OSCILACIÓN DE UN FLUIDO EN DEPÓSITOS CON SECCIÓN VARIABLE COMUNICADOS POR UNA TUBERIA

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UNMSMJuan Felipe Quiñonez

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K
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BD
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ASD
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2
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    
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 2 1 0
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dv g Le f
Z Z V V
dt L LD

   
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dz dv d z
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dt dt dt
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d z g Le f dz dz
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dt L LD dt dt
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2
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t t tQ A V 
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P á g i n a | 14
2 AHy h
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tx dy D Zt
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P á g i n a | 15
2
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P á g i n a | 16
2
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t t
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x dy D z
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 1 0z 
 
1/323
2
1
2
2 3
2 8 8
t AI tA AI AI
t
AI t A
D D Dh D D
z z
D D h
  
    
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( )TC tV f V
TC tQ Q
TC TC t tV A V A
2
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t tA D
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AI t
AI
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t t
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V
D D
D Z
h
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P á g i n a | 17
 0 0y y m x x  
1,
2
t
B
D
y h x
 
   
 
1,
2
B
B B
D
y H h x
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 
2 B
B t
H
m
D D
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BD
BH
1Bh

P á g i n a | 18
2
2 1
2
tB Dy h
x
m
 
  
 
1
2 2
0
4
z
t tx dy D z

  
0
2 2
1
4
t t
z
x dy D z



 
2( 0)z 
1
3
2 (108 68921) 41tz z  
sup ( )TC tV f V
supTC tQ Q
sup supTC TC t tV A V A
2
4
t tA D

 2
supTCA x
2
2 1
2
tB Dy h
x
m
 
  
 
1y Z
2
sup 2
2 1
2
t t
TC
tB
V D
V
DZ h
m

 
 
 

P á g i n a | 19
 2 0z 
1 1
3 3
2
(108 68921) (108 68921)
3 41
2 2
t tz i z
z
 
  
inf ( )TC tV f V
infTC tQ Q
inf infTC TC t tV A V A
2
4
t tA D

 2
infTCA x
2
2 1
2
tB Dy h
x
m
 
  
 
2y Z
2
inf 2
2 1
2
t t
TC
tB
V D
V
DZ h
m

 
 
 

P á g i n a | 20
( 0.5 )t s 
 
2
2
2 1 0
2
d z g Le f dz dz
Z Z
dt L LD dt dt

   
 2 1 0
2 t
dV g Le f
Z Z V V
dt L LD

   
1
g
C
L
 2
2 2t t
fe Le f
C
D LD

 
dz
V
dt
 1 1 2 2[ ( ) ( )]t t
dV
C z z z z C V V
dt
   
0 156.64444444tubzt z 
0 0V 
0.5t 
20mint 
1z (1)=7
2z (1)=-3.6741
1(1) 0V 
2 (1) 0V 

P á g i n a | 21
kz1=dtVm;
kv1=-dt(C1(Z1-Z2)+C2*Vm*abs(Vm));
kz2=dt(Vm+kv1/2);
kv2=-dt(C1*((Z1-Z2)+kz1/2)+C2*(Vm+kv1/2)*abs(Vm+kv1/2));
kz3=dt(Vm(+kv2/2);
kz4=dt(Vm+kv3/2);
dkz=(kz1+2kz2+2kz3+kz4)/6;
dkv=(kv1+2kv2+2kv3+kv4)/6;
dkz
dkv
t t
t t
z z
V V
 
 

P á g i n a | 22

P á g i n a | 23
t
(tiempo)
Tubería
Deposito
A
Deposito
B
Zt V Z1 V Z2 V
0.0000 156.6444 0.0000 7.0000 0.0000 -3.6741 0.0000
0.5000 156.6335 -0.0523 6.9993 -0.0032 -3.6738 0.0054
1.0000 156.5965 -0.1044 6.9971 -0.0064 -3.6728 0.0108
1.5000 156.5335 -0.1563 6.9932 -0.0096 -3.6712 0.0161
2.0000 156.4446 -0.2078 6.9878 -0.0127 -3.6689 0.0215
2.5000 156.3300 -0.2588 6.9807 -0.0158 -3.6660 0.0267
3.0000 156.1901 -0.3093 6.9722 -0.0189 -3.6623 0.0319
3.5000 156.0250 -0.3591 6.9621 -0.0219 -3.6581 0.0371
4.0000 155.8352 -0.4082 6.9505 -0.0249 -3.6532 0.0421
4.5000 155.6210 -0.4564 6.9375 -0.0278 -3.6476 0.0471
5.0000 155.3829 -0.5037 6.9230 -0.0306 -3.6415 0.0520
5.5000 155.1213 -0.5500 6.9071 -0.0334 -3.6348 0.0567
6.0000 154.8369 -0.5953 6.8898 -0.0361 -3.6274 0.0614
6.5000 154.5300 -0.6394 6.8712 -0.0387 -3.6195 0.0659
7.0000 154.2012 -0.6824 6.8514 -0.0412 -3.6111 0.0703
7.5000 153.8513 -0.7241 6.8303 -0.0436 -3.6020 0.0746
8.0000 153.4808 -0.7646 6.8080 -0.0459 -3.5925 0.0787
8.5000 153.0902 -0.8038 6.7846 -0.0482 -3.5825 0.0827
9.0000 152.6804 -0.8416 6.7600 -0.0503 -3.5719 0.0865
9.5000 152.2519 -0.8782 6.7344 -0.0524 -3.5609 0.0902
10.0000 151.8054 -0.9134 6.7079 -0.0543 -3.5495 0.0938
10.5000 151.3416 -0.9472 6.6803 -0.0562 -3.5376 0.0972
11.0000 150.8611 -0.9797 6.6519 -0.0579 -3.5252 0.1005
11.5000 150.3647 -1.0108 6.6226 -0.0596 -3.5125 0.1036
12.0000 149.8531 -1.0405 6.5925 -0.0611 -3.4994 0.1065
12.5000 149.3268 -1.0690 6.5616 -0.0626 -3.4859 0.1094
13.0000 148.7865 -1.0961 6.5300 -0.0640 -3.4721 0.1121
13.5000 148.2330 -1.1219 6.4977 -0.0653 -3.4580 0.1146
14.0000 147.6669 -1.1465 6.4648 -0.0665 -3.4435 0.1170
14.5000 147.0887 -1.1698 6.4313 -0.0676 -3.4288 0.1193
15.0000 146.4991 -1.1919 6.3973 -0.0687 -3.4137 0.1215
15.5000 145.8987 -1.2128 6.3628 -0.0696 -3.3985 0.1235
16.0000 145.2881 -1.2325 6.3278 -0.0705 -3.3829 0.1254
16.5000 144.6679 -1.2511 6.2924 -0.0713 -3.3671 0.1272
17.0000 144.0386 -1.2687 6.2565 -0.0721 -3.3512 0.1289
17.5000 143.4008 -1.2851 6.2204 -0.0728 -3.3350 0.1304
18.0000 142.7549 -1.3006 6.1839 -0.0734 -3.3186 0.1319
18.5000 142.1015 -1.3151 6.1471 -0.0739 -3.3020 0.1333
19.0000 141.4410 -1.3286 6.1100 -0.0744 -3.2853 0.1345

P á g i n a | 24
19.5000 140.7739 -1.3413 6.0727 -0.0749 -3.2684 0.1357
20.0000 140.1008 -1.3531 6.0352 -0.0752 -3.2514 0.1367
20.5000 139.4219 -1.3640 5.9975 -0.0756 -3.2343 0.1377
21.0000 138.7377 -1.3741 5.9597 -0.0759 -3.2170 0.1386
21.5000 138.0486 -1.3835 5.9217 -0.0761 -3.1996 0.1394
22.0000 137.3549 -1.3921 5.8836 -0.0763 -3.1822 0.1402
22.5000 136.6571 -1.4001 5.8454 -0.0765 -3.1646 0.1408
23.0000 135.9555 -1.4073 5.8072 -0.0766 -3.1470 0.1414
23.5000 135.2503 -1.4140 5.7689 -0.0767 -3.1293 0.1420
24.0000 134.5420 -1.4200 5.7306 -0.0767 -3.1115 0.1424
24.5000 133.8308 -1.4255 5.6922 -0.0767 -3.0937 0.1429
25.0000 133.1169 -1.4304 5.6539 -0.0767 -3.0758 0.1432
25.5000 132.4007 -1.4347 5.6155 -0.0767 -3.0579 0.1435
26.0000 131.6825 -1.4386 5.5772 -0.0766 -3.0399 0.1438
26.5000 130.9624 -1.4421 5.5389 -0.0765 -3.0219 0.1440
27.0000 130.2406 -1.4450 5.5007 -0.0764 -3.0039 0.1441
27.5000 129.5175 -1.4476 5.4625 -0.0763 -2.9859 0.1442
28.0000 128.7932 -1.4497 5.4244 -0.0761 -2.9679 0.1443
28.5000 128.0679 -1.4515 5.3864 -0.0760 -2.9498 0.1444
29.0000 127.3418 -1.4529 5.3484 -0.0758 -2.9318 0.1444
29.5000 126.6150 -1.4539 5.3106 -0.0756 -2.9137 0.1443
30.0000 125.8878 -1.4547 5.2729 -0.0754 -2.8957 0.1443
30.5000 125.1603 -1.4551 5.2352 -0.0751 -2.8777 0.1442
31.0000 124.4326 -1.4553 5.1977 -0.0749 -2.8596 0.1441
31.5000 123.7049 -1.4551 5.1604 -0.0746 -2.8416 0.1439
32.0000 122.9774 -1.4547 5.1231 -0.0744 -2.8237 0.1437
32.5000 122.2500 -1.4541 5.0860 -0.0741 -2.8057 0.1435
33.0000 121.5231 -1.4532 5.0490 -0.0738 -2.7878 0.1433
33.5000 120.7966 -1.4522 5.0122 -0.0735 -2.7699 0.1431
34.0000 120.0707 -1.4509 4.9755 -0.0732 -2.7520 0.1428
34.5000 119.3455 -1.4494 4.9390 -0.0729 -2.7342 0.1425
35.0000 118.6211 -1.4477 4.9026 -0.0726 -2.7164 0.1422
35.5000 117.8975 -1.4459 4.8664 -0.0723 -2.6986 0.1419
36.0000 117.1749 -1.4439 4.8303 -0.0719 -2.6809 0.1416
36.5000 116.4533 -1.4417 4.7944 -0.0716 -2.6632 0.1413
37.0000 115.7329 -1.4394 4.7587 -0.0713 -2.6455 0.1409
37.5000 115.0136 -1.4370 4.7231 -0.0709 -2.6280 0.1405
38.0000 114.2956 -1.4344 4.6878 -0.0706 -2.6104 0.1402
38.5000 113.5788 -1.4317 4.6525 -0.0703 -2.5929 0.1398
39.0000 112.8635 -1.4289 4.6175 -0.0699 -2.5755 0.1394
39.5000 112.1495 -1.4260 4.5826 -0.0696 -2.5581 0.1390
40.0000 111.4371 -1.4230 4.5479 -0.0692 -2.5407 0.1385
40.5000 110.7262 -1.4199 4.5134 -0.0689 -2.5234 0.1381
41.0000 110.0168 -1.4167 4.4790 -0.0685 -2.5062 0.1377
41.5000 109.3091 -1.4134 4.4449 -0.0681 -2.4890 0.1372

P á g i n a | 25
42.0000 108.6030 -1.4100 4.4109 -0.0678 -2.4719 0.1368
42.5000 107.8986 -1.4066 4.3770 -0.0674 -2.4548 0.1363
43.0000 107.1959 -1.4031 4.3434 -0.0671 -2.4378 0.1359
43.5000 106.4951 -1.3995 4.3099 -0.0667 -2.4208 0.1354
44.0000 105.7960 -1.3959 4.2767 -0.0664 -2.4039 0.1349
44.5000 105.0987 -1.3922 4.2435 -0.0660 -2.3871 0.1345
45.0000 104.4033 -1.3885 4.2106 -0.0657 -2.3703 0.1340
45.5000 103.7098 -1.3847 4.1779 -0.0653 -2.3535 0.1335
46.0000 103.0182 -1.3808 4.1453 -0.0650 -2.3369 0.1330
46.5000 102.3285 -1.3769 4.1129 -0.0646 -2.3203 0.1325
47.0000 101.6408 -1.3730 4.0807 -0.0642 -2.3037 0.1320
47.5000 100.9551 -1.3690 4.0486 -0.0639 -2.2873 0.1315
48.0000 100.2713 -1.3650 4.0168 -0.0635 -2.2708 0.1310
48.5000 99.5896 -1.3609 3.9851 -0.0632 -2.2545 0.1305
49.0000 98.9099 -1.3569 3.9535 -0.0628 -2.2382 0.1300
49.5000 98.2323 -1.3528 3.9222 -0.0625 -2.2220 0.1295
50.0000 97.5567 -1.3486 3.8910 -0.0621 -2.2058 0.1290
50.5000 96.8831 -1.3445 3.8600 -0.0618 -2.1897 0.1285
51.0000 96.2117 -1.3403 3.8292 -0.0615 -2.1737 0.1280
51.5000 95.5424 -1.3361 3.7985 -0.0611 -2.1577 0.1275
52.0000 94.8752 -1.3318 3.7681 -0.0608 -2.1418 0.1270
52.5000 94.2100 -1.3276 3.7377 -0.0604 -2.1259 0.1265
53.0000 93.5471 -1.3233 3.7076 -0.0601 -2.1101 0.1260
53.5000 92.8862 -1.3190 3.6776 -0.0598 -2.0944 0.1255
54.0000 92.2275 -1.3147 3.6478 -0.0594 -2.0787 0.1250
54.5000 91.5710 -1.3104 3.6182 -0.0591 -2.0631 0.1245
55.0000 90.9166 -1.3061 3.5887 -0.0588 -2.0476 0.1240
55.5000 90.2644 -1.3017 3.5594 -0.0584 -2.0321 0.1234
56.0000 89.6144 -1.2974 3.5302 -0.0581 -2.0167 0.1229
56.5000 88.9665 -1.2930 3.5012 -0.0578 -2.0014 0.1224
57.0000 88.3209 -1.2887 3.4724 -0.0575 -1.9861 0.1219
57.5000 87.6774 -1.2843 3.4437 -0.0571 -1.9709 0.1214
58.0000 87.0361 -1.2799 3.4152 -0.0568 -1.9558 0.1209
58.5000 86.3970 -1.2755 3.3869 -0.0565 -1.9407 0.1204
59.0000 85.7601 -1.2711 3.3587 -0.0562 -1.9256 0.1199
59.5000 85.1254 -1.2667 3.3307 -0.0559 -1.9107 0.1194
60.0000 84.4929 -1.2623 3.3028 -0.0556 -1.8958 0.1189
60.5000 83.8626 -1.2579 3.2751 -0.0552 -1.8810 0.1184
61.0000 83.2345 -1.2534 3.2476 -0.0549 -1.8662 0.1179
61.5000 82.6087 -1.2490 3.2202 -0.0546 -1.8515 0.1174
62.0000 81.9850 -1.2446 3.1929 -0.0543 -1.8368 0.1169
62.5000 81.3636 -1.2402 3.1658 -0.0540 -1.8223 0.1163
63.0000 80.7444 -1.2357 3.1389 -0.0537 -1.8077 0.1158
63.5000 80.1274 -1.2313 3.1121 -0.0534 -1.7933 0.1153
64.0000 79.5126 -1.2269 3.0854 -0.0531 -1.7789 0.1148

P á g i n a | 26
64.5000 78.9000 -1.2224 3.0589 -0.0528 -1.7646 0.1143
65.0000 78.2896 -1.2180 3.0326 -0.0525 -1.7503 0.1138
65.5000 77.6815 -1.2136 3.0064 -0.0522 -1.7361 0.1134
66.0000 77.0756 -1.2091 2.9803 -0.0519 -1.7219 0.1129
66.5000 76.4719 -1.2047 2.9544 -0.0517 -1.7079 0.1124
67.0000 75.8704 -1.2003 2.9286 -0.0514 -1.6938 0.1119
67.5000 75.2711 -1.1958 2.9030 -0.0511 -1.6799 0.1114
68.0000 74.6741 -1.1914 2.8776 -0.0508 -1.6660 0.1109
68.5000 74.0792 -1.1870 2.8522 -0.0505 -1.6521 0.1104
69.0000 73.4866 -1.1825 2.8270 -0.0502 -1.6384 0.1099
69.5000 72.8962 -1.1781 2.8020 -0.0499 -1.6247 0.1094
70.0000 72.3080 -1.1737 2.7771 -0.0497 -1.6110 0.1089
70.5000 71.7220 -1.1693 2.7523 -0.0494 -1.5974 0.1085
71.0000 71.1382 -1.1649 2.7276 -0.0491 -1.5839 0.1080
71.5000 70.5566 -1.1604 2.7031 -0.0488 -1.5704 0.1075
72.0000 69.9773 -1.1560 2.6788 -0.0486 -1.5570 0.1070
72.5000 69.4001 -1.1516 2.6546 -0.0483 -1.5436 0.1065
73.0000 68.8252 -1.1472 2.6305 -0.0480 -1.5304 0.1060
73.5000 68.2524 -1.1428 2.6065 -0.0478 -1.5171 0.1056
74.0000 67.6818 -1.1384 2.5827 -0.0475 -1.5040 0.1051
74.5000 67.1135 -1.1340 2.5590 -0.0472 -1.4908 0.1046
75.0000 66.5473 -1.1296 2.5354 -0.0470 -1.4778 0.1041
75.5000 65.9834 -1.1252 2.5120 -0.0467 -1.4648 0.1037
76.0000 65.4216 -1.1209 2.4887 -0.0464 -1.4519 0.1032
76.5000 64.8620 -1.1165 2.4655 -0.0462 -1.4390 0.1027
77.0000 64.3046 -1.1121 2.4425 -0.0459 -1.4262 0.1023
77.5000 63.7494 -1.1077 2.4196 -0.0457 -1.4134 0.1018
78.0000 63.1964 -1.1034 2.3968 -0.0454 -1.4007 0.1013
78.5000 62.6456 -1.0990 2.3741 -0.0452 -1.3881 0.1009
79.0000 62.0969 -1.0946 2.3516 -0.0449 -1.3755 0.1004
79.5000 61.5504 -1.0903 2.3292 -0.0447 -1.3630 0.0999
80.0000 61.0061 -1.0859 2.3069 -0.0444 -1.3505 0.0995
80.5000 60.4640 -1.0816 2.2847 -0.0442 -1.3381 0.0990
81.0000 59.9241 -1.0772 2.2627 -0.0439 -1.3257 0.0986
81.5000 59.3863 -1.0729 2.2408 -0.0437 -1.3134 0.0981
82.0000 58.8507 -1.0686 2.2190 -0.0434 -1.3012 0.0976
82.5000 58.3172 -1.0642 2.1973 -0.0432 -1.2890 0.0972
83.0000 57.7859 -1.0599 2.1758 -0.0430 -1.2769 0.0967
83.5000 57.2568 -1.0556 2.1543 -0.0427 -1.2648 0.0963
84.0000 56.7299 -1.0513 2.1330 -0.0425 -1.2528 0.0958
84.5000 56.2050 -1.0470 2.1118 -0.0422 -1.2409 0.0954
85.0000 55.6824 -1.0427 2.0908 -0.0420 -1.2290 0.0949
85.5000 55.1619 -1.0384 2.0698 -0.0418 -1.2171 0.0945
86.0000 54.6436 -1.0341 2.0490 -0.0415 -1.2053 0.0940
86.5000 54.1274 -1.0298 2.0283 -0.0413 -1.1936 0.0936

P á g i n a | 27
87.0000 53.6133 -1.0255 2.0077 -0.0411 -1.1819 0.0931
87.5000 53.1014 -1.0212 1.9872 -0.0408 -1.1703 0.0927
88.0000 52.5916 -1.0169 1.9668 -0.0406 -1.1587 0.0923
88.5000 52.0840 -1.0126 1.9465 -0.0404 -1.1472 0.0918
89.0000 51.5785 -1.0084 1.9264 -0.0402 -1.1358 0.0914
89.5000 51.0752 -1.0041 1.9063 -0.0399 -1.1244 0.0909
90.0000 50.5740 -0.9998 1.8864 -0.0397 -1.1130 0.0905
90.5000 50.0749 -0.9956 1.8666 -0.0395 -1.1017 0.0901
91.0000 49.5779 -0.9913 1.8469 -0.0393 -1.0905 0.0896
91.5000 49.0831 -0.9871 1.8273 -0.0391 -1.0793 0.0892
92.0000 48.5903 -0.9828 1.8078 -0.0388 -1.0682 0.0888
92.5000 48.0997 -0.9786 1.7885 -0.0386 -1.0571 0.0883
93.0000 47.6113 -0.9744 1.7692 -0.0384 -1.0461 0.0879
93.5000 47.1249 -0.9701 1.7501 -0.0382 -1.0351 0.0875
94.0000 46.6407 -0.9659 1.7310 -0.0380 -1.0242 0.0870
94.5000 46.1585 -0.9617 1.7121 -0.0377 -1.0134 0.0866
95.0000 45.6785 -0.9575 1.6932 -0.0375 -1.0026 0.0862
95.5000 45.2006 -0.9533 1.6745 -0.0373 -0.9918 0.0858
96.0000 44.7248 -0.9491 1.6559 -0.0371 -0.9811 0.0853
96.5000 44.2511 -0.9449 1.6374 -0.0369 -0.9705 0.0849
97.0000 43.7795 -0.9407 1.6190 -0.0367 -0.9599 0.0845
97.5000 43.3100 -0.9365 1.6007 -0.0365 -0.9493 0.0841
98.0000 42.8425 -0.9323 1.5825 -0.0363 -0.9388 0.0836
98.5000 42.3772 -0.9281 1.5644 -0.0361 -0.9284 0.0832
99.0000 41.9140 -0.9239 1.5464 -0.0359 -0.9180 0.0828
99.5000 41.4529 -0.9197 1.5285 -0.0357 -0.9077 0.0824
100.0000 40.9938 -0.9156 1.5107 -0.0355 -0.8974 0.0820

P á g i n a | 28
1149.0000 1.3008 0.0091 0.0458 0.0003 -0.0279 -0.0008
1149.5000 1.3053 0.0088 0.0460 0.0003 -0.0280 -0.0008
1150.0000 1.3096 0.0084 0.0461 0.0003 -0.0281 -0.0007
1150.5000 1.3137 0.0080 0.0463 0.0003 -0.0282 -0.0007
1151.0000 1.3177 0.0077 0.0464 0.0003 -0.0282 -0.0007
1151.5000 1.3214 0.0073 0.0465 0.0003 -0.0283 -0.0006
1152.0000 1.3250 0.0069 0.0466 0.0002 -0.0284 -0.0006
1152.5000 1.3283 0.0065 0.0468 0.0002 -0.0285 -0.0006
1153.0000 1.3315 0.0062 0.0469 0.0002 -0.0285 -0.0005
1153.5000 1.3345 0.0058 0.0470 0.0002 -0.0286 -0.0005
1154.0000 1.3373 0.0054 0.0471 0.0002 -0.0287 -0.0005
1154.5000 1.3400 0.0050 0.0472 0.0002 -0.0287 -0.0004
1155.0000 1.3424 0.0046 0.0473 0.0002 -0.0288 -0.0004
1155.5000 1.3447 0.0043 0.0473 0.0002 -0.0288 -0.0004
1156.0000 1.3467 0.0039 0.0474 0.0001 -0.0289 -0.0003
1156.5000 1.3486 0.0035 0.0475 0.0001 -0.0289 -0.0003
1157.0000 1.3503 0.0031 0.0475 0.0001 -0.0289 -0.0003
1157.5000 1.3517 0.0028 0.0476 0.0001 -0.0290 -0.0002
1158.0000 1.3530 0.0024 0.0476 0.0001 -0.0290 -0.0002
1158.5000 1.3542 0.0020 0.0477 0.0001 -0.0290 -0.0002
1159.0000 1.3551 0.0016 0.0477 0.0001 -0.0290 -0.0001
1159.5000 1.3558 0.0012 0.0477 0.0000 -0.0291 -0.0001
1160.0000 1.3564 0.0009 0.0478 0.0000 -0.0291 -0.0001
1160.5000 1.3567 0.0005 0.0478 0.0000 -0.0291 0.0000
1161.0000 1.3569 0.0001 0.0478 0.0000 -0.0291 0.0000
1161.5000 1.3569 -0.0003 0.0478 0.0000 -0.0291 0.0000
1162.0000 1.3567 -0.0006 0.0478 0.0000 -0.0291 0.0001
1162.5000 1.3563 -0.0010 0.0478 0.0000 -0.0291 0.0001
1163.0000 1.3557 -0.0014 0.0477 0.0000 -0.0291 0.0001
1163.5000 1.3549 -0.0018 0.0477 -0.0001 -0.0290 0.0002
1164.0000 1.3539 -0.0021 0.0477 -0.0001 -0.0290 0.0002
1164.5000 1.3528 -0.0025 0.0476 -0.0001 -0.0290 0.0002
1165.0000 1.3515 -0.0029 0.0476 -0.0001 -0.0290 0.0002
1165.5000 1.3499 -0.0033 0.0475 -0.0001 -0.0289 0.0003
1166.0000 1.3482 -0.0036 0.0475 -0.0001 -0.0289 0.0003
1166.5000 1.3463 -0.0040 0.0474 -0.0001 -0.0289 0.0003
1167.0000 1.3443 -0.0044 0.0473 -0.0002 -0.0288 0.0004

P á g i n a | 29
1167.5000 1.3420 -0.0047 0.0472 -0.0002 -0.0288 0.0004
1168.0000 1.3396 -0.0051 0.0472 -0.0002 -0.0287 0.0004
1168.5000 1.3369 -0.0055 0.0471 -0.0002 -0.0287 0.0005
1169.0000 1.3341 -0.0058 0.0470 -0.0002 -0.0286 0.0005
1169.5000 1.3311 -0.0062 0.0469 -0.0002 -0.0285 0.0005
1170.0000 1.3280 -0.0066 0.0468 -0.0002 -0.0285 0.0006
1170.5000 1.3246 -0.0069 0.0466 -0.0002 -0.0284 0.0006
1171.0000 1.3211 -0.0073 0.0465 -0.0003 -0.0283 0.0006
1171.5000 1.3174 -0.0076 0.0464 -0.0003 -0.0282 0.0007
1172.0000 1.3135 -0.0080 0.0462 -0.0003 -0.0281 0.0007
1172.5000 1.3094 -0.0083 0.0461 -0.0003 -0.0281 0.0007
1173.0000 1.3052 -0.0087 0.0459 -0.0003 -0.0280 0.0007
1173.5000 1.3007 -0.0091 0.0458 -0.0003 -0.0279 0.0008
1174.0000 1.2961 -0.0094 0.0456 -0.0003 -0.0278 0.0008
1174.5000 1.2914 -0.0098 0.0455 -0.0003 -0.0277 0.0008
1175.0000 1.2864 -0.0101 0.0453 -0.0004 -0.0276 0.0009
1175.5000 1.2813 -0.0104 0.0451 -0.0004 -0.0275 0.0009
1176.0000 1.2760 -0.0108 0.0449 -0.0004 -0.0273 0.0009
1176.5000 1.2705 -0.0111 0.0447 -0.0004 -0.0272 0.0010
1177.0000 1.2649 -0.0115 0.0445 -0.0004 -0.0271 0.0010
1177.5000 1.2591 -0.0118 0.0443 -0.0004 -0.0270 0.0010
1178.0000 1.2531 -0.0121 0.0441 -0.0004 -0.0269 0.0010
1178.5000 1.2470 -0.0125 0.0439 -0.0004 -0.0267 0.0011
1179.0000 1.2407 -0.0128 0.0437 -0.0005 -0.0266 0.0011
1179.5000 1.2342 -0.0131 0.0434 -0.0005 -0.0264 0.0011
1180.0000 1.2276 -0.0135 0.0432 -0.0005 -0.0263 0.0012
1180.5000 1.2208 -0.0138 0.0430 -0.0005 -0.0262 0.0012
1181.0000 1.2138 -0.0141 0.0427 -0.0005 -0.0260 0.0012
1181.5000 1.2067 -0.0144 0.0425 -0.0005 -0.0259 0.0012
1182.0000 1.1994 -0.0147 0.0422 -0.0005 -0.0257 0.0013
1182.5000 1.1920 -0.0150 0.0420 -0.0005 -0.0255 0.0013
1183.0000 1.1844 -0.0154 0.0417 -0.0005 -0.0254 0.0013
1183.5000 1.1767 -0.0157 0.0414 -0.0006 -0.0252 0.0013
1184.0000 1.1688 -0.0160 0.0411 -0.0006 -0.0250 0.0014
1184.5000 1.1607 -0.0163 0.0409 -0.0006 -0.0249 0.0014
1185.0000 1.1525 -0.0166 0.0406 -0.0006 -0.0247 0.0014
1185.5000 1.1442 -0.0169 0.0403 -0.0006 -0.0245 0.0014
1186.0000 1.1357 -0.0172 0.0400 -0.0006 -0.0243 0.0015
1186.5000 1.1270 -0.0175 0.0397 -0.0006 -0.0242 0.0015
1187.0000 1.1182 -0.0177 0.0394 -0.0006 -0.0240 0.0015
1187.5000 1.1093 -0.0180 0.0390 -0.0006 -0.0238 0.0015
1188.0000 1.1002 -0.0183 0.0387 -0.0006 -0.0236 0.0016
1188.5000 1.0910 -0.0186 0.0384 -0.0007 -0.0234 0.0016
1189.0000 1.0817 -0.0189 0.0381 -0.0007 -0.0232 0.0016
1189.5000 1.0722 -0.0192 0.0377 -0.0007 -0.0230 0.0016

P á g i n a | 30
1190.0000 1.0625 -0.0194 0.0374 -0.0007 -0.0228 0.0017
1190.5000 1.0528 -0.0197 0.0371 -0.0007 -0.0226 0.0017
1191.0000 1.0429 -0.0200 0.0367 -0.0007 -0.0223 0.0017
1191.5000 1.0328 -0.0202 0.0364 -0.0007 -0.0221 0.0017
1192.0000 1.0227 -0.0205 0.0360 -0.0007 -0.0219 0.0018
1192.5000 1.0124 -0.0207 0.0356 -0.0007 -0.0217 0.0018
1193.0000 1.0019 -0.0210 0.0353 -0.0007 -0.0215 0.0018
1193.5000 0.9914 -0.0212 0.0349 -0.0007 -0.0212 0.0018
1194.0000 0.9807 -0.0215 0.0345 -0.0008 -0.0210 0.0018
1194.5000 0.9699 -0.0217 0.0341 -0.0008 -0.0208 0.0019
1195.0000 0.9590 -0.0220 0.0338 -0.0008 -0.0205 0.0019
1195.5000 0.9480 -0.0222 0.0334 -0.0008 -0.0203 0.0019
1196.0000 0.9369 -0.0224 0.0330 -0.0008 -0.0201 0.0019
1196.5000 0.9256 -0.0226 0.0326 -0.0008 -0.0198 0.0019
1197.0000 0.9142 -0.0229 0.0322 -0.0008 -0.0196 0.0020
1197.5000 0.9028 -0.0231 0.0318 -0.0008 -0.0193 0.0020
1198.0000 0.8912 -0.0233 0.0314 -0.0008 -0.0191 0.0020
1198.5000 0.8795 -0.0235 0.0309 -0.0008 -0.0188 0.0020
1199.0000 0.8676 -0.0237 0.0305 -0.0008 -0.0186 0.0020
1199.5000 0.8557 -0.0239 0.0301 -0.0008 -0.0183 0.0021

P á g i n a | 31

P á g i n a | 32

P á g i n a | 33

P á g i n a | 34







P á g i n a | 35






P á g i n a | 36
%PARABOLA INVERTIDA SUPERIOR
%=======================================================
clear all
clc
%Datos:
Ds=5;
Di=8;
Dt=1.5;
hA1=7;
b=3;
Ha=hA1+b;
%Ecuacion Integrada y despejanda, z1 en funcion a zt
syms zt;
zp1=((Di^2*Ha)/(Di^2-Ds^2))-sqrt(((Di^2*Ha)/(Di^2-Ds^2))^2-
2*zt*(Dt^2*Ha)/(Di^2-Ds^2));
PI=inline(zp1);
%TRONCO DE CONO
%=========================================================
%Datos:
Di=8;
Dt=1.5;
hA2=20;
%Ecuacion despejada, z1 en funcion a zt
syms zt;
zc1=(2*hA2/(Di-Dt))*((Di/2)-((Di^3)/8-3*Dt^2*(Di-
Dt)*zt/(8*hA2))^(1/3));
TC=inline(zc1);
%CONO

P á g i n a | 37
%========================================================
%Datos:
Db=14;
Dt=1.5;
hB1=35;
Hb=50;
%Geometria del tronco de cono
m=2*Hb/(Db-Dt);
syms y; %x^2=fun
fun=(((y+hB1)/m)+Dt/2)^2;
%Integracion
syms z1;
vol=pi*int(fun,y,0,z1);
vol2=pi*int(fun,y,-z1,0);
%despejamos la ecuacion cuadratica que tiene a z1^2+....-zt=0=ec
syms zt;
ec=(vol*4/(pi*Dt^2))-zt;
ec2=(vol2*4/(pi*Dt^2))-zt;
%Desapejamos z1 en funcion de zt
Z=solve(ec==0,z1);
Z2=solve(ec2==0,z1);
%Ecuacion para z2 mayor a 0
conosup=inline(Z(1));
%Ecuacion para z2 menor a 0
conoinf=inline(Z2(2));
%---------------------------------------------------------------------
-
%----------------------------RUNGE KUTTA 4----------------------------
-
%=====================================================================
L=1000;
g=9.8;
Dt=1.5;
f=0.03;
%dt=0.2;
SumaK=12;
Lem=SumaK*Dt/f;
Le=Lem+L;
fe=f*Le/L;
%Datos de la ecuacion caracteristica
c1=g/L;
c2=fe/2*Dt;
%Condiciones iniciales de los depositos
Zm1(1)=7;
Zm2(1)=-3.6741;
ztub(1)=156.6444;
Vm(1)=0;
%Vm1(1)=0;
%Vm2(1)=0;
t(1)=0;
kz1(1)=0;
kv1(1)=0;
kz2(1)=0;
kv2(1)=0;
kz3(1)=0;
kv3(1)=0;
kz4(1)=0;
kv4(1)=0;

P á g i n a | 38
dkz(1)=0;
dkv(1)=0;
dt=0.5;
fprintf('n')
fprintf('Tiempo kz1 kv1 kz2 kv2 kz3 kv3 kz4
kv4 dkz dkv Alt.tub Var.tub Veloc Velocn')
fprintf('(seg)
(m) (m/s) Dep.1 Dep.2n')
fprintf('_____________________________________________________________
________________________________________________________n')
for i=2:2400
kz1(i)=dt*Vm(i-1);
kv1(i)=-dt*(c1*(Zm1(i-1)-Zm2(i-1))+c2*Vm(i-1)*abs(Vm(i-1)));
kz2(i)=dt*(Vm(i-1)+kv1(i)/2);
kv2(i)=-dt*(c1*((Zm1(i-1)-Zm2(i-1))+kz1(i)/2)+c2*(Vm(i-
1)+kv1(i)/2)*abs(Vm(i-1)+kv1(i)/2));
kz3(i)=dt*(Vm(i-1)+kv2(i)/2);
1)+kv2(i)/2)*abs(Vm(i-1)+kv2(i)/2));
kz4(i)=dt*(Vm(i-1)+kv3(i)/2);
1)+kv3(i)/2)*abs(Vm(i-1)+kv3(i)/2));
dkz(i)=(kz1(i)+2*kz2(i)+2*kz3(i)+kz4(i))/6;
dkv(i)=(kv1(i)+2*kv2(i)+2*kv3(i)+kv4(i))/6;
%Para un zt que disminuye un diferencial de longitud en funcion a Vm
ztub(i,1)=ztub(i-1)+dkz(i);
%Para las velocidades:
Vm(i)=Vm(i-1)+dkv(i);
%Variacion de tiempo:
t(i)=t(i-1)+dt;
if ztub(i)>=0
%Posiciones reales
Zm1(i,1)=PI(ztub(i));
Zm2(i,1)=-real(conoinf(ztub(i)));
%Velocidades reales
Vm1(i,1)=(Vm(i)*Dt^2)/(-(Di^2-Ds^2)*Zm1(i)/Ha+Di^2);
Vm2(i,1)=-(Vm(i)*Dt^2)/(((Zm2(i)+hB1)/m)+Dt/2)^2;
else if ztub(i)<0
%Posiciones reales
Zm1(i,1)=-(TC(-ztub(i)));
Zm2(i,1)=conosup(-ztub(i));
%Velocidades reales
Vm1(i,1)=(Vm(i)*Dt^2)/(Di+(Di-Dt)*Zm1(i)/hA2)^2;
Vm2(i,1)=-(Vm(i)*Dt^2)/(((Zm2(i)+hB1)/m)+Dt/2)^2;
end
end
fprintf('%1.3ft%1.3ft%1.3ft%1.3ft%1.3ft%1.3ft%1.3ft%1.3ft%1.3f
t%1.3ft%1.3ft%1.3ft%1.3ft%1.3ft%1.3fn',t(i),kz1(i),kv1(i),kz2(
i),kv2(i),kz3(i),kv3(i),kz4(i),kv4(i),dkz(i),dkv(i),ztub(i),Vm(i
),Vm1(i),Vm2(i))
end

OSCILACIÓN DE UN FLUIDO EN DEPÓSITOS CON SECCIÓN VARIABLE COMUNICADOS POR UNA TUBERIA

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OSCILACIÓN DE UN FLUIDO EN DEPÓSITOS CON SECCIÓN VARIABLE COMUNICADOS POR UNA TUBERIA