (m) Diametro (in)1 A-B 2000 609.6 162 B-C 800 243.84 123 B-D 600 182.88 104 D-E 800 243.84 85 C-E 1200 365.76 86 C-F 1300 396.24 67 E-F 900 274.32 8

Nodo Elevación (pie) Elevación (m)

A 180 54.864 0 0B 50 15.24 0 0C 30 9.144 400 0.030307D 80 24.384 1200 0.090922E 40 12.192 1400 0.106075F 60 18.288 1000 0.075768

Demanda externa (gpm)

Demanda externa (m3/s)

Diametro (m) Material de la tubería Acero comercial0.4064 0.450.30480.254

0.20320.20320.15240.2032

Rugosidad ε

PROCESO PREVIO AL CÁLCULO

CIRCUITO 1

Sección Longitud (pies) Longitud (m) Diametro (in) Diametro (m)B-D 600 182.88 10 0.254 187.409036D-E 800 243.84 8 0.2032 740.456935E-C 1200 365.76 8 0.2032 1110.6854C-B 800 243.84 12 0.3048 102.864297

CIRCUITO 2

Sección Longitud (pies) Longitud (m) Diametro (in) Diametro (m)E-F 900 274.32 8 0.2032 833.014052F-C 1300 396.24 6 0.1524 4881.70107C-E 1200 365.76 8 0.2032 1110.6854

Grafica

1. Señalar los nodos 2.Pre-establecer el sentido del flujo 3.Definir los circuitos 4. Definir el recorrido en el sentido de las manecillas del reloj 5. Construir una tabla para el cálculo iterativo.

a ij

a ij

Coeficiente de Hazen-Williams ACERO 130N 1.851

Nodos Caudal 0 (Gpm) Caudal 0 (m3/s)A-B 4000 0.25236B-C 1600 0.10094 QTB-D 2400 0.151416 Qs1D-E 1200 0.0757 Qs2C-E 600 0.03785 Qs3C-F 600 0.03785 Qs4E-F 400 0.02523

Q (m3/s) H(m) a*|Q|^N-1 a*Q*|Q|^N-1 Tramo compartida0.151416 5.69231 37.5938411751527 5.69230905538 -0.02091

0.0757 6.23313 82.3399119918415 6.23313133778 -0.02091-0.03785 -2.59174 68.4739105580805 -2.59173751462 -0.02091 -0.010493554500501-0.10094 -1.47498 14.6124329943715 -1.47497898645 -0.02091

7.85872 203.020096719446 7.85872389208 -0.08365

Q (m3/s) H(m) a*|Q|^N-1 a*Q*|Q|^N-1 Tramo compartida0.02523 0.91749 36.3650264385628 0.91748961704 0.0104935545

-0.03785 -11.39124 300.957554541363 -11.3912434394 0.01049355450.03785 2.59174 68.4739105580805 2.59173751462 0.0104935545 0.020912530216109

-7.88202 405.796491538006 -7.88201630772 0.03148

Iteración numero 15

Sección H(m) a*|Q|^N-1 a*Q*|Q|^N-1B-D 4.55247 33.923579895 4.55246754064008D-E 3.86593 66.104957179 3.86593250144288E-C -6.44418 104.08591598 -6.44417631311653C-B -1.97422 16.708275273 -1.97422083931132

0.00000 220.82272832 2.889655108751E-06

Caudal inicial = ∑ caudal salidas

DQ (m)

DQ (m)

Sección H(m) a*|Q|^N-1 a*Q*|Q|^N-1E-F 1.43066 44.605311196 1.4306627650434F-C -7.87484 253.97656397 -7.87484281489594C-E 6.44418 104.08591598 6.44417631311653

0.00000 402.66779114 -3.73673600418E-06

L/s m3/s75 0.0812 0.01221 0.02115 0.01522 0.22

1 2

Q (m3/s) H(m) a*|Q|^N-1 a*Q*|Q|^N-1 Tramo compartida Q (m3/s)0.13050347 4.32322 33.127212895 4.32321622702 0.00540 0.135900280.05478747 3.42609 62.534192151 3.42609016296 0.00540 0.06018428-0.06925608 -7.93010 114.50402877 -7.93010071705 0.00540 0.004732358021789 -0.05912691-0.12185253 -2.08999 17.151806458 -2.08999101472 0.00540 -0.11645572

-2.27079 227.31724028 -2.27078534178 0.02159

Q (m3/s) H(m) a*|Q|^N-1 a*Q*|Q|^N-1 Tramo compartida Q (m3/s)0.03572355 1.74651 48.889629624 1.74651134838 -0.00473236 0.0309912-0.02735645 -6.24552 228.30160218 -6.24552033751 -0.00473236 -0.03208880.06925608 7.93010 114.50402877 7.93010071705 -0.00473236 -0.005396811987233 0.05912691

3.43109 391.69526058 3.43109172791 -0.01420

15DQ (m)Tramo compartida Q (m3/s)0.00000 0.13419772660.00000 0.05848172660.00000 -5.0135E-09 -0.06191209930.00000 -0.11815827340.00000

Caudal inicial = ∑ caudal salidas

DQ (m)

DQ (m)

DQ (m)Tramo compartida Q (m3/s)5.01348E-09 0.0320738265.01348E-09 -0.0310061745.01348E-09 7.06962E-09 0.0619120993

0.00000

3

H(m) a*|Q|^N-1 a*Q*|Q|^N-1 Tramo compartida Q (m3/s) H(m)4.65995 34.289491974 4.65995162107 -0.00222 0.13368357 4.520234.07683 67.739175755 4.0768336406 -0.00222 0.05796757 3.80325-5.91787 100.08760206 -5.91787111025 -0.00222 -0.001508902447664 -0.06285253 -6.62653-1.92189 16.503175585 -1.9218891658 -0.00222 -0.11867243 -1.990150.89702 218.61944537 0.89702498562 -0.00887 -0.29320

H(m) a*|Q|^N-1 a*Q*|Q|^N-1 Tramo compartida Q (m3/s) H(m)1.34256 43.320769038 1.34256246485 0.0015089 0.0325001 1.46606-8.39134 261.50381628 -8.39134458075 0.0015089 -0.0305799 -7.675625.91787 100.08760206 5.91787111025 0.0015089 0.002216712310093 0.06285253 6.62653-1.13091 404.91218738 -1.13091100565 0.00453 0.41697

DQ (m)

DQ (m)

4

a*|Q|^N-1 a*Q*|Q|^N-1 Tramo compartidaQ (m3/s) H(m) a*|Q|^N-1 a*Q*|Q|^N-133.8129399 4.5202345 0.00071 0.13439829 4.56507 33.9667203 4.5650692965.6100423 3.80325468 0.00071 0.05868229 3.89051 66.2978337 3.89050902105.429885 -6.62653496 0.00071 0.00056101 -0.06157679 -6.37973 103.606018 -6.379726216.7701279 -1.99015184 0.00071 -0.11795771 -1.96802 16.6841374 -1.96802256221.622995 -0.29319761 0.00286 0.10783 220.554709 0.10782956

a*|Q|^N-1 a*Q*|Q|^N-1 Tramo compartidaQ (m3/s) H(m) a*|Q|^N-1 a*Q*|Q|^N-145.1093109 1.46605707 -0.00056101 0.03193909 1.41956 44.4458043 1.4195584251.002058 -7.67561811 -0.00056101 -0.03114091 -7.93830 254.915449 -7.93829989105.429885 6.62653496 -0.00056101 -0.00071473 0.06157679 6.37973 103.606018 6.3797262401.541254 0.41697391 -0.00168 -0.13902 402.967271 -0.13901529

DQ (m)

DQ (m)

5

Tramo compartidaQ (m3/s) H(m) a*|Q|^N-1 a*Q*|Q|^N-1 Tramo compartida-0.00026 0.13413417 4.54848 33.9099047 4.5484768 0.00009-0.00026 0.05841817 3.85816 66.043805 3.85815799 0.00009-0.00026 -0.00018637 -0.06202729 -6.46639 104.25072 -6.46639011 0.00009 6.80939E-05-0.00026 -0.11822183 -1.97619 16.7159244 -1.97618723 0.00009-0.00106 -0.03594 220.920354 -0.03594256 0.00035

Tramo compartidaQ (m3/s) H(m) a*|Q|^N-1 a*Q*|Q|^N-1 Tramo compartida0.00018637 0.03212546 1.43493 44.6664197 1.43492933 -6.8094E-050.00018637 -0.03095454 -7.85058 253.616552 -7.85058339 -6.8094E-050.00018637 0.00026413 0.06202729 6.46639 104.25072 6.46639011 -6.8094E-05 -8.7896E-05

0.00056 0.05074 402.533691 0.05073605 -0.00020

DQ (m) DQ (m)

DQ (m) DQ (m)

6 7

Q (m3/s) H(m) a*|Q|^N-1 a*Q*|Q|^N-1 Tramo compartidaQ (m3/s) H(m)0.13422206 4.55400 33.9288134 4.55399529 -0.00003 0.13418997 4.551980.05850606 3.86891 66.1283586 3.86890984 -0.00003 0.05847397 3.86498-0.06187131 -6.43632 104.027567 -6.43632135 -0.00003 -2.2744E-05 -0.06192614 -6.44688-0.11813394 -1.97347 16.7053476 -1.9734685 -0.00003 -0.11816603 -1.97446

0.01312 220.790086 0.01311528 -0.00013 -0.00438

Q (m3/s) H(m) a*|Q|^N-1 a*Q*|Q|^N-1 Tramo compartidaQ (m3/s) H(m)0.03205737 1.42930 44.5858377 1.42930458 2.27442E-05 0.03208011 1.43118-0.03102263 -7.88258 254.091252 -7.88257958 2.27442E-05 -0.03099989 -7.871890.06187131 6.43632 104.027567 6.43632135 2.27442E-05 3.20916E-05 0.06192614 6.44688

-0.01695 402.704657 -0.01695366 0.00007 0.00618

DQ (m)

DQ (m)

8

a*|Q|^N-1 a*Q*|Q|^N-1 Tramo compartidaQ (m3/s) H(m) a*|Q|^N-1 a*Q*|Q|^N-133.9219098 4.55198007 0.00001 0.13420069 4.55265 33.9242162 4.5526532866.0974893 3.86498263 0.00001 0.05848469 3.86629 66.1078025 3.86629444104.106022 -6.44688424 0.00001 8.2927E-06 -0.06190713 -6.44322 104.07882 -6.4432207216.7092095 -1.97446094 0.00001 -0.11815531 -1.97413 16.7079193 -1.97412936220.834631 -0.00438248 0.00004 0.00160 220.818758 0.00159764

a*|Q|^N-1 a*Q*|Q|^N-1 Tramo compartidaQ (m3/s) H(m) a*|Q|^N-1 a*Q*|Q|^N-144.6127559 1.43118218 -8.2927E-06 0.03207182 1.43050 44.6029417 1.43049746253.932714 -7.87188581 -8.2927E-06 -0.03100818 -7.87578 253.99052 -7.87578407104.106022 6.44688424 -8.2927E-06 -1.0721E-05 0.06190713 6.44322 104.07882 6.44322072402.651492 0.00618062 -0.00002 -0.00207 402.672281 -0.00206588

DQ (m)

DQ (m)

9

Tramo compartidaQ (m3/s) H(m) a*|Q|^N-1 a*Q*|Q|^N-1 Tramo compartida0.00000 0.13419678 4.55241 33.9233754 4.55240784 0.000000.00000 0.05848078 3.86582 66.1040426 3.86581616 0.000000.00000 -2.7717E-06 -0.06191381 -6.44451 104.088377 -6.44450777 0.00000 1.01033E-060.00000 -0.11815922 -1.97425 16.7083897 -1.97425024 0.00000-0.00002 -0.00053 220.824185 -0.00053401 0.00001

Tramo compartidaQ (m3/s) H(m) a*|Q|^N-1 a*Q*|Q|^N-1 Tramo compartida2.77171E-06 0.03207459 1.43073 44.606222 1.4307263 -1.0103E-062.77171E-06 -0.03100541 -7.87448 253.9712 -7.87448104 -1.0103E-062.77171E-06 3.90874E-06 0.06191381 6.44451 104.088377 6.44450777 -1.0103E-06 -1.3065E-06

0.00001 0.00075 402.665799 0.00075304 0.00000

DQ (m) DQ (m)

DQ (m) DQ (m)

10 11

Q (m3/s) H(m) a*|Q|^N-1 a*Q*|Q|^N-1 Tramo compartidaQ (m3/s) H(m)0.13419809 4.55249 33.9236564 4.55248987 0.00000 0.13419761 4.552460.05848209 3.86598 66.1052993 3.86597602 0.00000 0.05848161 3.86592-0.06191149 -6.44406 104.085063 -6.4440614 0.00000 -3.3772E-07 -0.0619123 -6.44422-0.11815791 -1.97421 16.7082325 -1.97420984 0.00000 -0.11815839 -1.97422

0.00019 220.822251 0.00019465 0.00000 -0.00007


-0.00025 402.668331 -0.00025171 0.00000 0.00009

DQ (m)

DQ (m)

12

a*|Q|^N-1 a*Q*|Q|^N-1 Tramo compartidaQ (m3/s) H(m) a*|Q|^N-1 a*Q*|Q|^N-133.923554 4.55245997 0.00000 0.13419777 4.55247 33.9235882 4.55246997

66.1048412 3.86591775 0.00000 0.05848177 3.86594 66.1049943 3.86593723104.086227 -6.44421822 0.00000 1.23099E-07 -0.06191202 -6.44416 104.085823 -6.4441638316.7082898 -1.97422457 0.00000 -0.11815823 -1.97422 16.7082706 -1.97421964220.822912 -6.5065E-05 0.00000 0.00002 220.822676 2.37166E-05

a*|Q|^N-1 a*Q*|Q|^N-1 Tramo compartidaQ (m3/s) H(m) a*|Q|^N-1 a*Q*|Q|^N-144.6054259 1.43067077 -1.231E-07 0.03207379 1.43066 44.6052802 1.43066061253.975888 -7.87479724 -1.231E-07 -0.03100621 -7.87486 253.976746 -7.87485511104.086227 6.44421822 -1.231E-07 -1.5918E-07 0.06191202 6.44416 104.085823 6.44416383402.667541 9.17503E-05 0.00000 -0.00003 402.66785 -3.0669E-05

DQ (m)

DQ (m)

13

Tramo compartidaQ (m3/s) H(m) a*|Q|^N-1 a*Q*|Q|^N-1 Tramo compartida0.00000 0.13419771 4.55247 33.9235757 4.55246632 0.000000.00000 0.05848171 3.86593 66.1049385 3.86593013 0.000000.00000 -4.1148E-08 -0.06191212 -6.44418 104.085965 -6.44418294 0.00000 1.49985E-080.00000 -0.11815829 -1.97422 16.7082776 -1.97422144 0.000000.00000 -0.00001 220.822757 -7.9276E-06 0.00000

Tramo compartidaQ (m3/s) H(m) a*|Q|^N-1 a*Q*|Q|^N-1 Tramo compartida4.11477E-08 0.03207384 1.43066 44.6053289 1.430664 -1.4998E-084.11477E-08 -0.03100616 -7.87484 253.976459 -7.87483576 -1.4998E-084.11477E-08 5.80233E-08 0.06191212 6.44418 104.085965 6.44418294 -1.4998E-08 -1.9395E-08

0.00000 0.00001 402.667754 1.11789E-05 0.00000

DQ (m) DQ (m)

DQ (m) DQ (m)

14 15

Q (m3/s) H(m) a*|Q|^N-1 a*Q*|Q|^N-1 Tramo compartidaQ (m3/s) H(m)0.13419773 4.55247 33.9235799 4.55246754 0.00000 0.13419773 4.552470.05848173 3.86593 66.1049572 3.8659325 0.00000 0.05848173 3.86593-0.06191209 -6.44418 104.085916 -6.44417631 0.00000 -5.0135E-09 -0.0619121 -6.44418-0.11815827 -1.97422 16.7082753 -1.97422084 0.00000 -0.11815827 -1.97422

0.00000 220.822728 2.88966E-06 0.00000 0.00000


0.00000 402.667791 -3.7367E-06 0.00000 0.00000

DQ (m)

DQ (m)

16

a*|Q|^N-1 a*Q*|Q|^N-1 Tramo compartidaQ (m3/s)33.9235784 4.5524671 0.00000 0.1341977366.1049504 3.86593164 0.00000 0.05848173104.085933 -6.44417864 0.00000 1.82743E-09 -0.061912116.7082761 -1.97422106 0.00000 -0.11815827220.822738 -9.6591E-07 0.00000

a*|Q|^N-1 a*Q*|Q|^N-1 Tramo compartidaQ (m3/s)44.6053171 1.43066318 -1.8274E-09 0.03207382253.976529 -7.87484046 -1.8274E-09 -0.03100618104.085933 6.44417864 -1.8274E-09 -2.3631E-09 0.0619121402.667779 1.36205E-06 0.00000

DQ (m)

DQ (m)

mecanica de fluidos punto 2 parcial.xlsx

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