ven te chow

ESTACION : HUAQUECHULA

1. PARAMETROS ESTADISTICOS

AÑO Pmax (mm) (P-P) (P-P)^2 (P-P)^31961 49.4 3.60 12.99 46.831962 31.0 -14.80 218.91 -3238.811963 32.0 -13.80 190.31 -2625.481964 46.0 0.20 0.04 0.011965 52.0 6.20 38.50 238.851966 38.0 -7.80 60.77 -473.721967 43.0 -2.80 7.81 -21.851968 48.0 2.20 4.86 10.711969 25.3 -20.50 420.06 -8609.401970 40.0 -5.80 33.59 -194.651971 36.5 -9.30 86.41 -803.181972 37.0 -8.80 77.36 -680.421973 38.1 -7.70 59.22 -455.721974 30.2 -15.60 243.22 -3793.101975 43.7 -2.10 4.39 -9.201976 42.5 -3.30 10.86 -35.791977 54.5 8.70 75.77 659.541978 32.2 -13.60 184.84 -2512.931979 57.5 11.70 137.00 1603.481980 42.0 -3.80 14.41 -54.681981 42.8 -3.00 8.97 -26.881982 20.5 -25.30 639.86 -16185.551983 52.0 6.20 38.50 238.851984 90.0 44.20 1954.04 86377.531985 50.0 4.20 17.68 74.331986 55.0 9.20 84.72 779.841987 60.5 14.70 216.22 3179.471988 50.0 4.20 17.68 74.331989 97.9 52.10 2714.88 141457.781990 41.0 -4.80 23.00 -110.281991 44.0 -1.80 3.22 -5.791992 63.0 17.20 296.00 5092.481993 36.0 -9.80 95.95 -939.881994 46.4 0.60 0.37 0.221995 51.5 5.70 32.54 185.641996 39.5 -6.30 39.63 -249.511997 39.0 -6.80 46.18 -313.801998 32.0 -13.80 190.31 -2625.481999 77.0 31.20 973.72 30384.602000 31.0 -14.80 218.91 -3238.812001 34.0 -11.80 139.13 -1641.132002 36.0 -9.80 95.95 -939.882003 58.0 12.20 148.95 1817.88

2004 49.0 3.20 10.27 32.912015.0 0.00 9888.00 222469.39

NUMERO DE DATOS = n = 44MEDIA MUESTRAL 45.80VARIANZA SESGADA 224.73VARIANZA INSESGADA 229.95COEF. ASIMETRIA SESGADA 2.36COEF. ASIMETRIA INSESGADA 2.36COEF. CURTOSIS SESGADO 5.96COEF. CURTOSIS INSESGADO 6.86DESVIACION ESTANDAR 15.16COEF. DE VARIACION 0.33MEDIA ARITMETICA DE LOGARITMOS 3.78DESVIACION ESTANDAR DE LOGARITMOS 0.30COEF. DE VARIACION DE LOGARITMOS 0.08VARIANZA DE LOGARITMOS 0.09

4.PARAMETROS DE UBICACIÓN ESCALA Y FORMA.

ESTIMACION POR MOMENTOS

A. DISTRIBUCION NORMAL

PARAMETRO UBICACIÓN m = 45.80PARAMETRO ESCALA s = 15.16

B. DISTRIBUCION LOG - NORMAL 2

PARAMETRO UBICACIÓN 3.78

PARAMETRO FORMA 0.09

C. DISTRIBUCION LOG - NORMAL 3 nx = 0.33

w = 0.37 nz = 0.68

PARAMETRO UBICACIÓN X o = 23.55PARANETRO ESCALA m = 2.91PARAMETRO FORMA s = 0.62

D. DISTRIBUCION GAMA 2.

PARAMETRO ESCALA 5.02PARAMETRO FORMA 9.12

my =

s y =

a =b =

E. DISTRIBUCION GAMA 3.

PARAMETRO FORMA 0.72PARAMETRO UBICACIÓN X o = 32.96PARAMETRO ESCALA 17.91

F. DISTRIBUCION LOG- PEARSON TIPO 3

PARAMETRO FORMA 309.63PARAMETRO UBICACIÓN X o = -1.56PARAMETRO ESCALA 0.02

G. DISTRIBUCION GUMBEL

PARAMETRO UBICACIÓN m = 38.97PARAMETRO ESCALA 11.83

5. ESTIMACION DE EVENTOS PARA DIFERENTES PERIODOS DE RETORNO

m Pr Tr F(x) V1 97.9 45.000 0.978 2.7592 90.0 22.500 0.956 2.4953 77.0 15.000 0.933 2.3274 63.0 11.250 0.911 2.2005 60.5 9.000 0.889 2.0966 58.0 7.500 0.867 2.0077 57.5 6.429 0.844 1.9298 55.0 5.625 0.822 1.8599 54.5 5.000 0.800 1.794

10 52.0 4.500 0.778 1.73411 52.0 4.091 0.756 1.67912 51.5 3.750 0.733 1.62613 50.0 3.462 0.711 1.57614 50.0 3.214 0.689 1.52815 49.4 3.000 0.667 1.48216 49.0 2.813 0.644 1.43817 48.0 2.647 0.622 1.39518 46.4 2.500 0.600 1.35419 46.0 2.368 0.578 1.31320 44.0 2.250 0.556 1.27421 43.7 2.143 0.533 1.23522 43.0 2.045 0.511 1.19623 42.8 1.957 0.489 1.19624 42.5 1.875 0.467 1.23525 42.0 1.800 0.444 1.27426 41.0 1.731 0.422 1.31327 40.0 1.667 0.400 1.354

b =

a =

b =

a =

a =

28 39.5 1.607 0.378 1.39529 39.0 1.552 0.356 1.43830 38.1 1.500 0.333 1.48231 38.0 1.452 0.311 1.52832 37.0 1.406 0.289 1.57633 36.5 1.364 0.267 1.62634 36.0 1.324 0.244 1.67935 36.0 1.286 0.222 1.73436 34.0 1.250 0.200 1.79437 32.2 1.216 0.178 1.85938 32.0 1.184 0.156 1.92939 32.0 1.154 0.133 2.00740 31.0 1.125 0.111 2.09641 31.0 1.098 0.089 2.20042 30.2 1.071 0.067 2.32743 25.3 1.047 0.044 2.49544 20.5 1.023 0.022 2.759

6. PRUEBA DE BONDAD DE AJUSTE

m Normal L. Normal 2 L. Normal 3 Gamma 2

1 462.31 2068.82 108.22 277.422 334.85 1523.08 186.08 238.623 69.68 725.83 46.36 43.394 10.99 185.81 8.74 18.895 15.07 136.78 5.03 19.146 22.17 93.66 4.66 22.927 13.82 92.24 0.25 12.018 23.63 56.07 1.32 18.839 16.88 53.88 0.00 11.31

10 29.56 26.70 1.18 20.2911 18.76 29.97 0.05 10.5112 14.27 27.71 0.81 6.5413 18.22 16.33 0.24 8.6314 10.86 18.54 2.25 3.5115 103.25 54.26 138.71 128.8616 78.19 45.37 117.53 102.7017 48.23 30.36 86.43 69.2818 19.92 13.59 51.02 35.0119 10.20 9.40 38.15 22.2020 0.11 0.72 12.94 3.6321 0.66 0.11 7.31 0.6322 5.58 0.35 1.93 0.5223 6.56 0.63 1.42 0.85

( Pr - Pc )2 ( Pr - Pc )2 ( Pr - Pc )2 ( Pr - Pc )2

24 4.06 0.76 2.26 0.1625 2.77 1.33 2.55 0.0126 3.26 3.74 1.39 0.0827 3.75 7.36 0.55 0.2328 2.42 8.94 0.63 0.0329 1.34 10.65 0.71 0.0230 1.30 15.48 0.23 0.0031 0.09 14.43 0.82 0.6132 0.10 20.78 0.19 0.3933 0.04 23.14 0.21 0.9634 0.55 25.53 0.23 1.8535 3.41 22.88 1.02 5.1636 1.04 42.26 0.21 1.4837 0.22 64.01 2.94 0.1738 2.65 62.06 1.84 1.5939 9.72 56.65 0.61 5.7140 14.37 66.18 1.37 6.8841 32.78 59.11 0.27 16.0542 52.73 63.28 0.35 23.2043 29.27 148.12 21.61 3.6844 28.17 254.06 69.46 0.00

1527.82 6180.96 930.11 1143.94

Normal L. Normal 2 L. Normal 3 Gamma 2E.E E.E E.E E.E

6.031 12.131 4.763 5.219

EL METODO QUE MEJOR SE AJUSTA ES EL DE : GUMBEL

7. PRECIPITACIONES MAXIMAS DE DISEÑO. METODO DE GUMBEL

Precipitación con duración de 1 hora y periodo de retrono de 2 años

De la figura 3.2 con P = 45.795 y días con lluvia mayor a 80, se obtiene ::

29.0

Precipitación con duración de 24 h y T = 2 años por el método de Gumbel.

43.31

E.E = (( S ( Xr-Xc )2 / ( N - P ))0.5

( P1h ) 2 años =

( P24 h ) 2 años=

Relacioón entre la precipitacion de 1 h y 24 h, con T = 2 años-

R = 0.670

El valor de R se multiplica por los de las precipitaciones con duración de 24 h

T ( años ) F(x)=1-(1/T)2 0.5000 43.315 0.8000 56.71

10 0.9000 65.5920 0.9500 74.1050 0.9800 85.12

100 0.9900 93.38500 0.9980 112.47

1000 0.9990 120.675000 0.9998 139.71

10000 0.9999 147.91

CURVAS P - D - T .

Estas se obtienen para los diferentes periodos de retorno. Graficando en el papel de la figura 3.3 las precipitaciones de 1 y 24

horas de la tabla anterior. Una vez hecho esto, de ellas se obtienen las precipitaciones para las diferentes duraciones

multiplicando los valores de la precipitación con d = 1 h por las constantes que se anexan. En tanto l os demás valores de las

otras duraciones se determinan de las curvas P - d - T construidas en papel doble logarítmico.

d ( h ) T = 2 años T = 5 años T = 10 años T = 20 años0.0833 8.70 11.39 13.18 14.890.1667 13.05 17.09 19.76 22.33

0.25 16.53 21.65 25.04 28.280.5 22.91 30.00 34.70 39.20

0.75 26.39 34.56 39.97 45.161 29.00 37.98 43.92 49.62

1.5 30.52 39.97 46.23 52.222 31.65 41.45 47.93 54.163 33.31 43.63 50.45 57.004 34.54 45.24 52.32 59.115 35.53 46.53 53.81 60.796 36.36 47.61 55.06 62.21

PT ( 24 h )

Valores de la precipitación en mm. Los valores de la precipitación con duracion de 5, 10, 15, 30 y 45 minutos se obtienen

7 37.07 48.55 56.14 63.438 37.70 49.37 57.10 64.519 38.27 50.11 57.95 65.47

10 38.78 50.78 58.73 66.3511 39.25 51.39 59.44 67.1512 39.68 51.96 60.10 67.8913 40.09 52.49 60.71 68.5814 40.46 52.98 61.28 69.2315 40.82 53.45 61.81 69.8316 41.15 53.88 62.32 70.4017 41.47 54.30 62.80 70.9418 41.77 54.69 63.25 71.4619 42.05 55.06 63.68 71.9520 42.32 55.42 64.10 72.4121 42.59 55.76 64.49 72.8622 42.84 56.09 64.87 73.2923 43.08 56.41 65.24 73.7024 43.31 56.71 65.59 74.10

9. INTENSIDADES MAXIMAS DE LLUVIA.

Los resultados de la tabla anterior se dividen entre la duración correspondiente.

VALORES DE LA INTENSIDAD DE PRECIPITACIONES EN mm / h

d ( h ) T = 2 años T = 5 años T = 10 años T = 20 años0.0833 104.44 136.77 158.18 178.710.1667 78.28 102.52 118.56 133.95

0.25 66.12 86.59 100.14 113.140.5 45.82 60.00 69.40 78.40

0.75 35.19 46.08 53.29 60.211 29.00 37.98 43.92 49.62

1.5 20.35 26.65 30.82 34.822 15.83 20.73 23.97 27.083 11.10 14.54 16.82 19.004 8.64 11.31 13.08 14.785 7.11 9.31 10.76 12.166 6.06 7.94 9.18 10.377 5.30 6.94 8.02 9.068 4.71 6.17 7.14 8.069 4.25 5.57 6.44 7.27

10 3.88 5.08 5.87 6.6411 3.57 4.67 5.40 6.1012 3.31 4.33 5.01 5.6613 3.08 4.04 4.67 5.2814 2.89 3.78 4.38 4.9415 2.72 3.56 4.12 4.66

16 2.57 3.37 3.89 4.4017 2.44 3.19 3.69 4.1718 2.32 3.04 3.51 3.9719 2.21 2.90 3.35 3.7920 2.12 2.77 3.20 3.6221 2.03 2.66 3.07 3.4722 1.95 2.55 2.95 3.3323 1.87 2.45 2.84 3.2024 1.80 2.36 2.73 3.09

CURVAS i - D - T

Con los valores de la intensidad de lluvia de 1 y 24 horas, de la tabla anterior, se pueden construir las curvas i - d - T;

de las cuales se puede obtener la intensidad máxima de diseño para la duración deseada.

5.3. METODO DE VEN TE CHOW

Ven T e Chow desarrolló un método para el cálculo del gasto pico de hidrogramas de diseño de alcantarillas y otras

tiene un área mayor, de cualquier manera se aplicará dicho método.

LAS FORMULAS QUE SE UTILIZAN EN EL METODO DE CHOW SON LAS SIGUIENTES :

GASTO PICO :

TIEMPO DE RETRASO :

PRECIPITACION EN EXCESO

estructuras de drenaje pequeñas en áreas no urbanas menores de 25 Km 2. Sin embargo, aunque en éste proyecto se

p

0.278 Pe Ac ZQ =

de

0.64L

t r = 0.005S

25080

P - + 50.8N

Pe =20320

P + - 203.2N

FACTOR DE REDUCCION : Z = 1 ; cuando : de / tr > 2.0

de = duración en exceso

LOS DATOS CON QUE SE CUENTA SON :

PRECIPITACIONES MAXIMAS ( SE OBTIENEN CON LAS CURVAS " P - d - T " )

PENDIENTE DEL CAUCE PRINCIPAL, EN % S = 15.6

LONGITUD DEL CAUCE PRINCIPAL L = 16000

AREA DE LA CUENCA A = 41.931

NUMERO DE ESCURRIMIENTO N = 81.87

TIEMPO DE RETRASO : tr = 1.018tr = 61.09

SOLUCION :

GASTO MAXIMO PARA T = 2 AÑOS

de (min) de ( h ) P ( mm ) Pe ( mm ) de / tr10 0.167 12.72 0.04 0.1615 0.250 16.11 0.39 0.2520 0.333 17.86 0.70 0.3330 0.500 22.33 1.82 0.4940 0.667 23.86 2.31 0.6545 0.750 25.72 2.96 0.7450 0.833 26.17 3.13 0.8260 1.000 28.26 3.95 0.9870 1.167 29.10 4.30 1.1580 1.333 29.86 4.63 1.3190 1.500 30.54 4.92 1.47

0.6652de

Z = 0.6315t r

0.974de

Z = 0.7401t r

100 1.667 31.16 5.20 1.64110 1.833 31.73 5.47 1.80120 2 32.26 5.72 1.96180 3 34.86 6.98 2.95240 4 36.83 8.00 3.93300 5 38.44 8.86 4.91360 6 39.80 9.61 5.89420 7 40.99 10.29 6.88480 8 42.05 10.90 7.86540 9 43.01 11.46 8.84600 10 43.88 11.98 9.82

1200 20 50.10 15.87 19.641440 24 51.87 17.04 23.57


de (min) de (Hrs) P (mm) Pe (mm) de / tr10 0.167 15.55 0.31 0.1615 0.250 19.65 1.09 0.2520 0.333 22.20 1.78 0.3330 0.500 27.30 3.56 0.4940 0.667 27.65 3.70 0.6545 0.750 27.83 3.77 0.7450 0.833 30.07 4.72 0.8260 1.000 34.55 6.83 0.9870 1.167 35.58 7.35 1.1580 1.333 36.50 7.82 1.3190 1.500 37.33 8.26 1.47

100 1.667 38.08 8.67 1.64110 1.833 38.78 9.05 1.80120 2.000 39.43 9.41 1.96130 2.167 40.03 9.74 2.13140 2.333 40.60 10.07 2.29150 2.5 41.14 10.37 2.46180 3 42.59 11.22 2.95240 4 44.99 12.65 3.93300 5 46.95 13.86 4.91360 6 48.61 14.91 5.89420 7 50.06 15.84 6.88480 8 51.35 16.69 7.86540 9 52.51 17.46 8.84600 10 53.57 18.17 9.82

1200 20 61.14 23.45 19.641440 24 63.30 25.01 23.57

Qmax = 32.95 m 3 / s

Qmax = 54.23 m3/s



100 1.667 42.48 11.15 1.64110 1.833 43.25 11.61 1.80120 2.000 43.98 12.04 1.96130 2.167 44.65 12.44 2.13140 2.333 45.29 12.83 2.29150 2.5 45.88 13.20 2.46180 3 47.50 14.21 2.95240 4 50.18 15.92 3.93300 5 52.35 17.36 4.91360 6 54.20 18.60 5.89420 7 55.82 19.70 6.88480 8 57.25 20.70 7.86540 9 58.55 21.61 8.84600 10 59.74 22.45 9.82

1200 20 68.16 28.62 19.641440 24 70.57 30.45 23.57



100 1.667 46.59 13.63 1.64

Qmax = 69.41 m3/s

110 1.833 47.44 14.17 1.80120 2.000 48.23 14.67 1.96130 2.167 48.97 15.14 2.13140 2.333 49.66 15.59 2.29150 2.5 50.32 16.01 2.46180 3 52.09 17.18 2.95240 4 55.02 19.16 3.93300 5 57.41 20.81 4.91360 6 59.43 22.23 5.89420 7 61.20 23.50 6.88480 8 62.78 24.63 7.86540 9 64.20 25.67 8.84600 10 65.50 26.63 9.82

1200 20 74.73 33.65 19.641440 24 77.36 35.72 23.57



100 1.667 53.98 18.45 1.64110 1.833 54.97 19.12 1.80120 2.000 55.89 19.75 1.96130 2.167 56.74 20.34 2.13140 2.333 57.55 20.90 2.29150 2.5 58.31 21.43 2.46180 3 60.36 22.89 2.95240 4 63.75 25.35 3.93300 5 66.51 27.39 4.91360 6 68.86 29.15 5.89420 7 70.90 30.70 6.88480 8 72.73 32.10 7.86540 9 74.37 33.38 8.84600 10 75.88 34.55 9.82

1200 20 86.56 43.11 19.641440 24 89.61 45.61 23.57

Qmax = 84.58 m3/s



100 1.667 55.60 19.55 1.64110 1.833 56.61 20.25 1.80120 2.000 57.55 20.91 1.96130 2.167 58.44 21.53 2.13140 2.333 59.26 22.11 2.29150 2.5 60.05 22.67 2.46180 3 62.16 24.19 2.95240 4 65.65 26.75 3.93300 5 68.49 28.87 4.91360 6 70.90 30.70 5.89420 7 73.01 32.32 6.88480 8 74.88 33.78 7.86540 9 76.58 35.10 8.84600 10 78.13 36.32 9.82

1200 20 89.11 45.21 19.641440 24 92.25 47.81 23.57


de (min) de (Hrs) P (mm) Pe (mm) de / tr10 0.167 28.25 3.94 0.1615 0.250 33.25 6.18 0.2520 0.333 37.52 8.37 0.3330 0.500 46.08 13.32 0.4940 0.667 50.75 16.29 0.6545 0.750 53.08 17.84 0.7450 0.833 54.83 19.02 0.8260 1.000 58.33 21.45 0.9870 1.167 60.06 22.68 1.1580 1.333 61.60 23.78 1.31

Qmax = 113.88 m3/s

Qmax = 120.56 m3/s

90 1.500 62.99 24.79 1.47100 1.667 64.26 25.72 1.64110 1.833 65.43 26.58 1.80120 2.000 66.52 27.39 1.96130 2.167 67.54 28.15 2.13140 2.333 68.49 28.87 2.29150 2.5 69.40 29.56 2.46180 3 71.84 31.42 2.95240 4 75.86 34.54 3.93300 5 79.14 37.13 4.91360 6 81.93 39.36 5.89420 7 84.36 41.32 6.88480 8 86.52 43.08 7.86540 9 88.47 44.68 8.84600 10 90.26 46.15 9.82600 10 90.26 46.15 9.82

1200 20 102.94 56.83 19.641440 24 106.56 59.94 23.57

Qmax = 157.96 m3/s

(P-P)^4 Ln P (LnP-P)^2168.81 3.90 0.02

47919.61 3.43 0.1236219.63 3.47 0.10

0.00 3.83 0.001481.97 3.95 0.033692.88 3.64 0.02

61.07 3.76 0.0023.62 3.87 0.01

176453.48 3.23 0.301128.11 3.69 0.017465.91 3.60 0.035984.57 3.61 0.033507.01 3.64 0.02

59155.09 3.41 0.1419.28 3.78 0.00

117.94 3.75 0.005740.96 4.00 0.05

34164.49 3.47 0.0918768.01 4.05 0.08

207.52 3.74 0.0080.51 3.76 0.00

409420.85 3.02 0.571481.97 3.95 0.03

3818279.51 4.50 0.52312.52 3.91 0.02

7178.10 4.01 0.0546752.67 4.10 0.11

312.52 3.91 0.027370593.27 4.58 0.65

528.83 3.71 0.0010.39 3.78 0.00

87613.86 4.14 0.139206.58 3.58 0.04

0.13 3.84 0.001058.97 3.94 0.031570.75 3.68 0.012132.43 3.66 0.01

36219.63 3.47 0.10948137.76 4.34 0.3247919.61 3.43 0.1219357.92 3.53 0.069206.58 3.58 0.04

22186.38 4.06 0.08

105.45 3.89 0.0113241947.16 166.21 3.96

5. ESTIMACION DE EVENTOS PARA DIFERENTES PERIODOS DE RETORNO

MODELO DE DISTRIBUCION DE PROBABILIBADESNormal L. Normal 2 L. Normal 3 Gamma 2 Gamma 3 Gumbel

VT Pc Pc Pc Pc Pc Pc 2.018 76.40 52.42 87.50 81.24 89.54 83.861.708 71.70 50.97 76.36 74.55 77.83 75.531.507 68.65 50.06 70.19 70.41 71.17 70.601.353 66.32 49.37 65.96 67.35 66.53 67.051.226 64.38 48.80 62.74 64.88 63.00 64.271.115 62.71 48.32 60.16 62.79 60.14 61.971.017 61.22 47.90 58.00 60.97 57.76 59.990.928 59.86 47.51 56.15 59.34 55.71 58.260.845 58.61 47.16 54.53 57.86 53.93 56.710.768 57.44 46.83 53.09 56.50 52.34 55.310.695 56.33 46.53 51.78 55.24 50.92 54.020.625 55.28 46.24 50.60 54.06 49.64 52.820.559 54.27 45.96 49.51 52.94 48.47 51.700.495 53.30 45.69 48.50 51.87 47.39 50.65-0.432 39.24 42.03 37.62 38.05 36.90 49.65-0.372 40.16 42.26 38.16 38.87 37.33 48.70-0.313 41.06 42.49 38.70 39.68 37.79 47.79-0.254 41.94 42.71 39.26 40.48 38.26 46.92-0.197 42.81 42.93 39.82 41.29 38.76 46.07-0.141 43.66 43.15 40.40 42.09 39.28 45.26-0.084 44.52 43.37 41.00 42.90 39.82 44.46-0.029 45.36 43.59 41.61 43.72 40.40 43.69-0.029 45.36 43.59 41.61 43.72 40.40 42.93-0.084 44.52 43.37 41.00 42.90 39.82 42.18-0.141 43.66 43.15 40.40 42.09 39.28 41.45-0.197 42.81 42.93 39.82 41.29 38.76 40.72-0.254 41.94 42.71 39.26 40.48 38.26 40.01

-0.313 41.06 42.49 38.70 39.68 37.79 39.29-0.372 40.16 42.26 38.16 38.87 37.33 38.58-0.432 39.24 42.03 37.62 38.05 36.90 37.86-0.495 38.30 41.80 37.09 37.22 36.49 37.14-0.559 37.32 41.56 36.57 36.38 36.09 36.41-0.625 36.31 41.31 36.04 35.52 35.71 35.67-0.695 35.26 41.05 35.52 34.64 35.35 34.92-0.768 34.15 40.78 34.99 33.73 35.01 34.14-0.845 32.98 40.50 34.46 32.78 34.68 33.34-0.928 31.73 40.20 33.91 31.79 34.37 32.51-1.017 30.37 39.88 33.36 30.74 34.08 31.63-1.115 28.88 39.53 32.78 29.61 33.81 30.69-1.226 27.21 39.14 32.17 28.38 33.57 29.66-1.353 25.28 38.69 31.52 26.99 33.35 28.52-1.507 22.94 38.16 30.79 25.38 33.16 27.19-1.708 19.89 37.47 29.95 23.38 33.02 25.54-2.018 15.19 36.44 28.83 20.51 32.96 23.16

Gamma 3 Gumbel

69.89 197.00148.13 209.3634.00 41.0012.49 16.436.23 14.224.59 15.740.07 6.220.51 10.640.33 4.900.12 10.931.16 4.063.47 1.742.36 2.896.83 0.42

156.22 0.06136.09 0.09104.30 0.0466.23 0.2752.44 0.0122.29 1.5815.02 0.586.77 0.475.77 0.02

( Pr - Pc )2 ( Pr - Pc )2

7.16 0.107.41 0.305.03 0.083.02 0.002.93 0.042.77 0.181.44 0.062.29 0.740.83 0.350.62 0.690.42 1.170.98 3.450.47 0.434.73 0.094.34 0.143.29 1.736.59 1.795.51 6.178.76 9.07

59.62 0.06155.19 7.08

1138.70 572.39

Gamma 3 GumbelE.E E.E

5.270 3.692

29.0037.9843.9249.6257.0062.5375.3180.8193.5699.05

Estas se obtienen para los diferentes periodos de retorno. Graficando en el papel de la figura 3.3 las precipitaciones de 1 y 24

horas de la tabla anterior. Una vez hecho esto, de ellas se obtienen las precipitaciones para las diferentes duraciones

multiplicando los valores de la precipitación con d = 1 h por las constantes que se anexan. En tanto l os demás valores de las

otras duraciones se determinan de las curvas P - d - T construidas en papel doble logarítmico.

T = 50 años T = 100 años T = 500 años Constantes17.10 18.76 22.59 0.3025.65 28.14 33.89 0.4532.49 35.64 42.93 0.5745.03 49.40 59.50 0.7951.87 56.90 68.53 0.91 m X57.00 62.53 75.31 1.00 1 059.99 65.81 79.26 1.5 1.6662.21 68.25 82.19 2 2.8565.48 71.83 86.51 3 4.5167.90 74.48 89.71 4 5.6969.83 76.61 92.27 5 6.6171.46 78.39 94.42 6 7.36

PT ( 1 h )

Los valores de la precipitación con duracion de 5, 10, 15, 30 y 45 minutos se obtienen

72.86 79.93 96.27 7 7.9974.10 81.29 97.91 8 8.5475.21 82.51 99.38 9 9.0276.22 83.61 100.71 10 9.4677.14 84.63 101.92 11 9.8577.99 85.56 103.05 12 10.2078.78 86.43 104.10 13 10.5379.52 87.24 105.07 14 10.8480.22 88.00 105.99 15 11.1280.87 88.72 106.86 16 11.3981.50 89.40 107.68 17 11.6382.09 90.05 108.46 18 11.8782.65 90.67 109.20 19 12.0983.18 91.26 109.91 20 12.3083.70 91.82 110.59 21 12.5084.19 92.36 111.24 22 12.6984.66 92.88 111.87 23 12.8885.12 93.38 112.47 24 13.05

T = 50 años T = 100 años T = 500 años205.29 225.21 271.23153.88 168.81 203.30129.97 142.57 171.7190.06 98.80 118.9969.16 75.87 91.3857.00 62.53 75.3139.99 43.88 52.8431.10 34.12 41.1021.83 23.94 28.8416.97 18.62 22.4313.97 15.32 18.4511.91 13.07 15.7410.41 11.42 13.759.26 10.16 12.248.36 9.17 11.047.62 8.36 10.077.01 7.69 9.276.50 7.13 8.596.06 6.65 8.015.68 6.23 7.515.35 5.87 7.07

5.05 5.55 6.684.79 5.26 6.334.56 5.00 6.034.35 4.77 5.754.16 4.56 5.503.99 4.37 5.273.83 4.20 5.063.68 4.04 4.863.55 3.89 4.69

Con los valores de la intensidad de lluvia de 1 y 24 horas, de la tabla anterior, se pueden construir las curvas i - d - T;

de las cuales se puede obtener la intensidad máxima de diseño para la duración deseada.

Ven T e Chow desarrolló un método para el cálculo del gasto pico de hidrogramas de diseño de alcantarillas y otras

LAS FORMULAS QUE SE UTILIZAN EN EL METODO DE CHOW SON LAS SIGUIENTES :

estructuras de drenaje pequeñas en áreas no urbanas menores de 25 Km 2. Sin embargo, aunque en éste proyecto se

25080

P - + 50.8N

Pe =20320

P + - 203.2N

; cuando 0.60 < ( de / tr ) < 2.0

; cuando ( de / tr ) < 0.60

PRECIPITACIONES MAXIMAS ( SE OBTIENEN CON LAS CURVAS " P - d - T " )

Z0.127 0.330.188 3.400.249 6.060.370 15.740.477 19.260.516 23.730.553 24.190.624 28.730.691 29.710.755 30.540.817 31.25

Q ( m 3/ s )

0.876 31.870.933 32.420.988 32.921.000 27.131.000 23.311.000 20.651.000 18.681.000 17.131.000 15.881.000 14.841.000 13.971.000 9.251.000 8.27

Z0.127 2.710.188 9.590.249 15.560.370 30.740.477 30.870.516 30.240.553 36.490.624 49.650.691 50.740.755 51.650.817 52.410.876 53.080.933 53.660.988 54.171.000 52.421.000 50.291.000 48.371.000 43.581.000 36.871.000 32.311.000 28.971.000 26.381.000 24.311.000 22.611.000 21.181.000 13.671.000 12.15

Q (m3/s)

Z0.127 5.290.188 15.080.249 19.910.370 31.090.477 48.640.516 56.800.553 59.410.624 64.850.691 65.960.755 66.860.817 67.620.876 68.270.933 68.840.988 69.331.000 66.951.000 64.101.000 61.541.000 55.211.000 46.401.000 40.461.000 36.131.000 32.811.000 30.161.000 27.991.000 26.171.000 16.681.000 14.79

Z0.127 8.380.188 20.960.249 30.700.370 54.000.477 66.450.516 71.130.553 74.070.624 80.220.691 81.290.755 82.160.817 82.880.876 83.50

Q (m3/s)

Q (m3/s)

0.933 84.020.988 84.481.000 81.461.000 77.881.000 74.671.000 66.761.000 55.831.000 48.511.000 43.191.000 39.131.000 35.901.000 33.251.000 31.051.000 19.621.000 17.35

Z0.127 13.150.188 29.550.249 41.770.370 70.360.477 84.080.516 90.680.553 94.010.624 101.010.691 111.170.755 111.900.817 112.500.876 112.990.933 113.400.988 113.751.000 109.441.000 104.421.000 99.951.000 88.951.000 73.871.000 63.851.000 56.631.000 51.131.000 46.781.000 43.231.000 40.281.000 25.131.000 22.16

Q (m3/s)

Z0.127 18.070.188 36.540.249 50.670.370 83.270.477 99.990.516 105.940.553 109.550.624 117.150.691 118.030.755 118.720.817 119.280.876 119.730.933 120.110.988 120.421.000 115.811.000 110.461.000 105.691.000 93.981.000 77.941.000 67.311.000 59.651.000 53.831.000 49.221.000 45.471.000 42.341.000 26.351.000 23.22

Z0.127 35.040.188 54.350.249 72.980.370 114.970.477 135.860.516 142.970.553 147.150.624 156.030.691 156.600.755 157.01

Q (m3/s)

Q (m3/s)

0.817 157.310.876 157.520.933 157.670.988 157.781.000 151.471.000 144.251.000 137.811.000 122.081.000 100.671.000 86.571.000 76.461.000 68.801.000 62.771.000 57.871.000 53.801.000 53.801.000 33.121.000 29.11

AVENIDA MAXIMA . HIDROGRAMA ADIMENSIONAL

DATOS .

AREA DE LA CUENCA A = 41.931

LONGITUD DEL CAUCE PRINCIPAL L = 16

PENDIENTE DEL CAUCE PRINCIPAL S = 0.156875

PRECIPITACION EFECTIVA (Tc=de=1.82=2h) Pe = 5.71 mmPe = 9.40 mmPe = 12.03 mmPe = 14.66 mmPe = 19.74 mmPe = 20.90mmPe = 27.39 mm

SOLUCION

TIEMPO DE CONCENTRACION

DURACION EFECTIVA

TIEMPO DE RETRASO Tr = 0.60 * Tc =

TIEMPO PICO Tp = (de / 2 ) + Tr =

TIEMPO BASE Tb = 5 * Tp =

GASTO PICO UNITARIO

t/tp T=(t/tp)*Tp0 0 0 0

0.1 0.015 0.15 0.09170.2 0.075 0.30 0.45840.3 0.16 0.45 0.97790.4 0.28 0.60 1.71120.5 0.43 0.75 2.62800.6 0.6 0.90 3.66700.8 0.89 1.20 5.43931 1 1.50 6.1116

1.2 0.92 1.80 5.62271.4 0.75 2.10 4.58371.6 0.56 2.39 3.42251.8 0.42 2.69 2.56692 0.32 2.99 1.9557

2.2 0.24 3.29 1.46682.4 0.18 3.59 1.10012.6 0.13 3.89 0.79452.8 0.098 4.19 0.59893 0.075 4.49 0.4584

3.5 0.036 5.24 0.2200

Tc = 0.000235 * ( L0.77 / S0.385 ) =

de = 2 * ( Tc )0.5 = 1.8196 =

qpu = A / ( 4.878 * Tp ) =

q / qu q=(q/qu)*qpu

00

.14

96

70

.29

93

40

.44

90

10

.59

86

80

.74

83

50

.89

80

21

.19

73

61

.49

67

1.7

96

04

2.0

95

38

2.3

94

72

2.6

94

06

2.9

93

43

.29

27

43

.59

20

83

.89

14

24

.19

07

64

.49

01

5.2

38

45

5.9

86

86

.73

51

57

.48

35

0

1

2

3

4

5

6

7

HIDROGRAMA UNITARIO ADIMENSIONAL

t (hrs)

q (

m3

/s/m

m)

4 0.018 5.99 0.11004.5 0.009 6.74 0.05505 0.004 7.48 0.0244

HIDROGRAMA ADIMENSIONAL PARA T = 500 AÑOS Pe = 27.39

t/tp T=(t/tp)*Tp Q = q * Pe0 0 0 0 0

0.1 0.015 0.15 0.0917 2.51100.2 0.075 0.30 0.4584 12.55480.3 0.16 0.45 0.9779 26.78350.4 0.28 0.60 1.7112 46.87110.5 0.43 0.75 2.6280 71.98060.6 0.6 0.90 3.6670 100.43800.8 0.89 1.20 5.4393 148.98311 1 1.50 6.1116 167.3967

1.2 0.92 1.80 5.6227 154.00501.4 0.75 2.10 4.5837 125.54751.6 0.56 2.39 3.4225 93.74221.8 0.42 2.69 2.5669 70.30662 0.32 2.99 1.9557 53.5670

2.2 0.24 3.29 1.4668 40.17522.4 0.18 3.59 1.1001 30.13142.6 0.13 3.89 0.7945 21.76162.8 0.098 4.19 0.5989 16.40493 0.075 4.49 0.4584 12.5548

3.5 0.036 5.24 0.2200 6.02634 0.018 5.99 0.1100 3.0131

4.5 0.009 6.74 0.0550 1.50665 0.004 7.48 0.0244 0.6696

q / qu q=(q/qu)*qpu

0

0.1

49

67

0.2

99

34

0.4

49

01

0.5

98

68

0.7

48

35

0.8

98

02

1.1

97

36

1.4

96

7

1.7

96

04

2.0

95

38

2.3

94

72

2.6

94

06

2.9

93

4

3.2

92

74

3.5

92

08

3.8

91

42

4.1

90

76

4.4

90

1

5.2

38

45

5.9

86

8

6.7

35

15

7.4

83

5

0

20

40

60

80

100

120

140

160

180

HIDROGRAMA ADIMENSIONAL. T = 500 AÑOS

t(hrs)

Q (

m3

/s)

HIDROGRAMA INSTANTANEO . T = 500 AÑOS

SE UTILIZARA EL HIDROGRAMA UNITARIO ADIMENSIONAL OBTENIDO ANTERIORMENTE, EN EL CUAL

de = 1.82 hrs. SE HA SUPUESTO QUE de=2.0 hrs, POR LO QUE EL GASTO PARA INCREMENTOS DE 2

hrs SE TIENE QUE INTERPOLAR;ADEMAS DE QUE EL HIETOGRAMA DEBE CALCULARSE CON de=2hrs

HIETOGRAMA T=(t/tp)*Tp q=(q/qu)*qpu TBARRA T Pe 0 0 0

--------- 0 0 0.14967 0.091674 0.149671 2 27.39 0.29934 0.45837 0.299342 4 7.15 0.44901 0.977856 0.449013 6 4.81 0.59868 1.711248 0.598684 8 3.72 0.74835 2.627988 0.748355 10 3.07 0.89802 3.66696 0.898026 12 2.63 1.19736 5.439324 1.197367 14 2.32 1.4967 6.1116 1.49678 16 2.08 1.79604 5.622672 1.796049 18 1.89 2.09538 4.5837 2

10 20 1.73 2.39472 3.422496 411 22 1.6 2.69406 2.566872 612 24 3.1 2.9934 1.955712

3.29274 1.4667843.59208 1.1000883.89142 0.7945084.19076 0.5989368

4.4901 0.458375.23845 0.2200176

5.9868 0.11000886.73515 0.0550044

7.4835 0.0244464

i U P1*U P2*U P3*U T1 4.912 134.5397 35.1208 23.6267 0.00002 0.723 19.8030 5.1695 3.4776 2.00003 0.11 3.0129 0.7865 0.5291 4.0000

6.00008.0000

10.000012.0000

0

0.1

49

67

0.2

99

34

0.4

49

01

0.5

98

68

0.7

48

35

0.8

98

02

1.1

97

36

1.4

96

7

1.7

96

04

2.0

95

38

2.3

94

72

2.6

94

06

2.9

93

4

3.2

92

74

3.5

92

08

3.8

91

42

4.1

90

76

4.4

90

1

5.2

38

45

5.9

86

8

6.7

35

15

7.4

83

5

0

20

40

60

80

100

120

140

160

180


t(hrs)

Q (

m3

/s)

0.0000 2.0000 4.0000 6.0000 8.0000 10.0000 12.00000

20

40

60

80

100

120

140

160

de = 1 hr. Tr = 0.4967 hrs Tp = Tr + de / 2 =

Tb = 5 * Tp = 5 8.6244

HIETOGRAMA .T=500 AÑOS HIDROGRAMA UNITARIO .

d (hrs) Pe (mm) Ape t/tp T=(t/tp)*Tp0 0.00 0 0 0 01 21.45 21.45 0.1 0.015 0.102 27.393 5.94 0.2 0.075 0.203 31.418 4.02 0.3 0.16 0.304 34.544 3.13 0.4 0.28 0.405 37.131 2.59 0.5 0.43 0.506 39.356 2.23 0.6 0.6 0.607 41.317 1.96 0.8 0.89 0.808 43.078 1.76 1 1 1.009 44.68 1.60 2 0.32 2.00

10 46.152 1.47 3 0.075 3.0011 4 0.018 4.0012 5 0.004 5.00

i U P1*U P2*U P3*U P4*U1 8.6244 184.9934 51.2548 34.7132 26.95992 2.7598 59.1977 11.1082 8.6271 7.13963 0.6468 13.8739 2.0219 1.6733 1.43914 0.1552 3.3290 0.4015 0.3453 0.3043

HIDROGRAMA ADIMENSIONAL 1 - A

Pe = 22.548 mm

t/tp T=(t/tp)*Tp Q = q * Pe0.0 0.000 0 0 00.1 0.015 0.04 0.0004 0.00880.2 0.075 0.09 0.0020 0.04400.3 0.160 0.13 0.0042 0.09380.4 0.280 0.18 0.0073 0.16410.5 0.430 0.22 0.0112 0.25210.6 0.600 0.27 0.0156 0.35170.8 0.890 0.35 0.0231 0.52181.0 1.000 0.44 0.0260 0.58621.2 0.920 0.53 0.0239 0.53931.4 0.750 0.62 0.0195 0.43971.6 0.560 0.71 0.0146 0.3283

qpu = A / ( 4.878 * Tp ) =

q / qu

q / qu q=(q/qu)*qu

0.0000 2.0000 4.0000 6.0000 8.0000 10.0000 12.00000

20

40

60

80

100

120

140

160

1.8 0.420 0.80 0.0109 0.24622.0 0.320 0.88 0.0083 0.18762.2 0.240 0.97 0.0062 0.14072.4 0.180 1.06 0.0047 0.10552.6 0.130 1.15 0.0034 0.07622.8 0.098 1.24 0.0025 0.05753.0 0.075 1.33 0.0020 0.04403.5 0.036 1.55 0.0009 0.02114.0 0.018 1.77 0.0005 0.01064.5 0.009 1.99 0.0002 0.00535.0 0.004 2.21 0.0001 0.0023

0

0.0

44

2

0.0

88

4

0.1

32

6

0.1

76

8

0.2

21

0.2

65

2

0.3

53

6

0.4

42

0.5

30

4

0.6

18

8

0.7

07

2

0.7

95

6

0.8

84

0.9

72

4

1.0

60

8

1.1

49

2

1.2

37

6

1.3

26

1.5

47

1.7

68

1.9

89

2.2

1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

t (h)

Q (

m3

/ s

)

Km

T = 2 AÑOST = 5 AÑOST = 10 AÑOST = 20 AÑOST = 50 AÑOST=100 AÑOST=500 AÑOS

0.8278

2

0.4967

1.4967

7.0325

6.1116

Km2

00

.14

96

70

.29

93

40

.44

90

10

.59

86

80

.74

83

50

.89

80

21

.19

73

61

.49

67

1.7

96

04

2.0

95

38

2.3

94

72

2.6

94

06

2.9

93

43

.29

27

43

.59

20

83

.89

14

24

.19

07

64

.49

01

5.2

38

45

5.9

86

86

.73

51

57

.48

35

0

1

2

3

4

5

6

7

HIDROGRAMA UNITARIO ADIMENSIONAL

t (hrs)

q (

m3

/s/m

m)

mm

0

0.1

49

67

0.2

99

34

0.4

49

01

0.5

98

68

0.7

48

35

0.8

98

02

1.1

97

36

1.4

96

7

1.7

96

04

2.0

95

38

2.3

94

72

2.6

94

06

2.9

93

4

3.2

92

74

3.5

92

08

3.8

91

42

4.1

90

76

4.4

90

1

5.2

38

45

5.9

86

8

6.7

35

15

7.4

83

5

0

20

40

60

80

100

120

140

160

180


t(hrs)

Q (

m3

/s)

q0

0.0916740.45837

0.9778561.7112482.627988

3.666965.439324

6.11165.622672

4.9120.723

0.11

Q0

134.5454.9231.794.250.52

0

0

0.1

49

67

0.2

99

34

0.4

49

01

0.5

98

68

0.7

48

35

0.8

98

02

1.1

97

36

1.4

96

7

1.7

96

04

2.0

95

38

2.3

94

72

2.6

94

06

2.9

93

4

3.2

92

74

3.5

92

08

3.8

91

42

4.1

90

76

4.4

90

1

5.2

38

45

5.9

86

8

6.7

35

15

7.4

83

5

0

20

40

60

80

100

120

140

160

180


t(hrs)

Q (

m3

/s)

0.9967

00.12940.64681.37992.41483.70855.17467.67578.62442.75980.64680.15520.0345

Q0

184.9934110.4525

59.6953

Pe = 22.548 mm

q=(q/qu)*qpu

0

0.0

44

2

0.0

88

4

0.1

32

6

0.1

76

8

0.2

21

0.2

65

2

0.3

53

6

0.4

42

0.5

30

4

0.6

18

8

0.7

07

2

0.7

95

6

0.8

84

0.9

72

4

1.0

60

8

1.1

49

2

1.2

37

6

1.3

26

1.5

47

1.7

68

1.9

89

2.2

1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

t (h)

Q (

m3

/ s

)

ven te chow

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