Caracterización de flujo no permanente en un sistema acoplado (Reservorio, canal, disipador, tubería de presión) con el método de las características programado en Matlab.

1. Ingeniería Mecánica de Fluidos – UNMSM
Flujo no Permanente

2. Flujo no Permanente - Juan Felipe Quiñonez 2
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Flujo no Permanente

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5. Flujo no Permanente - Juan Felipe Quiñonez 5
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






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




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

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
1S
2S
1D
0
1
2
3 4
Hr
Dc
pD
b
ph

14. Flujo no Permanente - Juan Felipe Quiñonez 14
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2D
1f
2f
1C
2C
Hr
0
1
2
3
4
ph
pD
ft
2
( ) 0
H H C V
V VSen
t s g s

  
   
  
0
2
V VV V H
V g f
t s s D
  
   
  

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 1 1 02H S Sen    
1H 
      2 2 1 2 3H S Sen sen Sen      
2H 
 2 4fH S Sen   
fH 
0 1 2H Hr H H  
0H 
0n fH H H 
nH 
4
1 2 2
1 2
1 1 2
fL
L D L
h f f
D D D
 
  
 
fLh 
2
1
t
fL
g H
V
h



tV 
2
2
1
c t
D
V V
D
 
  
 
CV 

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2
1 1
0
12
c
n
n f S V
H H
gD
  
 
2
1 1
1 0
1
1
2
cf S V
H H
gD
  
 
2
1 1
2 0
1
2
2
cf S V
H H
gD
  
 
2
1 1
3 0
1
3
2
cf S V
H H
gD
  
 
2
1 1
4 0
1
4
2
cf S V
H H
gD
  
 
4 4E DH H
4 4 4E D SV V V 
2
2 2
4 4
22
c
n S
n f S V
H H
gD

  
 
4 4S DH H

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2
2 2
5 4
2
1
2
c
S
f S V
H H
gD
  
 
2
2 2
6 4
2
2
2
c
S
f S V
H H
gD
  
 
2
2 2
7 4
2
3
2
c
S
f S V
H H
gD
  
 
2
2 2
8 4
2
4
2
c
S
f S V
H H
gD
  
 
2
2 2
9 4
2
5
2
c
S
f S V
H H
gD
  
 
T
1
1
1
S
t Cr
C

  2
2
2
S
t Cr
C

 
min
S
t Cr
C

 
 0 1 25G t Sen   
 1 2 0G t Sen   
 2 3 65G t Sen   
 3 4 15G t Sen   
 4 5 40G t Sen   

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 5 6 8G t Sen   
 6 7 0G t Sen   
1
1
C
Z
g

2
2
C
Z
g

1 1
1
12
C t f
R
gD
 

2 2
2
22
C t f
R
gD
 

2
1
1
4
D
A


2
2
2
4
D
A


1 2
1 2
1 2
m
L L
C
L L
C C



2
m
L
TR
C


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Tc TR
10Tc TR
2
4
c
D
D
A


 
 4 22
c p p
D
p
D D Z D
A
h b
  
  
  
Dc
pD
b
ph

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 Tc TR
R R R R R p p RH ZV GV RV V H ZV C 
       
S S S S S p p SH ZV GV RV V H ZV C 
       
0pH H
 S C C D
C T
V V V V
S

  

 S C C D
C T
H H H H
S

  

S S S S S SH ZV GV RV V C 
    
0 S
p
H C
V
Z


pV 
 R C C I
C T
V V V V
S

  

 R C C I
C T
H H H H
S

  

 S C C D
C T
V V V V
S

  


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 S C C D
C T
H H H H
S

  

R R R R R RH ZV GV RV V C 
    
S S S S S SH ZV GV RV V C 
    
 
1
2
p S RH C C  
 
1
2
p S RV C C
Z
 
 
1
2
p S RH C C  
 
1
2
p S RV C C
Z
 
   1 2
2 2
1 2
1 2
1 2
2
2
R S
C C
p
C C
A AAD
Z Q C H C H
t Z Z
Z
A A AD
Z Z t
      


 

 2
p p
AD
Q Z Z Q
t
  

1 2 2p p pH H Z H   

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2
1
1
R p
p
C
C Z H
V
Z
  
 
2
2
2
S p
p
C
C Z H
V
Z
  
 
2Z H H 
1
1
C
g
Z
C

2
2
C
g
Z
C

4 4 4E D SH H H 
4DV 
 R C C I
C T
V V V V
S

  

 R C C I
C T
H H H H
S

  

 S C C D
C T
V V V V
S

  

 S C C D
C T
H H H H
S

  


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R R R R R RH ZV GV RV V C 
    
S S S S S SH ZV GV RV V C 
    
 
1
2
p S RH C C  
 
1
2
p S RV C C
Z
 
 
1
2
p S RH C C  
 
1
2
p S RV C C
Z
 
2p C p RH Z V C 
  
2( )p R C pH C Z V
  
R R R R R RC H ZV GV RV V
    
 R C C I
C T
V V V V
S

  


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 R C C I
C T
H H H H
S

  

2
4
2
k k k
p
B B C
V
  

2( )p R C pH C Z V
  
kB k Z 
 
2
2
neta
nV
k
H

( )k R fC k C H 
 1 1
Bn
f
C
t
n n
t
 
   
 
 10Tc TR

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26. Para
Tc=TR
t=20mi
n
Canal de Aduccion Disipador y cambio de diametro Tuberia de presion
t H,V 0 100 200 300 400 A 400 D 400 S 460 520 580 640 700
0
H 176.940233 169.988075 163.035916 156.083757 149.131599 149.131599 149.131599 128.014417 106.897235 85.7800531 64.6628712 43.5456892
V 11.679099 11.679099 11.679099 11.679099 11.679099 0 26.2779727 26.2779727 26.2779727 26.2779727 26.2779727 26.2779727
0.066
H 176.940233 169.659021 162.871389 156.083757 149.12374 149.12374 149.12374 127.447261 106.560904 85.3389208 64.7847774 196.595021
V 11.6820335 11.679099 11.6776317 11.679099 11.6791691 -0.23577516 26.2951933 26.2668484 26.2865809 26.2705068 26.2793015 24.609735
0.13
H 176.940233 169.690502 162.706868 155.957833 149.108034 149.108034 149.108034 127.662857 105.891949 85.5595996 215.97898 241.462811
V 11.6849622 11.6801704 11.6761675 11.6780784 11.679309 -0.23533273 26.2902674 26.2813202 26.276759 26.2728888 24.6191404 24.1233103
0.2
H 176.940233 169.817753 162.713704 155.792732 149.092287 149.092287 149.092287 127.541243 106.655025 235.234214 260.581173 297.937362
V 11.6863112 11.6815242 11.6763132 11.6768399 11.6778829 -0.23692923 26.3019735 26.2776383 26.2850125 24.6244987 24.1377224 23.5237601
0.26
H 176.940233 169.903253 162.807386 155.809558 149.076474 149.076474 149.076474 128.070225 255.632245 280.010894 316.382243 368.211754
V 11.6868213 11.6824038 11.6773497 11.6761203 11.6756283 -0.23732416 26.2995069 26.283194 24.6562171 24.1528554 23.5403535 22.7703392
0.33
H 176.940233 169.938911 162.935112 155.976853 149.060638 149.060638 149.060638 275.872475 299.828859 335.952229 386.649618 455.067124
V 11.6870373 11.6828929 11.6779065 11.6758447 11.6747218 -0.23761803 26.2990305 24.6695554 24.1856994 23.5665696 22.7984825 21.8439722
0.4
H 176.940233 169.981336 163.074775 156.122189 149.055231 149.055231 149.055231 319.169338 355.402408 405.464002 473.441144 561.121046
V 11.6872172 11.6828858 11.677701 11.676114 11.6753861 0.07556341 23.1006321 24.1969792 23.6044565 22.8279967 21.885196 20.723487
0.46
H 176.940233 170.059582 163.16959 156.174689 149.063338 149.063338 149.063338 228.983177 423.849321 491.686861 578.534122 688.002785
V 11.6869822 11.6824179 11.6774055 11.6768266 11.6766231 0.16762151 22.1635949 22.0363241 22.8653536 21.9222071 20.7701352 19.3868202
0.53
H 176.940233 170.11769 163.194664 156.163908 149.078256 149.078256 149.078256 254.276434 365.213442 595.511144 704.647232 835.689676
V 11.6860678 11.681791 11.6775006 11.6776412 11.6776985 0.27996817 21.0180067 20.8384339 20.3936921 20.8092847 19.4429617 17.8233402

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0.6
H 176.940233 170.101209 163.159905 156.135705 149.101667 149.101667 149.101667 284.929794 425.946262 577.61595 850.903044 1003.6813
V 11.6849895 11.6812452 11.6778194 11.6783158 11.678332 0.42252114 19.5610061 19.3761306 18.8264052 17.9303448 17.8832754 16.0574808
0.66
H 176.940233 170.027089 163.084469 156.111187 149.135604 149.135604 149.135604 320.361544 496.551575 680.837684 875.669691 1186.9966
V 11.6844146 11.6809382 11.6779889 11.6786505 11.678559 0.59597081 17.7835899 17.5538465 16.9479525 15.9211505 14.5762066 14.1132518
0.73
H 176.940233 169.949303 163.002012 156.087088 149.182401 149.182401 149.182401 360.340772 574.468541 793.467574 1016.09187 1183.04672
V 11.6845238 11.6809563 11.6778817 11.6785257 11.6783656 0.80868769 15.596842 15.3643229 14.6846692 13.6079075 12.1839957 11.1549751
0.8
H 176.940233 169.907154 162.948495 156.071101 149.244668 149.244668 149.244668 402.901412 656.53658 908.70452 1099.91134 1299.96664
V 11.6850746 11.6812314 11.677639 11.6779606 11.677622 1.06072906 12.9948066 12.7399458 12.0599908 10.9627581 10.2073217 9.04027744
0.86
H 176.940233 169.908658 162.947179 156.090478 149.325143 149.325143 149.325143 445.125424 736.556259 962.366938 1191.98562 1389.64376
V 11.6856963 11.6815912 11.6773837 11.6770737 11.67634 1.35598635 9.93025273 9.70485986 9.05140199 8.67232562 7.83604209 7.0145084
0.93
H 176.940233 169.944343 163.005342 156.166556 149.426484 149.426484 149.426484 482.777972 750.717909 1019.54998 1251.6946 1436.10584
V 11.6861128 11.6818239 11.6770659 11.6760123 11.6747697 1.68833136 6.45673811 6.25620702 6.34433224 5.93523328 5.49446142 5.15466391
1
H 176.940233 170.00514 163.114625 156.296422 149.550971 149.550971 149.550971 455.066102 765.754513 1039.92686 1263.52902 1429.93148
V 11.686159 11.6817312 11.6765482 11.6749033 11.6732103 2.05266254 2.61510624 3.10711748 3.15989264 3.1755744 3.26471972 3.5416164
1.06
H 176.940233 170.084433 163.255134 156.459267 149.696266 149.696266 149.696266 432.658905 744.321599 1009.79092 1218.19058 1358.53443
V 11.6857062 11.6811777 11.6757482 11.6738045 11.6718404 2.3156807
-
0.22258549
-
0.47477209
-
0.04840112
0.49509153 1.2294596 2.22560789
1.13
H 176.940233 170.171275 163.403643 156.630736 149.860435 149.860435 149.860435 439.025853 676.728247 922.668515 1104.85548 1217.49504
V 11.6846649 11.6801159 11.6746623 11.6727087 11.6706248 2.62183937
-
3.55751296
-
3.37611488
-
3.13514208
-
1.99235912
-0.5411438 1.23653718
1.2
H 176.940233 170.25074 163.539365 156.796397 150.043554 150.043554 150.043554 394.043178 617.499299 772.011596 922.0421 1002.96692
V 11.6830486 11.6785755 11.6733134 11.6715302 11.6693846 2.88765507 -6.524446
-
6.21254331
-
5.31831102
-4.1689898
-
1.98440952
0.56953911
1.26
H 176.940233 170.310829 163.65069 156.95305 150.24211 150.24211 150.24211 328.813766 489.64652 617.316455 670.376923 722.678087
V 11.68098 11.6766454 11.6716856 11.6701214 11.6679471 3.08847694 -8.8612012
-
8.45455494
-
7.24292294
-
5.30440573
-3.0558 0.18997084
1.3
H 176.940233 170.34974 163.738606 157.100685 150.451243 150.451243 150.451243 246.315065 329.2663 388.742233 418.367818 387.491874
V 11.6786348 11.6744259 11.6697247 11.6683483 11.6661734 3.20798999 -10.380448
-
9.87638694
-
8.43725116
-
6.12219645
-
3.12702313
0.03075967
1.4 H 176.940233 170.376738 163.812274 157.241336 150.665049 150.665049 150.665049 151.521229 146.28242 131.333864 106.416081 131.763365

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V 11.6761443 11.6719845 11.667398 11.666124 11.66397 3.23068719
-
10.8929622
-
10.3493565
-
8.75537427
-
6.25211756
-
3.03296678
0.00022483
1.46
H 176.940233 170.404334 163.88457 157.379221 150.876995 150.876995 150.876995 51.3149884 -45.434459
-
134.941518
-
154.687396
-
171.577067
V 11.6735317 11.6693451 11.6647136 11.6634291 11.6613066 3.15282637
-
10.3274915
-
9.76332042
-
8.16878293
-
5.66039159
-
3.12208846
0.00022483
1.53
H 176.940233 170.441208 163.966827 157.519353 151.080429 151.080429 151.080429
-
45.4500202
-
229.016339
-
330.528853
-
412.456946
-440.84007
V 11.6707388 11.6664833 11.6617024 11.6603138 11.6582326 2.97442445
-
8.65053294
-8.1451732
-
6.67777105
-
5.03519546
-
2.62536585
0.00022483
1.6
H 176.940233 170.490193 164.064043 157.664035 151.269166 151.269166 151.269166
-
128.795524
-
329.984583
-
505.919435
-
616.302739
-
653.126045
V 11.6676756 11.6633454 11.6583937 11.6568794 11.6548696 2.70953481
-
5.98418373
-
5.56924404
-
5.02316375
-
3.64154395
-
1.91231826
0.00022483
1.66
H 176.940233 170.549003 164.173124 157.809688 151.438091 151.438091 151.438091
-
133.141999
-
405.482619
-
615.414343
-
746.390482
-
791.653574
V 11.6642608 11.659879 11.6548146 11.6532441 11.6513692 2.37660732
-
2.50802663
-
2.86822413
-
2.54406332
-
1.90122236
-
1.01635754
0.00022483

29. Flujo no Permanente - Juan Felipe Quiñonez 29
29
2015
1198.8
H 176.940233 176.882 176.823808 176.765676 176.707642 176.707642 176.707642 179.174542 180.254744 178.617655 177.066083 175.101056
V 1.0737665 1.07339536 1.07301901 1.07300737 1.07299459 0.01611303
-
0.36275951
-
0.36064595
-
0.32274428
-
0.24790917
-
0.14333794
0.00022483
1198.86667
H 176.940233 176.882484 176.824651 176.766715 176.708752 176.708752 176.708752 176.654227 173.727936 170.438293 165.476852 163.895815
V 1.07376078 1.07339004 1.0730144 1.07300304 1.07298983 0.01717119
-
0.38771722
-0.3618945
-
0.30130242
-0.2155595 -0.104679 0.00022483
1198.93333
H 176.940233 176.882876 176.825393 176.767714 176.709859 176.709859 176.709859 171.264386 166.836434 160.590162 157.268401 155.852982
V 1.07375219 1.07338207 1.07300781 1.07299757 1.07298494 0.01605708
-
0.36148278
-
0.32806818
-
0.25490497
-
0.15792968
-
0.07201398
0.00022483
1199
H 176.940233 176.883171 176.825999 176.768589 176.710799 176.710799 176.710799 166.893982 158.124573 153.668964 150.966427 150.641145
V 1.0737415 1.07337196 1.07299915 1.07299072 1.07298042 0.01212715
-
0.26888246
-
0.25420809
-
0.18487005
-
0.11123883
-
0.05303863
0.00022483
1199.06667
H 176.940233 176.883389 176.826456 176.769219 176.711435 176.711435 176.711435 163.571017 153.724239 148.502381 147.041716 146.079957
V 1.0737293 1.0733602 1.07298873 1.07298297 1.07297647 0.00696969
-
0.14734372
-
0.12545766
-
0.11068417
-
0.07989042
-
0.03900895
0.00022483
1199.13333
H 176.940233 176.883542 176.826724 176.769522 176.711667 176.711667 176.711667 163.539847 153.947231 147.097478 143.615885 143.442333
V 1.07371601 1.07334728 1.07297746 1.07297505 1.07297332 -3.3217E-05 0.01769805
-
0.00366914
-
0.02057674
-
0.03839669
-
0.02663355
0.00022483
1199.2
H 176.940233 176.883598 176.826757 176.769452 176.711492 176.711492 176.711492 167.08445 156.912438 149.059706 143.498121 141.151834
V 1.073702 1.07333396 1.07296633 1.07296777 1.07297077
-
0.00521827
0.13989937 0.12262295 0.06856893 0.03270703 0.00083291 0.00022483
1199.26667
H 176.940233 176.883507 176.826513 176.769029 176.71102 176.71102 176.71102 170.080141 162.196805 153.310899 146.595915 143.553908
V 1.07368813 1.07332109 1.07295623 1.07296151 1.07296809
-
0.00894076
0.22762831 0.21208243 0.17591633 0.10779212 0.05956531 0.00022483
1199.33333
H 176.940233 176.883239 176.825988 176.768349 176.710343 176.710343 176.710343 171.820343 166.47849 159.729651 153.367005 152.039887
V 1.0736756 1.07330968 1.07294762 1.0729559 1.07296493
-
0.01135317
0.28447631 0.28076949 0.25136533 0.20271583 0.10718759 0.00022483
1199.4
H 176.940233 176.882814 176.825262 176.767503 176.709516 176.709516 176.709516 173.106572 169.352943 166.530726 165.173659 163.179751
V 1.07366565 1.07330061 1.07294043 1.07295059 1.0729613
-
0.01346433
0.33422011 0.32354309 0.30769069 0.25065748 0.14338295 0.00022483

31. Flujo no Permanente - Juan Felipe Quiñonez 31
31
2015

32. Flujo no Permanente - Juan Felipe Quiñonez 32
32
2015

33. Para
Tc=10TR
t=20min
Canal de Aduccion Disipador y cambio de diametro Tuberia de presion
t H,V 0 100 200 300 400 A 400 D 400 S 460 520 580 640 700
0
H 176.940233 169.988075 163.035916 156.083757 149.131599 149.131599 149.131599 128.014417 106.897235 85.7800531 64.6628712 43.5456892
V 11.679099 11.679099 11.679099 11.679099 11.679099 0 26.2779727 26.2779727 26.2779727 26.2779727 26.2779727 26.2779727
0.066
H 176.940233 169.659021 162.871389 156.083757 149.12374 149.12374 149.12374 127.447261 106.560904 85.3389208 64.7847774 164.134037
V 11.6820335 11.679099 11.6776317 11.679099 11.6791691 -0.23577516 26.2951933 26.2668484 26.2865809 26.2705068 26.2793015 24.9635597
0.13
H 176.940233 169.690502 162.706868 155.957833 149.108034 149.108034 149.108034 127.662857 105.891949 85.5595996 183.786196 167.448678
V 11.6849622 11.6801704 11.6761675 11.6780784 11.679309 -0.23533273 26.2902674 26.2813202 26.276759 26.2728888 24.9700418 24.9300644
0.2
H 176.940233 169.817753 162.713704 155.792732 149.092287 149.092287 149.092287 127.541243 106.655025 203.309126 187.172147 170.927377
V 11.6863112 11.6815242 11.6763132 11.6768399 11.6778829 -0.23692923 26.3019735 26.2776383 26.2850125 24.9724821 24.9378808 24.9023686
0.26
H 176.940233 169.903253 162.807386 155.809558 149.076474 149.076474 149.076474 128.070225 223.963599 207.206012 190.396849 174.431081
V 11.6868213 11.6824038 11.6773497 11.6761203 11.6756283 -0.23732416 26.2995069 26.283194 25.0014054 24.9464286 24.9078765 24.8694591
0.33
H 176.940233 169.938911 162.935112 155.976853 149.060638 149.060638 149.060638 244.468906 227.602752 210.979027 194.406357 178.021346
V 11.6870373 11.6828929 11.6779065 11.6758447 11.6747218 -0.23761803 26.2990305 25.0118543 24.9729639 24.9229025 24.8810263 24.8359687
0.4
H 176.940233 169.981336 163.074775 156.122189 149.053015 149.053015 149.053015 247.541779 231.418189 214.732142 198.537451 181.83736
V 11.6872172 11.6828858 11.677701 11.676114 11.6754058 0.0090696 23.7797625 24.9777196 24.9502803 24.8937059 24.8539858 24.8116732
0.46
H 176.940233 170.059582 163.16959 156.17307 149.053848 149.053848 149.053848 136.91115 234.608843 218.902375 202.100857 185.759467
V 11.6869822 11.6824179 11.6774055 11.676841 11.6767077 0.01592861 23.7126889 23.7079555 24.9154241 24.8675431 24.827339 24.787359
0.53
H 176.940233 170.11769 163.193481 156.156546 149.055063 149.055063 149.055063 137.052884 125.247669 221.909788 206.063574 189.703028
V 11.6860678 11.681791 11.6775111 11.6777068 11.6779051 0.02051186 23.6685821 23.6404521 23.6521906 24.8352799 24.8038694 24.7570097

34. Flujo no Permanente - Juan Felipe Quiñonez 34
34
2015
0.6
H 176.940233 170.100345 163.154213 156.116808 149.056658 149.056658 149.056658 137.38043 125.230176 113.287912 209.452644 193.836955
V 11.6849895 11.6812529 11.6778701 11.6784841 11.6787325 0.02735395 23.6005721 23.593514 23.5874754 23.5850289 24.7679774 24.7320622
0.66
H 176.940233 170.022701 163.069153 156.073289 149.058648 149.058648 149.058648 137.225248 125.415485 113.672295 101.903059 197.828039
V 11.6844259 11.6809774 11.6781254 11.6789878 11.6792431 0.03233971 23.5507936 23.5283292 23.5428179 23.5169825 23.5260911 24.6902013
0.73
H 176.940233 169.937408 162.970259 156.020806 149.061009 149.061009 149.061009 137.088814 125.660206 114.019225 102.906681 170.934733
V 11.684584 11.6810705 11.6781643 11.679115 11.6794438 0.03850044 23.4883069 23.4808746 23.4742858 23.4712857 23.4523565 22.5891535
0.8
H 176.940233 169.88326 162.891977 155.964819 149.063722 149.063722 149.063722 137.486641 125.686667 114.879472 182.429369 173.687846
V 11.6852514 11.6814902 11.6781475 11.6789048 11.6792276 0.04287768 23.4430814 23.4150983 23.4257904 23.3971505 22.5443551 22.4975041
0.86
H 176.940233 169.86802 162.856413 155.930312 149.066801 149.066801 149.066801 137.649851 126.694203 193.473919 185.029051 176.937706
V 11.6860877 11.6820939 11.6782252 11.6784995 11.6786303 0.04950641 23.3739873 23.3688607 23.3543841 22.4930448 22.4524107 22.4347983
0.93
H 176.940233 169.881846 162.86984 155.936738 149.07025 149.07025 149.07025 138.261075 204.842428 196.208564 187.942004 179.798793
V 11.686848 11.6827023 11.6783809 11.6780769 11.6779283 0.05397531 23.3266989 23.2942615 22.4588222 22.4039598 22.3869717 22.3413836
1
H 176.940233 169.915107 162.922902 155.97963 149.074106 149.074106 149.074106 215.648663 207.173184 199.261485 190.935268 183.110497
V 11.6874017 11.6831526 11.6785139 11.6777989 11.6774509 0.06170428 23.2465906 22.4042533 22.3666264 22.3410312 22.296392 22.2725763
1.06
H 176.940233 169.960585 162.994678 156.036837 149.083831 149.083831 149.083831 217.365922 210.026518 201.852224 194.383067 186.167046
V 11.6876584 11.683348 11.6785802 11.677761 11.6773252 0.23004376 21.5261348 22.3067653 22.3024315 22.2474223 22.2300915 22.182656
1.13
H 176.940233 170.006792 163.060986 156.089806 149.099537 149.099537 149.099537 144.00758 212.006571 205.099155 197.039775 189.685284
V 11.6875711 11.6832825 11.6786167 11.6779323 11.6775216 0.24121902 21.4114887 21.412831 22.2035137 22.179923 22.1371453 22.1165716
1.2
H 176.940233 170.038381 163.105374 156.12748 149.115878 149.115878 149.115878 144.294541 139.586476 207.149555 200.35823 192.785785
V 11.6871981 11.6830299 11.6786427 11.6782278 11.6779362 0.24915734 21.3297772 21.2969446 21.3122119 22.0817521 22.0698592 22.0201627
1.26
H 176.940233 170.046809 163.120249 156.143942 149.132863 149.132863 149.132863 144.684962 139.952861 135.366205 202.853776 196.414745
V 11.686709 11.6826917 11.6786453 11.678558 11.6783947 0.26056293 21.2125215 21.2123736 21.1970877 21.1968546 21.9682746 21.9504836

35. Flujo no Permanente - Juan Felipe Quiñonez 35
35
2015
1.3
H 176.940233 170.034457 163.10608 156.141416 149.150511 149.150511 149.150511 144.782864 140.456238 136.18451 131.915874 199.492989
V 11.6862783 11.6823766 11.6786168 11.6788062 11.6787469 0.26901809 21.1250299 21.0959759 21.1124679 21.0784896 21.086838 21.8440389
1.4
H 176.940233 170.009565 163.073869 156.126488 149.168811 149.168811 149.168811 144.915451 141.004906 136.990667 133.322031 179.752488
V 11.6860157 11.6821726 11.6785529 11.6788856 11.678883 0.28016089 21.0093295 21.0085239 20.9927766 20.9918024 20.9637214 20.4172007
1.46
H 176.940233 169.983021 163.039117 156.109247 149.187759 149.187759 149.187759 145.381949 141.440829 138.125091 184.463022 182.054498
V 11.6859605 11.6821051 11.6784581 11.6787677 11.6787537 0.28847548 20.9218085 20.8896392 20.9032291 20.8674621 20.3295915 20.286045
1.53
H 176.940233 169.964818 163.015856 156.100261 149.207371 149.207371 149.207371 145.702966 142.489769 188.550348 186.49125 184.950042
V 11.6860705 11.6821464 11.6783351 11.6784794 11.6783911 0.30009717 20.7996349 20.8001066 20.7796338 20.2343232 20.197231 20.1865188
1.6
H 176.940233 169.960934 163.013129 156.106305 149.227657 149.227657 149.227657 146.304245 192.470934 190.489792 189.007381 187.294147
V 11.6862486 11.6822286 11.6781826 11.6780862 11.6778923 0.30868995 20.7080096 20.6733724 20.150033 20.1027965 20.094912 20.0525034

36. Flujo no Permanente - Juan Felipe Quiñonez 36
36
2015
1198.2
H 176.940233 176.881253 176.822312 176.763393 176.704472 176.704472 176.704472 176.668683 176.632736 176.600207 176.57614 176.567209
V 1.07370811 1.07334011 1.07297207 1.07297165 1.07297108 0.00079451 -0.00181245 -0.00171505 -0.00145072 -0.00104822 -0.00054299 1.9742E-07
1198.26667
H 176.940233 176.881267 176.822339 176.763433 176.704525 176.704525 176.704525 176.652054 176.603864 176.562828 176.535611 176.526306
V 1.07370961 1.07334161 1.07297358 1.07297317 1.07297262 0.00077399 -0.00132551 -0.00123989 -0.00100885 -0.00068804 -0.00034422 1.9742E-07
1198.33333
H 176.940233 176.88128 176.822365 176.763472 176.704575 176.704575 176.704575 176.6397 176.58213 176.53927 176.512993 176.504012
V 1.07371101 1.07334302 1.072975 1.07297462 1.07297408 0.00074624 -0.00066822 -0.00061805 -0.00047796 -0.0003043 -0.00014491 1.9742E-07
1198.4
H 176.940233 176.881292 176.82239 176.763509 176.704624 176.704624 176.704624 176.634641 176.575094 176.532294 176.507672 176.49968
V 1.07371234 1.07334435 1.07297634 1.07297598 1.07297546 0.00071423 8.9215E-05 9.4497E-05 8.604E-05 6.548E-05 4.0084E-05 1.9742E-07
1198.46667
H 176.940233 176.881304 176.822413 176.763544 176.70467 176.70467 176.70467 176.640003 176.584798 176.543489 176.518982 176.511331
V 1.07371358 1.0733456 1.07297761 1.07297726 1.07297677 0.00068173 0.00085788 0.00079353 0.00063781 0.00043049 0.00021059 1.9742E-07
1198.53333
H 176.940233 176.881315 176.822435 176.763577 176.704715 176.704715 176.704715 176.654809 176.608397 176.571475 176.547151 176.538284
V 1.07371476 1.07334678 1.07297879 1.07297847 1.072978 0.00065463 0.00149941 0.0014008 0.00113818 0.00078273 0.00039063 1.9742E-07
1198.6
H 176.940233 176.881325 176.822456 176.763608 176.704758 176.704758 176.704758 176.67309 176.641489 176.612042 176.590779 176.58297
V 1.07371586 1.07334788 1.07297991 1.0729796 1.07297915 0.00063578 0.00194617 0.00184313 0.00154625 0.00109791 0.00057239 1.9742E-07
1198.66667
H 176.940233 176.881335 176.822475 176.763638 176.7048 176.7048 176.7048 176.691423 176.676743 176.660776 176.647865 176.643274
V 1.0737169 1.07334892 1.07298096 1.07298066 1.07298022 0.00062553 0.00218998 0.00209024 0.00180366 0.0013353 0.00070755 1.9742E-07
1198.73333
H 176.940233 176.881344 176.822494 176.763668 176.704842 176.704842 176.704842 176.708442 176.710719 176.712549 176.713275 176.71276
V 1.07371787 1.0733499 1.07298194 1.07298165 1.07298121 0.00062359 0.00223788 0.00214884 0.0018803 0.00141254 0.0007632 1.9742E-07

37. Flujo no Permanente - Juan Felipe Quiñonez 37
37
2015
1198.8
H 176.940233 176.881353 176.822514 176.763698 176.704883 176.704883 176.704883 176.724131 176.744259 176.763203 176.777447 176.783275
V 1.07371879 1.07335082 1.07298286 1.07298256 1.07298212 0.00062904 0.00211146 0.00202615 0.00175883 0.00130735 0.00070529 1.9742E-07
1198.86667
H 176.940233 176.881363 176.822533 176.763729 176.704926 176.704926 176.704926 176.740698 176.776629 176.809147 176.833206 176.842134
V 1.07371964 1.07335167 1.0729837 1.07298339 1.07298295 0.00064157 0.00181814 0.00171969 0.0014543 0.00105074 0.00054445 1.9742E-07
1198.93333
H 176.940233 176.881373 176.822554 176.76376 176.704969 176.704969 176.704969 176.757425 176.805601 176.846625 176.873835 176.883137
V 1.07372043 1.07335246 1.07298448 1.07298416 1.07298369 0.0006623 0.00133138 0.0012447 0.00101258 0.00069066 0.00034574 1.9742E-07
1199
H 176.940233 176.881384 176.822576 176.763793 176.705014 176.705014 176.705014 176.769877 176.827436 176.870287 176.896557 176.905536
V 1.07372116 1.07335317 1.07298518 1.07298484 1.07298436 0.00069024 0.00067424 0.000623 0.00048182 0.00030702 0.00014648 1.9742E-07
1199.06667
H 176.940233 176.881395 176.822599 176.763828 176.705061 176.705061 176.705061 176.775036 176.834575 176.877369 176.901987 176.909977
V 1.0737218 1.07335381 1.07298581 1.07298545 1.07298494 0.00072244 -8.3082E-05 -8.9434E-05 -8.2089E-05 -6.2687E-05 -3.8482E-05 1.9742E-07
1199.13333
H 176.940233 176.881408 176.822623 176.763865 176.705111 176.705111 176.705111 176.769775 176.824976 176.866283 176.890788 176.898439
V 1.07372237 1.07335438 1.07298636 1.07298598 1.07298544 0.0007551 -0.00085167 -0.0007884 -0.0006338 -0.00042766 -0.00020896 1.9742E-07
1199.2
H 176.940233 176.881421 176.822649 176.763904 176.705162 176.705162 176.705162 176.755069 176.801483 176.838407 176.862732 176.8716
V 1.07372285 1.07335485 1.07298682 1.07298642 1.07298587 0.00078236 -0.0014932 -0.00139566 -0.00113417 -0.0007799 -0.00038901 1.9742E-07
1199.26667
H 176.940233 176.881434 176.822677 176.763944 176.705215 176.705215 176.705215 176.736889 176.768497 176.797948 176.819215 176.827025
V 1.07372324 1.07335524 1.0729872 1.07298678 1.07298621 0.00080135 -0.00194 -0.00183804 -0.00154228 -0.00109511 -0.00057079 1.9742E-07
1199.33333
H 176.940233 176.881449 176.822705 176.763986 176.705268 176.705268 176.705268 176.718657 176.733347 176.749323 176.762238 176.766831
V 1.07372354 1.07335554 1.07298749 1.07298706 1.07298648 0.00081173 -0.00218391 -0.00208524 -0.00179978 -0.00133256 -0.00070598 1.9742E-07
1199.4
H 176.940233 176.881463 176.822734 176.764028 176.705323 176.705323 176.705323 176.701737 176.699474 176.697654 176.696935 176.697451
V 1.07372375 1.07335574 1.07298769 1.07298725 1.07298667 0.00081378 -0.00223196 -0.00214398 -0.00187654 -0.00140988 -0.00076167 1.9742E-07

39. Flujo no Permanente - Juan Felipe Quiñonez 39
39
2015

40. Flujo no Permanente - Juan Felipe Quiñonez 40
40
2015

41. Flujo no Permanente - Juan Felipe Quiñonez 41
41
2015












 (1967)

42. Flujo no Permanente - Juan Felipe Quiñonez 42
42
2015
clear all
clc
%DATOS GENERALES
g=9.81;
L1=400;
ds1=100;
L2=300;
ds2=60;
D1=3;
f1=.03;
D2=2;
f2=.02;
c1=1100;
c2=900;
cm=2/((1/c1)+(1/c2));
Hrr=15;
a0=25;
a1=0;
a2=65;
a3=15;
a4=40;
a5=8;

43. Flujo no Permanente - Juan Felipe Quiñonez 43
43
2015
a6=0;
B=2.5;
cr=1;
tr=2*(L1+L2)/cm;
tc=10*tr;
dt=ds2*cr/c2;
z1=c1/g;
z2=c2/g;
R1=f1*dt*c1/(2*g*D1);
R2=f2*dt*c2/(2*g*D2);
G(1)=-sind(a0)*dt;
G(2)=sind(a1)*dt;
G(3)=-sind(a2)*dt;
G(4)=sind(a3)*dt;
G(5)=-sind(a4)*dt;
G(6)=sind(a5)*dt;
G(7)=sind(a6)*dt;
Dc=4;
hp=20;
b=5;
Dp=7;
A1=(pi/4)*D1^2;
A2=(pi/4)*D2^2;
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
%Estado permanente
dh1=2*ds1*sind(a0);
dh2=ds2*(sind(a2)-sind(a3)+sind(a4));
Hi=Hrr+dh1+dh2;
Hf=ds2*sind(a5);
dH=Hi-Hf;
%k=(1-(D2/D1)^2)^2;
hfun=f1*(L1/D1)*((D2/D1)^4)+f2*(L2/D2);
V2=sqrt(2*g*dH/(1+hfun));
V1=V2*(D2^2/D1^2);
%kp=k*(V2^2)/(2*g);
%En el canal de aducción
for i=1:5
H(1,i)=Hi-((i-1)*(f1*ds1*(V1^2))/(2*g*D1));
end
H(1,6)=H(1,5);
H(1,7)=H(1,5);
for i=8:12
H(1,i)=H(1,7)-((i-7)*(f2*ds2*(V2^2))/(2*g*D2));
end
for i=1:5
V(1,i)=V1;
end
V(1,6)=0;
for i=1:6
V(1,i+6)=V2;
end
===============================================================
%Estado no permanente
%En la entrada
for j=1:17991;
Vs(1)=V(j,1)-(c1*dt/ds1)*(V(j,1)-V(j,2));
Hs(1)=Hi-(c1*dt/ds1)*(Hi-H(j,2));
Cs(1)=-Hs(1)+z1*Vs(1)-G(1)*Vs(1)-R1*Vs(1)*abs(Vs(1));

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V(j+1,1)=(Hi+Cs(1))/z1;
H(j+1,1)=H(1,1);
%En el tunel de conduccion
i=2;
Vr(i)=V(j,i)-(c1*dt/ds1)*(V(j,i)-V(j,i-1));
Hr(i)=H(j,i)-(c1*dt/ds1)*(H(j,i)-H(j,i-1));
Vs(i)=V(j,i)-(c1*dt/ds1)*(V(j,i)-V(j,i+1));
Hs(i)=H(j,i)-(c1*dt/ds1)*(H(j,i)-H(j,i+1));
Cr(i)=-Hr(i)-z1*Vr(i)-G(1)*Vr(i)+R1*Vr(i)*abs(Vr(i));
Cs(i)=-Hs(i)+z1*Vs(i)-G(1)*Vs(i)-R1*Vs(i)*abs(Vs(i));
H(j+1,i)=-.5*(Cs(i)+Cr(i));
V(j+1,i)=(.5/z1)*(Cs(i)-Cr(i));
i=3;
Vr(i)=V(j,i)-(c1*dt/ds1)*(V(j,i)-V(j,i-1));
Hr(i)=H(j,i)-(c1*dt/ds1)*(H(j,i)-H(j,i-1));
Vs(i)=V(j,i)-(c1*dt/ds1)*(V(j,i)-V(j,i+1));
Hs(i)=H(j,i)-(c1*dt/ds1)*(H(j,i)-H(j,i+1));
Cr(i)=-Hr(i)-z1*Vr(i)-G(1)*Vr(i)+R1*Vr(i)*abs(Vr(i));
Cs(i)=-Hs(i)+z1*Vs(i)-G(2)*Vs(i)-R1*Vs(i)*abs(Vs(i));
H(j+1,i)=-.5*(Cs(i)+Cr(i));
V(j+1,i)=(.5/z1)*(Cs(i)-Cr(i));
i=4;
Vr(i)=V(j,i)-(c1*dt/ds1)*(V(j,i)-V(j,i-1));
Hr(i)=H(j,i)-(c1*dt/ds1)*(H(j,i)-H(j,i-1));
Vs(i)=V(j,i)-(c1*dt/ds1)*(V(j,i)-V(j,i+1));
Hs(i)=H(j,i)-(c1*dt/ds1)*(H(j,i)-H(j,i+1));
Cr(i)=-Hr(i)-z1*Vr(i)-G(2)*Vr(i)+R1*Vr(i)*abs(Vr(i));
Cs(i)=-Hs(i)+z1*Vs(i)-G(2)*Vs(i)-R1*Vs(i)*abs(Vs(i));
H(j+1,i)=-.5*(Cs(i)+Cr(i));
V(j+1,i)=(.5/z1)*(Cs(i)-Cr(i));
%EN EL CAMBIO DE DIAMETRO
a=H(1,6)-dh2-hp;
if H(j,6)>dh2+a
a=H(1,6)-dh2-hp;
Z(1)=H(1,6);
Q(1)=0;
Vr(5)=V(j,5)-(c1*dt/ds1)*(V(j,5)-V(j,4));
Hr(5)=H(j,5)-(c1*dt/ds1)*(H(j,5)-H(j,4));
Vs(5)=V(j,7)-(c2*dt/ds2)*(V(j,7)-V(j,8));
Hs(5)=H(j,7)-(c2*dt/ds2)*(H(j,7)-H(j,8));
Cr(5)=-Hr(5)-z1*Vr(5)-G(2)*Vr(5)+R1*Vr(5)*abs(Vr(5));
Cs(5)=-Hs(5)+z2*Vs(5)-G(3)*Vs(5)-R2*Vs(5)*abs(Vs(5));
Ad=pi*(((Dp-Dc)/(2*(hp+b)))*(Z(j)-dh2-a)+Dc/2)^2;
Z(j+1)=(2*(Ad/dt)*Z(j)+Q(j)-(A1/z1)*(Cr(5)+dh2)-
(A2/z2)*(Cs(5)+dh2))/((A1/z1)+(A2/z2)+2*(Ad/dt));
Q(j+1)=2*(Ad/dt)*(Z(j+1)-Z(j))-Q(j);
H(j+1,5)=Z(j+1);
H(j+1,6)=Z(j+1);
H(j+1,7)=Z(j+1);
V(j+1,5)=-(Cr(5)+Z(j+1))/z1;
V(j+1,7)=(Cs(5)+Z(j+1))/z2;
V(j+1,6)=(Q(j+1))/Ad
a=H(1,6)-dh2-hp;
Z(1)=H(j,6);
Q(1)=0;
Vr(5)=V(j,5)-(c1*dt/ds1)*(V(j,5)-V(j,4));
Hr(5)=H(j,5)-(c1*dt/ds1)*(H(j,5)-H(j,4));
Vs(5)=V(j,5)-(c2*dt/ds2)*(V(j,5)-V(j,7));
Hs(5)=H(j,5)-(c2*dt/ds2)*(H(j,5)-H(j,7));

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Cr(5)=-Hr(5)-z1*Vr(5)-G(2)*Vr(5)+R1*Vr(5)*abs(Vr(5));
Cs(5)=-Hs(5)+z2*Vs(5)-G(3)*Vs(5)-R2*Vs(5)*abs(Vs(5));
Ad=pi*(Dc/2)^2;
Z(2)=(2*(Ad/dt)*Z(1)+Q(j)-(A1/z1)*(Cr(5)+dh2)-
(A2/z2)*(Cs(5)+dh2))/((A1/z1)+(A2/z2)+2*(Ad/dt));
Q(j+1)=2*(Ad/dt)*(Z(2)-Z(1))-Q(j);
H(j+1,5)=Z(2);
H(j+1,6)=Z(2);
H(j+1,7)=Z(2);
V(j+1,5)=-(Cr(5)+Z(2)+dh2)/z1;
V(j+1,7)=(Cs(5)+Z(2)+dh2)/z2;
V(j+1,6)=(Q(j+1))/Ad
end
%TUBERIA DE PRESION
for i=8:11
Vr(i)=V(j,i)-(c2*dt/ds2)*(V(j,i)-V(j,i-1));
Hr(i)=H(j,i)-(c2*dt/ds2)*(H(j,i)-H(j,i-1));
Vs(i)=V(j,i)-(c2*dt/ds2)*(V(j,i)-V(j,i+1));
Hs(i)=H(j,i)-(c2*dt/ds2)*(H(j,i)-H(j,i+1));
Cr(i)=-Hr(i)-z2*Vr(i)-G(i-5)*Vr(i)+R2*Vr(i)*abs(Vr(i));
Cs(i)=-Hs(i)+z2*Vs(i)-G(i-4)*Vs(i)-R2*Vs(i)*abs(Vs(i));
H(j+1,i)=-.5*(Cs(i)+Cr(i));
V(j+1,i)=(.5/z2)*(Cs(i)-Cr(i));
end
%EN LA VALVULA
t(1)=0;
t(j+1,1)=j*dt;
nf=0;
np=(1-(1-nf)*t(j+1)/tc)^B;
kf=((np*V2)^2)/dH;
Bk=kf*z2;
if t(j+1)<tc
Vr(12)=V(j,12)-(c2*dt/ds2)*(V(j,12)-V(j,11));
Hr(12)=H(j,12)-(c2*dt/ds2)*(H(j,12)-H(j,11));
Cr(12)=-Hr(12)-z2*Vr(12)-G(7)*Vr(12)+R2*Vr(12)*abs(Vr(12));
Ck=kf*(Cr(12)+Hf);
V(j+1,12)=(-Bk+sqrt(Bk^2-4*Ck))/2;
H(j+1,12)=-(Cr(12)+z2*V(j+1,12));
elseif t(j+1)>=tc
Vr(12)=V(j,12)-(c2*dt/ds2)*(V(j,12)-V(j,11));
Hr(12)=H(j,12)-(c2*dt/ds2)*(H(j,12)-H(j,11));
Cr(12)=-Hr(12)-z2*Vr(12)-G(7)*Vr(12)+R2*Vr(12)*abs(Vr(12));
Ck=kf*(Cr(12)+Hf);
V(j+1,12)=V(j,12);
H(j+1,12)=-(Cr(12)+z2*V(j+1,12));
end
end