Problema Analisis de Frecuencia -Villon

Hidrologia General UNSCH

Curso : Hidrologa GeneralAlumno : AYALA BIZARRO, Rocky Giban Cdigo :

Problema de anlisis de frecuencia de tormentas

5 10 15 20 30 40 60 80 100Telpatlan.Pue

1956 Jun-15 120 81.5 54.8 41.7Ago-20 36 34.8 25.7 21.5 18.2

1957 Feb-23 51 36 28.8 20.4 16.1 12.7 12.3 10.9Jun-27 84Jul-26

1958 Jun-16 20.7Ago-01 11.6Set-11 23.4 16.5 13.7 11.6Set-15 116.4 58.2 40.4 30.3

1959 Jun-07 48.1 38 32.2Set-26 240 162 128 111 84 67.5

1960 Ago-18 122.4Set-09 42.6 31.4 18 17.3Set-20 23Oct-28 122.4 59 52 30

1961 May-23 15.8 13.9Jul-30 48Jul-31 25.6 21.9 18.2 11.8 11.7Set-10 30

1962 Abr-11 120 120 84 82.8 60 48.9 32.7 24.5 19.61963 Ago-10

Nov-26 116.4 58.2 51.6 44.7 36.4 29 19.3 14.5 11.61964 Jun-15 36 27 26 24 16.6 12.8

Ago-22 9.5 8.1 7.11965 Oct-06 78 55.2 48 48 41.8 34.2 29.5 22.9 18.71966 Oct-18 78 60 52 47.4 46 40.5 29.2 22.9 18.91967 Jun-17 54 34 23.4 18.8 14 11.6 11.6

Jun-22 45 28.51968 Jun-29 84 48 32 24 16 12 8 6

Jul-02 6Oct-12 5.3

1969 Ago-19 54 54 45.2 41.7 31.8 25.1 17.8 13.4Ago-19Ago-29 12

1970 Jun-25 120 84 72 57.6 41 31.1 22.5 17 13.7Ago-04

FechasDuracin (min)

Universidad Nacional de san Cristbal de Huamanga

16110956

Escuela de Formacin Profesional de Ingeniera Civil

Ayala Bizarro Rocky Pag. 1


PREGUNTA 01

Tabla 01: Intensidad maxima para periodos de duracion de 5, 10, 15, 20, 30, 40, 60, 80, 100, 120

5 10 15 20 30 40 60 80 100 1201956 120.0 81.5 54.8 41.7 36.0 34.8 25.7 21.5 18.2 16.81957 84.0 51.0 36.0 28.8 20.4 16.1 12.7 12.3 10.9 9.51958 116.4 58.2 40.4 30.3 23.4 20.7 16.5 13.7 11.6 10.11959 240.0 162.0 128.0 111.0 84.0 67.5 48.1 38.0 32.2 27.61960 122.4 59.0 52.0 42.6 31.4 30.0 23.0 18.0 17.3 15.51961 48.0 30.0 25.6 21.9 18.2 15.8 13.9 11.8 11.7 10.31962 120.0 120.0 84.0 82.8 60.0 48.9 32.7 24.5 19.6 16.41963 116.4 58.2 51.6 44.7 36.4 29.0 19.3 14.5 11.6 10.11964 36.0 27.0 26.0 24.0 16.6 12.8 9.5 8.1 7.1 6.31965 78.0 55.2 48.0 48.0 41.8 34.2 29.5 22.9 18.7 15.91966 78.0 60.0 52.0 47.4 46.0 40.5 29.2 22.9 18.9 16.31967 54.0 45.0 34.0 28.5 23.4 18.8 14.0 11.6 11.6 10.61968 84.0 48.0 32.0 24.0 16.0 12.0 8.0 6.0 5.3 4.71969 54.0 54.0 45.2 41.7 31.8 25.1 17.8 13.4 12.0 10.01970 120.0 84.0 72.0 57.6 41.0 31.1 22.5 17.0 13.7 12.0

Periodo de Retorno :

5 10 15 20 30 40 60 80 100 1201 16.00 240.0 162.0 128.0 111.0 84.0 67.5 48.1 38.0 32.2 27.62 8.00 122.4 120.0 84.0 82.8 60.0 48.9 32.7 24.5 19.6 16.83 5.33 120.0 84.0 72.0 57.6 46.0 40.5 29.5 22.9 18.9 16.44 4.00 120.0 81.5 54.8 48.0 41.8 34.8 29.2 22.9 18.7 16.35 3.20 120.0 60.0 52.0 47.4 41.0 34.2 25.7 21.5 18.2 15.96 2.67 116.4 59.0 52.0 44.7 36.4 31.1 23.0 18.0 17.3 15.57 2.29 116.4 58.2 51.6 42.6 36.0 30.0 22.5 17.0 13.7 12.08 2.00 84.0 58.2 48.0 41.7 31.8 29.0 19.3 14.5 12.0 10.69 1.78 84.0 55.2 45.2 41.7 31.4 25.1 17.8 13.7 11.7 10.310 1.60 78.0 54.0 40.4 30.3 23.4 20.7 16.5 13.4 11.6 10.111 1.45 78.0 51.0 36.0 28.8 23.4 18.8 14.0 12.3 11.6 10.112 1.33 54.0 48.0 34.0 28.5 20.4 16.1 13.9 11.8 11.6 10.013 1.23 54.0 45.0 32.0 24.0 18.2 15.8 12.7 11.6 10.9 9.514 1.14 48.0 30.0 26.0 24.0 16.6 12.8 9.5 8.1 7.1 6.315 1.07 36.0 27.0 25.6 21.9 16.0 12.0 8.0 6.0 5.3 4.7

Construimos la curva i-d-p (intensidad-duracion-periodo de retorno)

Eje X = Duraciones (min)Eje Y = Intensidades (mm/hr)

m

FechasDuracin (min)

Ordenamos en forma decreciente e independiente del tiempo(ao) los valore de i(max), calcular su periodo de retorno para cada valor utilizando la formula de Weibull.

Ordenamos los datos tomando la intensidad mayor de cada ao para cada peridodo

Duracin (min)Periodo Retorno

1



PREGUNTA 02

1. Hubicamos en el eje X, la duracion de 45 min2. Trazamos una paralela hasta ubicar el periodo de retorno de 10 aos, como no existe haremos un trazo por interpolacin

Nos pide hallar la intensidad maxima con una duracion de 45 min, que tiene un periodo de duracion de 10 aos

Haciendo los trazos en los ejes e interpolando el periodo de retorno para 10 aos, se obtiene que la intensidad mxima resulta 50 mm/hr.

0.0

50.0

100.0

150.0

200.0

250.0

300.0

0 10 20 30 40 50 60 70 80 90 100 110 120 130

Inte

nsid

ad (

mm

/hr)

Duracion (min)

CURVAIDP

16 aos

8 aos

4 aos

2 aos

1.07 aos

0

50

100

150

200

250

300

0 10 20 30 40 50 60 70 80 90 100 110 120 130

Inte

nsid

ad (

mm

/hr)

Duracion (min)

CURVAIDP

16aos

8aos



PREGUNTA 03

Usando la formula de Talbot :

a,b : parametros que dependen de la localidad y del periodo de retorno.D: duracion de la precipitacion en min

Nos piden hallar las ecuaciones para periodos de retorno de 16, 10, 8, 4 y 2 aos

Para tiempo de retorno de 16 aos

5 240.0 0.0042 0.021 2510 162.0 0.0062 0.062 10015 128.0 0.0078 0.117 22520 111.0 0.009 0.180 40030 84.0 0.0119 0.357 90040 67.5 0.0148 0.593 160060 48.1 0.0208 1.247 360080 38.0 0.0263 2.105 6400100 32.2 0.0311 3.106 10000

n=10 120 27.6 0.0362 4.348 14400Suma 480 938.4 0.1683 12.14 37650

(Suma X)^2 = 230400PROM X = 48.0PROM Y = 0.0168

b1= 0.00028 a = 3599.78a1= 0.00349 b = 12.575

Entonces la intensidad maxima tendra la formula sigueinte :


5 122.4 0.0082 0.041 2510 120.0 0.0083 0.083 10015 84.0 0.0119 0.179 22520 82.8 0.0121 0.242 40030 60.0 0.0167 0.500 90040 48.9 0.0204 0.818 160060 32.7 0.0306 1.835 360080 24.5 0.0408 3.265 6400100 19.6 0.051 5.102 10000

n=10 120 16.8 0.0595 7.143 14400Suma 480 611.7 0.2595 19.21 37650

X^2X=D Imax Y=1/Imax

XY

X=D Imax Y=1/Imax

XY X^2

3599.812.578




b1= 0.00046 a = 2164.68a1= 0.00378 b = 8.183



5 120.0 0.0083 0.042 2510 81.5 0.0123 0.123 10015 54.8 0.0182 0.274 22520 48.0 0.0208 0.417 40030 41.8 0.0239 0.718 90040 34.8 0.0287 1.149 160060 29.2 0.0342 2.055 360080 22.9 0.0437 3.493 6400100 18.7 0.0535 5.348 10000

n=10 120 16.3 0.0613 7.362 14400Suma 480 468 0.3051 20.98 37650


b1= 0.00043 a = 2306a1= 0.00969 b = 22.352



5 84.0 0.0119 0.060 2510 58.2 0.0172 0.172 10015 48.0 0.0208 0.313 22520 41.7 0.024 0.480 40030 31.8 0.0314 0.943 90040 29.0 0.0345 1.379 160060 19.3 0.0518 3.109 360080 14.5 0.069 5.517 6400

X=D Imax Y=1/Imax

XY X^2

X=D Imax Y=1/Imax

XY X^2

2164.78.183

230622.352



100 12.0 0.0833 8.333 10000n=10 120 10.6 0.0943 11.321 14400Suma 480 349.1 0.4383 31.63 37650


b1= 0.00072 a = 1379.77a1= 0.00904 b = 12.473



16 aos 10 aos8 aos240.0 169.4 122.4162.0 136.6 120.0128.0 97.66 84.0111.0 92.3 82.884.0 67.41 60.067.5 54.82 48.948.1 37.55 32.738.0 28.94 24.532.2 23.89 19.627.6 20.62 16.8

Con los datos obtenido de la interpolacion podemos continuar utilizando la formula de Talbot

5 169.4 0.0059 0.030 2510 136.6 0.0073 0.073 10015 97.7 0.0102 0.154 22520 92.3 0.0108 0.217 40030 67.4 0.0148 0.445 90040 54.8 0.0182 0.730 160060 37.6 0.0266 1.598 360080 28.9 0.0346 2.764 6400100 23.9 0.0419 4.185 10000

n=10 120 20.6 0.0485 5.819 14400Suma 480 729.24 0.2189 16.01 37650

(Suma X)^2 = 230400PROM X = 48.0

X=D Imax Y=1/Imax

XY X^2

Para este caso no se tienen valores de i max para un periodo de retorno de T=10 aos, por ello se calculavalores interpolando entre T=16 aos y T=8 aos

Tiempo de Retorno

1379.812.473



PROM Y = 0.0219

b1= 0.00038 a = 2653.09a1= 0.00380 b = 10.076


PREGUNTA 04

Ecuacion para T= 10aos

Reemplazando para un D=45 min

i max = 48.1698 mm/hr

PREGUNTA 05

a,b,k : parametros utilizando la formula de correlacion potencial multiple.Usando este mtodo hallaremos a,b, k que son los parmetros regionales.

Aplicando logaritmos linealizamos la ecuacin donde:

D min T aos I mm/hr

5 16.00 240.010 16.00 162.0

Hallamos el i max para T=10 aos y una duracion D= 45min, esto utilizando la ecuacion obtenida depregunta 3

La intensidad maxima para T=10 aos con la formula obtenida en la interpolacion de la formula de Tes 48.17 mm/hr

Tomamos un tiempo de retorno, las duraciones dadas a este tiempo de retorno y las

intensidades para este tiempo de retorno. Repetimos estos datos para todos los tiempos de retorno. En la tabla se observa para todos los tiempos dretorno.

Usando la formula de USA :

265310.076

265310.076

265310.076 45



15 16.00 128.020 16.00 111.030 16.00 84.040 16.00 67.560 16.00 48.180 16.00 38.0100 16.00 32.2120 16.00 27.65 8.00 122.410 8.00 120.015 8.00 84.020 8.00 82.830 8.00 60.040 8.00 48.960 8.00 32.780 8.00 24.5100 8.00 19.6120 8.00 16.85 5.33 120.010 5.33 84.015 5.33 72.020 5.33 57.630 5.33 46.040 5.33 40.560 5.33 29.580 5.33 22.9100 5.33 18.9120 5.33 16.45 4.00 120.010 4.00 81.515 4.00 54.820 4.00 48.030 4.00 41.840 4.00 34.860 4.00 29.280 4.00 22.9100 4.00 18.7120 4.00 16.35 3.20 120.010 3.20 60.015 3.20 52.020 3.20 47.430 3.20 41.040 3.20 34.260 3.20 25.780 3.20 21.5100 3.20 18.2



120 3.20 15.95 2.67 116.410 2.67 59.015 2.67 52.020 2.67 44.730 2.67 36.440 2.67 31.160 2.67 23.080 2.67 18.0100 2.67 17.3120 2.67 15.55 2.29 116.410 2.29 58.215 2.29 51.620 2.29 42.630 2.29 36.040 2.29 30.060 2.29 22.580 2.29 17.0100 2.29 13.7120 2.29 12.05 2.00 84.010 2.00 58.215 2.00 48.020 2.00 41.730 2.00 31.840 2.00 29.060 2.00 19.380 2.00 14.5100 2.00 12.0120 2.00 10.65 1.78 84.010 1.78 55.215 1.78 45.220 1.78 41.730 1.78 31.440 1.78 25.160 1.78 17.880 1.78 13.7100 1.78 11.7120 1.78 10.35 1.60 78.010 1.60 54.015 1.60 40.420 1.60 30.330 1.60 23.440 1.60 20.7



60 1.60 16.580 1.60 13.4100 1.60 11.6120 1.60 10.15 1.45 78.010 1.45 51.015 1.45 36.020 1.45 28.830 1.45 23.440 1.45 18.860 1.45 14.080 1.45 12.3100 1.45 11.6120 1.45 10.15 1.33 54.010 1.33 48.015 1.33 34.020 1.33 28.530 1.33 20.440 1.33 16.160 1.33 13.980 1.33 11.8100 1.33 11.6120 1.33 10.05 1.23 54.010 1.23 45.015 1.23 32.020 1.23 24.030 1.23 18.240 1.23 15.860 1.23 12.780 1.23 11.6100 1.23 10.9120 1.23 9.55 1.14 48.010 1.14 30.015 1.14 26.020 1.14 24.030 1.14 16.640 1.14 12.860 1.14 9.580 1.14 8.1100 1.14 7.1120 1.14 6.35 1.07 36.010 1.07 27.015 1.07 25.6



20 1.07 21.930 1.07 16.040 1.07 12.060 1.07 8.080 1.07 6.0100 1.07 5.3120 1.07 4.7

Se resuelve el siguiente sistema de ecuaciones lineales, de donde obtendremos

Donde:

Hallamos las respectivas sumatorias y lo reemplazamos los valores de la frmula anterior

x1=log(T) x2=log(D) y=log(I) x1^2 x1*x2 x2^2 x1*y x2*y

1.204 0.699 2.380 1.450 0.842 0.489 2.866 1.6641.204 1.000 2.210 1.450 1.204 1.000 2.661 2.2101.204 1.176 2.107 1.450 1.416 1.383 2.537 2.4781.204 1.301 2.045 1.450 1.567 1.693 2.463 2.6611.204 1.477 1.924 1.450 1.779 2.182 2.317 2.8421.204 1.602 1.829 1.450 1.929 2.567 2.203 2.9311.204 1.778 1.682 1.450 2.141 3.162 2.026 2.9911.204 1.903 1.580 1.450 2.292 3.622 1.902 3.0061.204 2.000 1.508 1.450 2.408 4.000 1.816 3.0161.204 2.079 1.441 1.450 2.504 4.323 1.735 2.9960.903 0.699 2.088 0.816 0.631 0.489 1.885 1.4590.903 1.000 2.079 0.816 0.903 1.000 1.878 2.0790.903 1.176 1.924 0.816 1.062 1.383 1.738 2.2630.903 1.301 1.918 0.816 1.175 1.693 1.732 2.4950.903 1.477 1.778 0.816 1.334 2.182 1.606 2.6270.903 1.602 1.689 0.816 1.447 2.567 1.526 2.7060.903 1.778 1.515 0.816 1.606 3.162 1.368 2.6930.903 1.903 1.389 0.816 1.719 3.622 1.255 2.6440.903 2.000 1.292 0.816 1.806 4.000 1.167 2.5850.903 2.079 1.225 0.816 1.878 4.323 1.107 2.5480.727 0.699 2.079 0.529 0.508 0.489 1.512 1.4530.727 1.000 1.924 0.529 0.727 1.000 1.399 1.9240.727 1.176 1.857 0.529 0.855 1.383 1.350 2.1840.727 1.301 1.760 0.529 0.946 1.693 1.280 2.2900.727 1.477 1.663 0.529 1.074 2.182 1.209 2.4560.727 1.602 1.607 0.529 1.165 2.567 1.169 2.5750.727 1.778 1.470 0.529 1.293 3.162 1.069 2.614



0.727 1.903 1.360 0.529 1.384 3.622 0.989 2.5880.727 2.000 1.276 0.529 1.454 4.000 0.928 2.5530.727 2.079 1.215 0.529 1.512 4.323 0.883 2.5260.602 0.699 2.079 0.362 0.421 0.489 1.252 1.4530.602 1.000 1.911 0.362 0.602 1.000 1.151 1.9110.602 1.176 1.739 0.362 0.708 1.383 1.047 2.0450.602 1.301 1.681 0.362 0.783 1.693 1.012 2.1870.602 1.477 1.621 0.362 0.889 2.182 0.976 2.3950.602 1.602 1.542 0.362 0.965 2.567 0.928 2.4700.602 1.778 1.465 0.362 1.071 3.162 0.882 2.6060.602 1.903 1.360 0.362 1.146 3.622 0.819 2.5880.602 2.000 1.272 0.362 1.204 4.000 0.766 2.5440.602 2.079 1.212 0.362 1.252 4.323 0.730 2.5200.505 0.699 2.079 0.255 0.353 0.489 1.050 1.4530.505 1.000 1.778 0.255 0.505 1.000 0.898 1.7780.505 1.176 1.716 0.255 0.594 1.383 0.867 2.0180.505 1.301 1.676 0.255 0.657 1.693 0.847 2.1800.505 1.477 1.613 0.255 0.746 2.182 0.815 2.3820.505 1.602 1.534 0.255 0.809 2.567 0.775 2.4580.505 1.778 1.410 0.255 0.898 3.162 0.712 2.5070.505 1.903 1.332 0.255 0.961 3.622 0.673 2.5360.505 2.000 1.260 0.255 1.010 4.000 0.637 2.5200.505 2.079 1.201 0.255 1.050 4.323 0.607 2.4980.426 0.699 2.066 0.181 0.298 0.489 0.880 1.4440.426 1.000 1.771 0.181 0.426 1.000 0.754 1.7710.426 1.176 1.716 0.181 0.501 1.383 0.731 2.0180.426 1.301 1.650 0.181 0.554 1.693 0.703 2.1470.426 1.477 1.561 0.181 0.629 2.182 0.665 2.3060.426 1.602 1.493 0.181 0.682 2.567 0.636 2.3910.426 1.778 1.362 0.181 0.757 3.162 0.580 2.4210.426 1.903 1.255 0.181 0.811 3.622 0.535 2.3890.426 2.000 1.238 0.181 0.852 4.000 0.527 2.4760.426 2.079 1.190 0.181 0.886 4.323 0.507 2.4750.359 0.699 2.066 0.129 0.251 0.489 0.742 1.4440.359 1.000 1.765 0.129 0.359 1.000 0.634 1.7650.359 1.176 1.713 0.129 0.422 1.383 0.615 2.0140.359 1.301 1.629 0.129 0.467 1.693 0.585 2.1200.359 1.477 1.556 0.129 0.530 2.182 0.559 2.2990.359 1.602 1.477 0.129 0.575 2.567 0.530 2.3660.359 1.778 1.352 0.129 0.638 3.162 0.485 2.4040.359 1.903 1.230 0.129 0.683 3.622 0.442 2.3420.359 2.000 1.137 0.129 0.718 4.000 0.408 2.2730.359 2.079 1.079 0.129 0.746 4.323 0.387 2.2440.301 0.699 1.924 0.091 0.210 0.489 0.579 1.3450.301 1.000 1.765 0.091 0.301 1.000 0.531 1.7650.301 1.176 1.681 0.091 0.354 1.383 0.506 1.9770.301 1.301 1.620 0.091 0.392 1.693 0.488 2.1080.301 1.477 1.502 0.091 0.445 2.182 0.452 2.2190.301 1.602 1.462 0.091 0.482 2.567 0.440 2.3430.301 1.778 1.286 0.091 0.535 3.162 0.387 2.2860.301 1.903 1.161 0.091 0.573 3.622 0.350 2.2100.301 2.000 1.079 0.091 0.602 4.000 0.325 2.158



0.301 2.079 1.025 0.091 0.626 4.323 0.309 2.1320.250 0.699 1.924 0.062 0.175 0.489 0.481 1.3450.250 1.000 1.742 0.062 0.250 1.000 0.435 1.7420.250 1.176 1.655 0.062 0.294 1.383 0.414 1.9470.250 1.301 1.620 0.062 0.325 1.693 0.405 2.1080.250 1.477 1.497 0.062 0.369 2.182 0.374 2.2110.250 1.602 1.400 0.062 0.400 2.567 0.350 2.2420.250 1.778 1.250 0.062 0.444 3.162 0.312 2.2230.250 1.903 1.137 0.062 0.476 3.622 0.284 2.1630.250 2.000 1.068 0.062 0.500 4.000 0.267 2.1360.250 2.079 1.013 0.062 0.520 4.323 0.253 2.1060.204 0.699 1.892 0.042 0.143 0.489 0.386 1.3230.204 1.000 1.732 0.042 0.204 1.000 0.354 1.7320.204 1.176 1.606 0.042 0.240 1.383 0.328 1.8890.204 1.301 1.481 0.042 0.266 1.693 0.302 1.9270.204 1.477 1.369 0.042 0.302 2.182 0.279 2.0220.204 1.602 1.316 0.042 0.327 2.567 0.269 2.1080.204 1.778 1.217 0.042 0.363 3.162 0.249 2.1650.204 1.903 1.127 0.042 0.388 3.622 0.230 2.1450.204 2.000 1.064 0.042 0.408 4.000 0.217 2.1290.204 2.079 1.004 0.042 0.424 4.323 0.205 2.0880.163 0.699 1.892 0.026 0.114 0.489 0.308 1.3230.163 1.000 1.708 0.026 0.163 1.000 0.278 1.7080.163 1.176 1.556 0.026 0.191 1.383 0.253 1.8300.163 1.301 1.459 0.026 0.212 1.693 0.237 1.8990.163 1.477 1.369 0.026 0.240 2.182 0.223 2.0220.163 1.602 1.274 0.026 0.261 2.567 0.207 2.0410.163 1.778 1.146 0.026 0.289 3.162 0.187 2.0380.163 1.903 1.090 0.026 0.310 3.622 0.177 2.0740.163 2.000 1.064 0.026 0.325 4.000 0.173 2.1290.163 2.079 1.004 0.026 0.338 4.323 0.163 2.0880.125 0.699 1.732 0.016 0.087 0.489 0.216 1.2110.125 1.000 1.681 0.016 0.125 1.000 0.210 1.6810.125 1.176 1.531 0.016 0.147 1.383 0.191 1.8010.125 1.301 1.455 0.016 0.163 1.693 0.182 1.8930.125 1.477 1.310 0.016 0.185 2.182 0.164 1.9340.125 1.602 1.207 0.016 0.200 2.567 0.151 1.9330.125 1.778 1.143 0.016 0.222 3.162 0.143 2.0320.125 1.903 1.072 0.016 0.238 3.622 0.134 2.0400.125 2.000 1.064 0.016 0.250 4.000 0.133 2.1290.125 2.079 1.000 0.016 0.260 4.323 0.125 2.0790.090 0.699 1.732 0.008 0.063 0.489 0.156 1.2110.090 1.000 1.653 0.008 0.090 1.000 0.149 1.6530.090 1.176 1.505 0.008 0.106 1.383 0.136 1.7700.090 1.301 1.380 0.008 0.117 1.693 0.124 1.7960.090 1.477 1.260 0.008 0.133 2.182 0.114 1.8610.090 1.602 1.199 0.008 0.144 2.567 0.108 1.9200.090 1.778 1.104 0.008 0.160 3.162 0.100 1.9630.090 1.903 1.064 0.008 0.172 3.622 0.096 2.0260.090 2.000 1.037 0.008 0.180 4.000 0.094 2.0750.090 2.079 0.978 0.008 0.187 4.323 0.088 2.0330.058 0.699 1.681 0.003 0.041 0.489 0.097 1.175



0.058 1.000 1.477 0.003 0.058 1.000 0.086 1.4770.058 1.176 1.415 0.003 0.068 1.383 0.082 1.6640.058 1.301 1.380 0.003 0.075 1.693 0.080 1.7960.058 1.477 1.220 0.003 0.086 2.182 0.071 1.8020.058 1.602 1.107 0.003 0.093 2.567 0.064 1.7740.058 1.778 0.978 0.003 0.103 3.162 0.057 1.7390.058 1.903 0.908 0.003 0.110 3.622 0.053 1.7290.058 2.000 0.851 0.003 0.116 4.000 0.049 1.7030.058 2.079 0.799 0.003 0.121 4.323 0.046 1.6620.028 0.699 1.556 0.001 0.020 0.489 0.044 1.0880.028 1.000 1.431 0.001 0.028 1.000 0.040 1.4310.028 1.176 1.408 0.001 0.033 1.383 0.039 1.6560.028 1.301 1.340 0.001 0.036 1.693 0.038 1.7440.028 1.477 1.204 0.001 0.041 2.182 0.034 1.7790.028 1.602 1.079 0.001 0.045 2.567 0.030 1.7290.028 1.778 0.903 0.001 0.050 3.162 0.025 1.6060.028 1.903 0.778 0.001 0.053 3.622 0.022 1.4810.028 2.000 0.724 0.001 0.056 4.000 0.020 1.4490.028 2.079 0.672 0.001 0.058 4.323 0.019 1.397

Suma = 59.45 225.24 218.82 39.71 89.27 366.29 95.70 310.59* Los valores que estn en negrita son las respectivas sumatorias de cada columna.

Reemplazamos estos valores en la frmula anterior y se obtiene:

Estos valores en la frmula anterior y se obtiene:

Resolviendo el sistema de ecuaciones :a0= 2.200a1= 0.555a2= -0.640

Hallamos a, b y ka0= log(k) = 2.200

k = 158.498a1= a= 0.555a2= b= -0.640

La frmula final sale:

Para :D= 45 minT= 10 aos

Imax = 49.770 mm/hr

150 59.45 225.2459.45 39.71 89.27225.24 89.27 366.29

218.8295.70310.59

158.498.

.



PREGUNTA 06 Resultados obtenidos por los difenrentes mtodos para:Tiempo de retorno = 10 aos

Duracion = 45 min

Metodo Grfico : 50.00 mm/hrFormula de Talbot : 48.17 mm/hrFormula de U.S.A. : 49.77 mm/hr

El metodo Grafico, al igual que la frmula de Talbot tendra errores en la interpolacion.

El metodo Talbot, utiliza un interpolacion simple para poder hallar Imax en TR y tiempo de duraciones que no esten en su rango, por ello tendra error en la interpolacion.

El metodo que tiene mayor precisin para hallar en un determinado periodo de retorno es la Formula de U.S.A. ya que utiliza una interpolacion multiple


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Problema Analisis de Frecuencia -Villon