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EXCEL CURVAS REMANSO
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EXCEL CURVAS REMANSO
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Miguel Luis Ma Nu
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METODO DE TRAMOS FIJOS DATOS: 2 m3/s
Q= n=
0.03
So =
0
y1= Longitud=
b=
1m
Z=
2
1.5 m 2000 m
X
∆X
So∆X
Y
A
P
R
R^2/3
V
V^2/(2g)
E
So∆X+E
SE
SE
SE∆X
E+SE∆X
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
-
-
0.00 200.00 0.1000 1.5000
6.0000
7.7082
0.7784
0.8462
0.3333
0.0057 1.50566 1.60566
0.000087
200.00 200.00 0.1000 1.4400
5.5872
7.4399
0.7510
0.8262
0.3580
0.0065 1.44653 1.54653
0.000103 0.0000950 0.019007 1.46554
400.00 200.00 0.1000 1.3470
4.9758
7.0240
0.7084
0.7947
0.4019
0.0082 1.35523 1.45523
0.000137 0.0001202 0.024048 1.37928
600.00 200.00 0.1000 1.2820
4.5690
6.7333
0.6786
0.7722
0.4377
0.0098 1.29177 1.39177
0.000169 0.0001531 0.030622 1.32239
800.00 200.00 0.1000 1.2240
4.2204
6.4739
0.6519
0.7518
0.4739
0.0114 1.23545 1.33545
0.000205 0.0001872 0.037435 1.27288
1000.00 200.00 0.1000 1.1770
3.9477
6.2637
0.6302
0.7351
0.5066
0.0131 1.19008 1.29008
0.000242 0.0002236 0.044712 1.23479
1200.00 200.00 0.1000 1.1390
3.7336
6.0938
0.6127
0.7214
0.5357
0.0146 1.15362 1.25362
0.000277 0.0002595 0.051901 1.20553
1400.00 200.00 0.1000 1.1110
3.5796
5.9685
0.5998
0.7112
0.5587
0.0159 1.12691 1.22691
0.000307 0.0002923 0.058454 1.18536
1600.00 200.00 0.1000 1.0900
3.4662
5.8746
0.5900
0.7035
0.5770
0.0170 1.10697 1.20697
0.000333 0.0003200 0.063992 1.17096
1800.00 200.00 0.1000 1.0760
3.3916
5.8120
0.5835
0.6983
0.5897
0.0177 1.09372 1.19372
0.000351 0.0003417 0.068340 1.16206
2000.00 200.00 0.1000 1.0660
3.3387
5.7673
0.5789
0.6946
0.5990
0.0183 1.08429 1.18429
0.000365 0.0003577 0.071540 1.15583
Perfil M. Tramos Fijos 2.0000 Perfil
1.5000 1.0000 0.5000 0.0000 0.00
1000.00
2000.00
3000.00
0.0000
IGUALES 1.6057 1.5465 1.4552 1.3918 1.3354 1.2901 1.2536 1.2269 1.2070 1.1937 1.1843
1.4655 1.3793 1.3224 1.2729 1.2348 1.2055 1.1854 1.1710 1.1621 1.1558
0.5000 0.0000 0.00
1000.00
2000.00
3000.00
METODO DIRECTO POR TRAMOS DATOS: Q=
0.35 m3/s
n=
0.02
So =
0 0.4 m
b= Z=
Y1= 0.34 Y2= 0.5 ∆Y= 0.02 CURVA M2
0.75
Y
A
T
R
R^2/3
V
3
4
5
V^2/(2g)
E 8
∆E
SE
9
10
ŜE
SE-S0
∆X
11
12
13
L
1
2
6
7
0.340
0.22 1.2996 0.1782 0.3166
1.57
0.1259
0.4659
0.0000
###
0.360
0.24 1.3525 0.1855 0.3253
1.45
0.1073
0.4673
0.0014
###
0.0050
-0.00401
-0.3563
-0.36
0.380
0.26 1.4054 0.1928 0.3338
1.34
0.0921
0.4721
0.0048
###
0.0041
-0.00306
-1.5755
-1.93
0.400
0.28 1.4583 0.2000 0.3420
1.25
0.0796
0.4796
0.0075
###
0.0033
-0.00233
-3.2160
-5.15
0.420
0.30 1.5112 0.2071 0.3500
1.17
0.0692
0.4892
0.0096
###
0.0028
-0.00175
-5.4837
-10.63
0.440
0.32 1.5641 0.2141 0.3579
1.09
0.0605
0.5005
0.0113
###
0.0023
-0.00129
-8.7474
-19.38
0.460
0.34 1.6170 0.2211 0.3656
1.02
0.0532
0.5132
0.0126
###
0.0019
-0.00092 -13.7382
-33.12
0.480
0.36 1.6700 0.2280 0.3732
0.96
0.0469
0.5269
0.0138
###
0.0016
-0.00062 -22.1413
-55.26
0.500
0.39 1.7229 0.2348 0.3806
0.90
0.0416
0.5416
0.0147
###
0.0014
-0.00038 -38.9075
-94.17
Perfil M. Directo por Tramos 0.600 0.500
Perfil
0.400 0.300 0.200 0.100 0.000 -100.00
-50.00
0.00
14 0.00
METODO DE LA INTEGRACION DIRECTA DATOS: Caudal (Q) 0.9 Ancho de solera (b) 1
yp/b =
Talud (z) 1 Pendiente (So) 0 Tirante normal (yn)0.68 Tirante critico (yc)0.38 Tirante inicial (y1)0.38 Tirante final (y2) 0.57 Numero de tramos 10
0.48
RESULTADOS PARCIALES Δy = 0.02
Valor de M 3.4802 Valor de N 3.6437 Valor de J 3.1317 y 0.38 0.4 0.42 0.44 0.46 0.48 0.5 0.51 0.53 0.55 0.57
u=y/yn 0.5636 0.5919 0.6201 0.6484 0.6766 0.7049 0.7331 0.7614 0.7896 0.8179 0.8462
RESULTADOS X 0.00 0.53 2.05 5.22 9.84 16.82 26.04 38.82 55.64
Y 0.38 0.4 0.42 0.44 0.46 0.48 0.5 0.51 0.53
78.05 108.05
0.55 0.57
v=u^(N/J) 0.5132 0.5432 0.5735 0.6040 0.6348 0.6657 0.6969 0.7282 0.7597 0.7915 0.8234
F(u,N) 0.58 0.61 0.65 0.68 0.72 0.76 0.8 0.84 0.89 0.94 1
F(v,J) 0.53 0.56 0.6 0.64 0.68 0.72 0.76 0.81 0.86 0.92 0.99
delta x x 61.8037 0.00 61.2749 0.53 59.7505 2.05 56.5860 5.22 51.9641 9.84 44.9857 16.82 35.7614 26.04 22.9867 38.82 6.1592 55.64 -16.2417 78.05 -46.2457 108.05
Perfil M. Integracion Directa 1 1
0.00
Perfil
20.00 40.00 60.00 80.00 100.00 120.00
CALCULO DE LAS INTEGRALES POR EL METODO DE TRAPECIO F(u,N) a b (u) h
integral trapecios 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0001 1.0000 1.0001 1.0001 1.0001 1.0001 1.0002 1.0001 1.0002 1.0002 1.0003 1.0003 1.0004 1.0004 1.0005 1.0005 1.0007 1.0006 1.0009 1.0008 1.0011 1.0010 1.0013 1.0012 1.0015 1.0014 1.0018 1.0017 1.0022 1.0020
0.9958
0 0.0085 0.0169 0.0254 0.0338 0.0423 0.0508 0.0592 0.0677 0.0762 0.0846 0.0931 0.1015 0.1100 0.1185 0.1269 0.1354 0.1439 0.1523 0.1608 0.1692 0.1777
0 0.85 0.01 1 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0001 1.0001 1.0001 1.0002 1.0002 1.0003 1.0004 1.0005 1.0007 1.0009 1.0011 1.0013 1.0015 1.0018
0.1862 0.1946 0.2031
1.0022 1.0026 1.0030
1.0026 1.0030 1.0035
1.0024 1.0028 1.0033
F(v,J) a b (v) h
0.9880
0.0085 0.0085 0.0085 0.0085 0.0085 0.0085 0.0085 0.0085 0.0085 0.0085 0.0085 0.0085 0.0085 0.0085 0.0085 0.0085 0.0085 0.0085 0.0085 0.0085 0.0085 0.0085
0 integral 0.82 0.01 0 1 0.01 1.0000 0.02 1.0000 0.02 1.0000 0.03 1.0000 0.04 1.0000 0.05 1.0001 0.06 1.0001 0.07 1.0002 0.07 1.0003 0.08 1.0004 0.09 1.0005 0.1 1.0007 0.11 1.0009 0.12 1.0012 0.12 1.0014 0.13 1.0018 0.14 1.0021 0.15 1.0025 0.16 1.0030 0.16 1.0035 0.17 1.0041
1.0000 1.0000 1.0000 1.0000 1.0000 1.0001 1.0001 1.0002 1.0003 1.0004 1.0005 1.0007 1.0009 1.0012 1.0014 1.0018 1.0021 1.0025 1.0030 1.0035 1.0041 1.0048
1.0000 1.0000 1.0000 1.0000 1.0000 1.0001 1.0001 1.0002 1.0002 1.0003 1.0005 1.0006 1.0008 1.0010 1.0013 1.0016 1.0019 1.0023 1.0028 1.0033 1.0038 1.0044
0.0082 0.0082 0.0082 0.0082 0.0082 0.0082 0.0082 0.0082 0.0082 0.0082 0.0082 0.0082 0.0082 0.0082 0.0082 0.0082 0.0082 0.0083 0.0083 0.0083 0.0083 0.0083
0.0085 0.0085 0.0085
0.18 0.19 0.2
1.0055 1.0063 1.0071
1.0051 1.0059 1.0067
0.0083 0.0083 0.0083
1.0048 1.0055 1.0063
0.2116 0.2200 0.2285 0.2369 0.2454 0.2539 0.2623 0.2708 0.2792 0.2877 0.2962 0.3046 0.3131 0.3216 0.3300 0.3385 0.3469 0.3554 0.3639 0.3723 0.3808 0.3893 0.3977 0.4062 0.4146 0.4231 0.4316 0.4400 0.4485 0.4569 0.4654 0.4739 0.4823 0.4908 0.4993 0.5077 0.5162 0.5246 0.5331 0.5416 0.5500
1.0035 1.0040 1.0046 1.0053 1.0060 1.0068 1.0077 1.0086 1.0097 1.0108 1.0120 1.0133 1.0147 1.0163 1.0179 1.0197 1.0216 1.0236 1.0258 1.0281 1.0306 1.0332 1.0360 1.0390 1.0422 1.0455 1.0491 1.0529 1.0569 1.0612 1.0657 1.0704 1.0755 1.0808 1.0865 1.0924 1.0987 1.1054 1.1124 1.1199 1.1277
1.0040 1.0046 1.0053 1.0060 1.0068 1.0077 1.0086 1.0097 1.0108 1.0120 1.0133 1.0147 1.0163 1.0179 1.0197 1.0216 1.0236 1.0258 1.0281 1.0306 1.0332 1.0360 1.0390 1.0422 1.0455 1.0491 1.0529 1.0569 1.0612 1.0657 1.0704 1.0755 1.0808 1.0865 1.0924 1.0987 1.1054 1.1124 1.1199 1.1277 1.1360
1.0038 1.0043 1.0050 1.0057 1.0064 1.0073 1.0082 1.0092 1.0102 1.0114 1.0127 1.0140 1.0155 1.0171 1.0188 1.0206 1.0226 1.0247 1.0269 1.0293 1.0319 1.0346 1.0375 1.0406 1.0438 1.0473 1.0510 1.0549 1.0590 1.0634 1.0680 1.0730 1.0781 1.0836 1.0894 1.0956 1.1021 1.1089 1.1161 1.1238 1.1319
0.0085 0.0085 0.0085 0.0085 0.0085 0.0085 0.0085 0.0085 0.0085 0.0086 0.0086 0.0086 0.0086 0.0086 0.0086 0.0086 0.0087 0.0087 0.0087 0.0087 0.0087 0.0088 0.0088 0.0088 0.0088 0.0089 0.0089 0.0089 0.0090 0.0090 0.0090 0.0091 0.0091 0.0092 0.0092 0.0093 0.0093 0.0094 0.0094 0.0095 0.0096
0.21 0.21 0.22 0.23 0.24 0.25 0.26 0.26 0.27 0.28 0.29 0.3 0.3 0.31 0.32 0.33 0.34 0.35 0.35 0.36 0.37 0.38 0.39 0.4 0.4 0.41 0.42 0.43 0.44 0.44 0.45 0.46 0.47 0.48 0.49 0.49 0.5 0.51 0.52 0.53 0.54
1.0071 1.0081 1.0091 1.0102 1.0114 1.0127 1.0141 1.0156 1.0172 1.0189 1.0207 1.0227 1.0248 1.0270 1.0293 1.0318 1.0345 1.0373 1.0403 1.0434 1.0467 1.0502 1.0539 1.0578 1.0619 1.0662 1.0707 1.0755 1.0805 1.0858 1.0913 1.0971 1.1032 1.1097 1.1164 1.1235 1.1309 1.1387 1.1468 1.1554 1.1644
1.0081 1.0091 1.0102 1.0114 1.0127 1.0141 1.0156 1.0172 1.0189 1.0207 1.0227 1.0248 1.0270 1.0293 1.0318 1.0345 1.0373 1.0403 1.0434 1.0467 1.0502 1.0539 1.0578 1.0619 1.0662 1.0707 1.0755 1.0805 1.0858 1.0913 1.0971 1.1032 1.1097 1.1164 1.1235 1.1309 1.1387 1.1468 1.1554 1.1644 1.1739
1.0076 1.0086 1.0096 1.0108 1.0120 1.0134 1.0148 1.0164 1.0180 1.0198 1.0217 1.0237 1.0259 1.0282 1.0306 1.0332 1.0359 1.0388 1.0418 1.0451 1.0485 1.0521 1.0558 1.0598 1.0640 1.0685 1.0731 1.0780 1.0831 1.0885 1.0942 1.1002 1.1064 1.1130 1.1199 1.1272 1.1348 1.1427 1.1511 1.1599 1.1691
0.0083 0.0083 0.0083 0.0083 0.0083 0.0083 0.0084 0.0084 0.0084 0.0084 0.0084 0.0084 0.0084 0.0085 0.0085 0.0085 0.0085 0.0086 0.0086 0.0086 0.0086 0.0087 0.0087 0.0087 0.0088 0.0088 0.0088 0.0089 0.0089 0.0090 0.0090 0.0091 0.0091 0.0092 0.0092 0.0093 0.0093 0.0094 0.0095 0.0096 0.0096
0.5585 0.5670 0.5754 0.5839 0.5923 0.6008 0.6093 0.6177 0.6262 0.6347 0.6431 0.6516 0.6600 0.6685 0.6770 0.6854 0.6939 0.7023 0.7108 0.7193 0.7277 0.7362 0.7447 0.7531 0.7616 0.7700 0.7785 0.7870 0.7954 0.8039 0.8124 0.8208 0.8293 0.8377 0.8462
1.1360 1.1448 1.1541 1.1639 1.1742 1.1852 1.1967 1.2090 1.2220 1.2357 1.2503 1.2658 1.2822 1.2996 1.3181 1.3378 1.3588 1.3812 1.4051 1.4306 1.4579 1.4872 1.5187 1.5526 1.5890 1.6285 1.6711 1.7174 1.7678 1.8228 1.8831 1.9494 2.0225 2.1035 2.1938
1.1448 1.1541 1.1639 1.1742 1.1852 1.1967 1.2090 1.2220 1.2357 1.2503 1.2658 1.2822 1.2996 1.3181 1.3378 1.3588 1.3812 1.4051 1.4306 1.4579 1.4872 1.5187 1.5526 1.5890 1.6285 1.6711 1.7174 1.7678 1.8228 1.8831 1.9494 2.0225 2.1035 2.1938
1.1404 1.1494 1.1590 1.1690 1.1797 1.1910 1.2029 1.2155 1.2289 1.2430 1.2580 1.2740 1.2909 1.3089 1.3280 1.3483 1.3700 1.3931 1.4178 1.4443 1.4726 1.5030 1.5356 1.5708 1.6087 1.6498 1.6943 1.7426 1.7953 1.8530 1.9162 1.9859 2.0630 2.1487
0.0097 0.0097 0.0098 0.0099 0.0100 0.0101 0.0102 0.0103 0.0104 0.0105 0.0106 0.0108 0.0109 0.0111 0.0112 0.0114 0.0116 0.0118 0.0120 0.0122 0.0125 0.0127 0.0130 0.0133 0.0136 0.0140 0.0143 0.0147 0.0152 0.0157 0.0162 0.0168 0.0175 0.0182
0.54 0.55 0.56 0.57 0.58 0.58 0.59 0.6 0.61 0.62 0.63 0.63 0.64 0.65 0.66 0.67 0.68 0.68 0.69 0.7 0.71 0.72 0.72 0.73 0.74 0.75 0.76 0.77 0.77 0.78 0.79 0.8 0.81 0.82 0.82
1.1739 1.1838 1.1942 1.2052 1.2167 1.2287 1.2415 1.2548 1.2689 1.2837 1.2994 1.3158 1.3332 1.3515 1.3709 1.3913 1.4130 1.4359 1.4603 1.4861 1.5135 1.5428 1.5739 1.6071 1.6426 1.6806 1.7214 1.7653 1.8125 1.8636 1.9188 1.9788 2.0441 2.1154 2.1937
1.1838 1.1942 1.2052 1.2167 1.2287 1.2415 1.2548 1.2689 1.2837 1.2994 1.3158 1.3332 1.3515 1.3709 1.3913 1.4130 1.4359 1.4603 1.4861 1.5135 1.5428 1.5739 1.6071 1.6426 1.6806 1.7214 1.7653 1.8125 1.8636 1.9188 1.9788 2.0441 2.1154 2.1937
1.1788 1.1890 1.1997 1.2109 1.2227 1.2351 1.2482 1.2619 1.2763 1.2915 1.3076 1.3245 1.3423 1.3612 1.3811 1.4022 1.4245 1.4481 1.4732 1.4998 1.5281 1.5583 1.5905 1.6249 1.6616 1.7010 1.7434 1.7889 1.8381 1.8912 1.9488 2.0114 2.0798 2.1546
0.0097 0.0098 0.0099 0.0100 0.0101 0.0102 0.0103 0.0104 0.0105 0.0106 0.0108 0.0109 0.0111 0.0112 0.0114 0.0115 0.0117 0.0119 0.0121 0.0123 0.0126 0.0128 0.0131 0.0134 0.0137 0.0140 0.0144 0.0147 0.0151 0.0156 0.0160 0.0166 0.0171 0.0177
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