Problema 2AOPANUAL (cm)mPANUAL (cm)ProbabTmPANUAL ordenado(cm)196013011600.0423.011600.0423.019618421430.0911.521430.0911.519627631300.137.731300.137.719638941250.175.841250.175.8196411251200.224.651200.224.619659661120.263.861120.263.819668071080.303.371080.303.3196712581060.352.981060.352.9196814391020.392.691020.392.619698910960.432.310960.432.319707811950.482.111950.482.119719012900.521.912900.521.9197210213890.571.813890.571.8197310814890.611.614890.611.619746015850.651.515850.651.519757516840.701.416840.701.4197612017830.741.417830.741.4197716018800.781.318800.781.319788519780.831.219780.831.2197910620760.871.220760.871.219808321750.911.121750.911.1198195N=22600.961.022600.961.0a)Precp =139.5cmT =10aosP =186.7cmT =50aosb)Precip =100.0cmT =2.60aosPrec =100cmP =0.0c)P =0.75T =1.3333333333aosPrecp =80.5cm

Problema 2

Periodo de retorno (aos)

Precipitacin (cm)

P vs T

Problema 3

Prec vs T

Periodo de retorno T (aos)

Precipitacin (cm)

Problema 4Hora (A)Intervalo de tiempo (min) (B)Tiempo Acumulado (min) (C )Lluvia Parcial (mm) (D)Lluvia acumulada (mm) (E )Intensidad (mm/h) (F)4000006120120331.58120240582.5101203604122121204801130.513605406196146060042341560660427416607206336176078043741860840643622240108010532.52412012004572256012602592a)b)c)i max =6mm/ht = 60 mini max =6mm/ht = 30 mini max =6mm/ht = 10 minPara t = 90 min

Problema 4

Pacum vs tiempo

Tiempo (min)

Precipitacin acum (mm)

Curva masa de Precipitacin

Problema 5

Tiempo (min)

Intensidad (mm/h)

Hietograma

Problema 6Alturas de Precipitacin (mm) para diferentes duraciones (min)Tiempo (min)Precipitacin acumulada (mm)30609012015018021024027000.0306.06.06018.012.018.09021.03.015.021.012036.015.018.030.036.015043.07.022.025.037.043.018049.06.013.028.031.043.049.021052.03.09.016.031.034.046.052.024053.01.04.010.017.032.035.047.053.027054.01.02.05.011.018.033.036.048.054.0Pmax152230374349525354Determinando intensidadesIntensidades (mm/h) para diferentes duraciones (min)Tiempo (min)Precipitacin acumulada (mm)30609012015018021024027000.0306.012.06018.024.018.09021.06.015.014.012036.030.018.020.018.015043.014.022.016.718.517.218049.012.013.018.715.517.216.321052.06.09.010.715.513.615.314.924053.02.04.06.78.512.811.713.413.327054.02.02.03.35.57.211.010.312.012.0imax30.0022.0020.0018.5017.2016.3314.8613.2512.00a) Hietograma para 30 min. Graficamos columna B vs Columna C de la tabla anteriorb) y c) Para las curvas i vs d y P vs d, graficamos las filas 28 vs 17 y 13 vs 2 respectivamente

Problema 6

Hietograma para 30 min

duracin t (min)

intensidad (mm/h)

Problema 7_Grunsky

i vs d

P vs d

Duracin (min)

intensidad mxima (mm/h)

Precipitacin (mm)

Hoja1i ) Determinando intensidadesAoDuracin (min)AoDuracin (min)15301530Precipitacin (mm)intensidad (mm/h)200310.417.5200341.63520049.113.7200436.427.420059.614.9200538.429.820069.113.1200636.426.220078.413.2200733.626.4200811.818.7200847.237.420097.47.65200929.615.3ii ) Ordenando las series de forma decreciente y asignando un periodo de retorno con la funcin WeibullmDuracin (min)T (aos)1530intensidad (mm/h)147.237.48.00241.6354.00338.429.82.67436.427.42.00536.426.41.60633.626.21.33729.615.31.14iii) Encontrando relacin de ajuste para los datos de i vs T,iv) Determinando intensidades para distintos periodos de retorno con las funciones establecidas en la apartado iii)Ti (mm/h)(aos)15 min30 min236.2426.64543.6335.221049.2141.712054.8048.195062.1856.7710067.7763.26

Hoja1

i15 vs T

i30 vs T

Periodo de Retorno (aos)

intenisdad (mm/h)

Duracion 15

Duracion 30

AoDuracin (min)5101530609012020033.807.4010.4017.5020.9023.2025.2020044.808.109.1013.7022.7027.1030.0020054.306.909.6014.9021.4027.5029.9520063.806.809.1013.1016.8018.7519.5020073.605.908.4013.2017.8020.6021.7020085.808.8011.8018.7023.8523.8523.8520094.106.907.407.658.7510.5011.95iii) Determinando intensidades (mm/h)AoDuracin (min)51015306090120200345.6044.4041.6035.0020.9015.4712.60200457.6048.6036.4027.4022.7018.0715.00200551.6041.4038.4029.8021.4018.3314.98200645.6040.8036.4026.2016.8012.509.75200743.2035.4033.6026.4017.8013.7310.85200869.6052.8047.2037.4023.8515.9011.93200949.2041.4029.6015.308.757.005.98iv) Ordenando de forma decreciente y asignado funcin weibullmDuracin (min)T (aos)51015306090120169.6052.8047.2037.4023.8518.3315.008.0257.6048.6041.6035.0022.7018.0714.984.0351.6044.4038.4029.8021.4015.9012.602.7449.2041.4036.4027.4020.9015.4711.932.0545.6041.4036.4026.4017.8013.7310.851.6645.6040.8033.6026.2016.8012.509.751.3743.2035.4029.6015.308.757.005.981.1v y vi) Estimando valores intensidad para distintos periodos de retorno con funcion de ajusteT (aos)Duracin (min)51015306090120249.5342.1836.2426.6417.8713.6210.90561.7149.5943.6335.2223.4118.0014.621070.9155.1949.2141.7127.6021.3217.431576.3058.4652.4845.5030.0523.2619.082080.1260.7954.8048.2031.7924.6320.255092.3068.1962.1856.7737.3329.0123.97100101.5073.7967.7763.2641.5232.3326.78vii) Estimando coeficientes de la ecuacin de IDF. Determinando coeficiente cC =1010.T (aos)Duracin (min)1520254070100130249.5342.1836.2426.6417.8713.6210.90561.7149.5943.6335.2223.4118.0014.621070.9155.1949.2141.7127.6021.3217.431576.3058.4652.4845.5030.0523.2619.082080.1260.7954.8048.2031.7924.6320.255092.3068.1962.1856.7737.3329.0123.97100101.5073.7967.7763.2641.5232.3326.78Determinando coeficiente k,n y m aplicando regresin linealx2(LOG(D+C))x1(log T)yx1yx2yx1x2x1x2Duracin1.180.301.6950.5101.9930.0911.3830.3545 min1.180.701.7901.2512.1060.4891.3830.8221.181.001.8511.8512.1771.0001.3831.1761.181.181.8832.2142.2141.3831.3831.3831.181.301.9042.4772.2391.6931.3831.5301.181.701.9653.3392.3112.8861.3831.9981.182.002.0064.0132.3604.0001.3832.3521.300.301.6250.4892.1140.0911.6930.39210 min1.300.701.6951.1852.2060.4891.6930.9091.301.001.7421.7422.2661.0001.6931.3011.301.181.7672.0782.2991.3831.6931.5301.301.301.7842.3212.3211.6931.6931.6931.301.701.8343.1152.3862.8861.6932.2101.302.001.8683.7362.4304.0001.6932.6021.400.301.5590.4692.1800.0911.9540.42115 min1.400.701.6401.1462.2920.4891.9540.9771.401.001.6921.6922.3651.0001.9541.3981.401.181.7202.0232.4041.3831.9541.6441.401.301.7392.2622.4311.6931.9541.8191.401.701.7943.0472.5072.8861.9542.3751.402.001.8313.6622.5604.0001.9542.7961.600.301.4260.4292.2840.0912.5670.48230 min1.600.701.5471.0812.4780.4892.5671.1201.601.001.6201.6202.5961.0002.5671.6021.601.181.6581.9502.6561.3832.5671.8841.601.301.6832.1902.6961.6932.5672.0841.601.701.7542.9802.8102.8862.5672.7221.602.001.8013.6022.8864.0002.5673.2041.850.301.2520.3772.3100.0913.4040.55560 min1.850.701.3690.9572.5270.4893.4041.2901.851.001.4411.4412.6591.0003.4041.8451.851.181.4781.7382.7271.3833.4042.1701.851.301.5021.9542.7721.6933.4042.4011.851.701.5722.6712.9012.8863.4043.1351.852.001.6183.2362.9864.0003.4043.6902.000.301.1340.3412.2690.0914.0000.60290 min2.000.701.2550.8772.5110.4894.0001.3982.001.001.3291.3292.6581.0004.0002.0002.001.181.3671.6072.7331.3834.0002.3522.001.301.3921.8102.7831.6934.0002.6022.001.701.4632.4852.9252.8864.0003.3982.002.001.5103.0193.0194.0004.0004.0002.110.301.0370.3122.1930.0914.4690.636120 min2.110.701.1650.8142.4630.4894.4691.4782.111.001.2411.2412.6241.0004.4692.1142.111.181.2811.5062.7071.3834.4692.4862.111.301.3061.7002.7621.6934.4692.7502.111.701.3802.3442.9162.8864.4693.5922.112.001.4282.8563.0184.0004.4694.228N80.05357.23377.39193.093123.02780.791136.28993.50349FORMANDO SISTEMA DE ECUACIONES:RESOLVIENDO TENEMOS:MATRIZaoa1a2indepao =2.3664957.23380.05377.391a1 =0.19457.23380.79193.50393.093a2 =-0.62080.05393.503136.289123.027Por tanto:INVERSA MATRIZFINALMENTE OBTENEMOS LA ECUACION0.603-0.084-0.297m =0.194-0.0840.072-0.000n =0.620-0.297-0.0000.182k =232.011i0TdTDINTENSIDAD27.724498401100120

Duracin (min)

duracion de 5

t (min)

i (mm/h)

CURVAS IDF

i) Determinando intensidadesAoMesPmax en 24 horas (mm)imax diario (mm/h)2005Nov54.62.282006Ene48.02.002007Oct51.62.152008Ene46.71.952009Feb32.21.342010Feb63.22.632011Feb68.52.852012Nov45.71.902013Dic33.81.412014Ene33.01.38ii) Ordenando de forma decreciente y asignando un periodo de retorno con funcin Weibullmimax (mm/h)T (aos)12.8511.0022.635.5032.283.6742.152.7552.002.2061.951.8371.901.5781.411.3891.381.22101.341.10iii) Encontrando relacin de ajuste para los datos de i vs T,iv) Determinando intensidades para distintos periodos de retorno con las funcin establecida en la apartado iii)v) Estableciendo intensidades para diferentes duraciones mediante la frmula de GrunskyTi24Intensidades mximas (mm/h) para diferentes duraciones (min) utilizando la frmula de Grunsky(aos)(mm/h)510152030609012018036021.8631.5122.2818.1915.7612.869.107.436.435.253.7152.4842.0729.7524.2921.0317.1712.149.928.597.014.96102.9550.0635.3928.9025.0320.4414.4511.8010.228.345.90153.2254.7338.7031.6027.3622.3415.8012.9011.179.126.45203.4258.0441.0433.5129.0223.7016.7613.6811.859.676.84504.0468.6048.5139.6134.3028.0119.8016.1714.0011.438.081004.5176.5954.1644.2238.2931.2722.1118.0515.6312.769.03vi) Aplicando regresin lineal multiple para encontrar ecuacin IDFx1x2yt0.3010.6991.4985 minao =1.8090.6990.6991.624a1 =0.2231.0000.6991.699a2 =-0.5001.1760.6991.7381.3010.6991.764Por tanto:1.6990.6991.8362.0000.6991.884m =0.2230.3011.0001.34810 minn =0.5000.6991.0001.473k =64.4471.0001.0001.5491.1761.0001.5881.3011.0001.6131.6991.0001.6862.0001.0001.7340.3011.1761.26015 min0.6991.1761.385vii) Generando curva IDF con la ecuacin obtenida1.0001.1761.4611.1761.1761.500Ti24Intensidades mximas (mm/h) para diferentes duraciones (min) utilizando la frmula de Grunsky1.3011.1761.525(aos)(mm/h)51015203060901201803601.6991.1761.59821.8633.6423.7919.4216.8213.739.717.936.875.613.962.0001.1761.64652.4841.2729.1823.8220.6316.8511.919.738.426.884.860.3011.3011.19720 min102.9548.1634.0627.8124.0819.6613.9011.359.838.035.680.6991.3011.323153.2252.7237.2830.4426.3621.5215.2212.4310.768.796.211.0001.3011.398203.4256.2139.7532.4628.1122.9516.2313.2511.479.376.621.1761.3011.437504.0468.9648.7639.8134.4828.1519.9116.2514.0811.498.131.3011.3011.4631004.5180.4956.9146.4740.2432.8623.2318.9716.4313.419.491.6991.3011.5352.0001.3011.5830.3011.4771.10930 min0.6991.4771.2351.0001.4771.3101.1761.4771.3491.3011.4771.3751.6991.4771.4472.0001.4771.4950.3011.7780.95960 min0.6991.7781.0841.0001.7781.1601.1761.7781.1991.3011.7781.2241.6991.7781.2972.0001.7781.3450.3011.9540.87190 min0.6991.9540.9961.0001.9541.0721.1761.9541.1111.3011.9541.1361.6991.9541.2092.0001.9541.2570.3012.0790.808120 min0.6992.0790.9341.0002.0791.0091.1762.0791.0481.3012.0791.0741.6992.0791.1462.0002.0791.1940.3012.2550.720180 min0.6992.2550.8461.0002.2550.9211.1762.2550.9601.3012.2550.9861.6992.2551.0582.0002.2551.1060.3012.5560.570360 min0.6992.5560.6951.0002.5560.7711.1762.5560.8101.3012.5560.8351.6992.5560.9082.0002.5560.955

i15 vs T

Periodo de Retorno (aos)

intenisdad (mm/h)

T = 2 aos

T = 5 aos

T = 10 aos

T = 15 aos

T = 20 aos

T = 50 aos

T = 100 aos

Duracin (min)

Intensidad (mm/h)

Hora (A)Intervalo de tiempo (min) (B)Tiempo Acumulado (min) (C )Lluvia acumulada (mm) (E )Intervalo de tiempo (min) (B)Lluvia acumulada (mm) (E )30 min6090120240300360600900120012604000300.750.7561201203601.50.751.5081202408902.250.751.502.25101203601212030.751.502.25312120480131504.251.252.002.753.51360540191805.51.252.503.2541460600232106.751.252.503.754.515606602724081.252.503.755816607203327091.002.253.504.758.25176078037300101.002.003.254.58.510186084043330111.002.003.004.258.7510.2522240108053360121.002.003.004910.5122412012005739012.250.251.252.253.2581011.5256012605942012.50.250.501.502.579.51145012.750.250.500.751.7568.510.5480130.250.500.75157.510510163.003.253.503.7579.2511.75540193.006.006.256.591113.5570212.005.008.008.25101214.25600232.004.007.001011131523630252.004.006.00912.75141624.25660272.004.006.00814.5151725.5690303.005.007.00917.2517.751927.75720333.006.008.00102020.52130750352.005.008.00101922.2522.7530.75780372.004.007.0010182424.531.5810403.005.007.0010192427.2533.25840433.006.008.00102024303587044.251.254.257.259.2519.2523.2528.2535.2590045.51.252.505.508.518.522.526.535.545.593046.751.252.503.756.7516.7521.7525.7535.7546960481.252.503.7551521253646.599049.251.252.503.75514.2519.2524.253747102050.51.252.503.75513.517.523.53847.5105051.751.252.503.75511.7516.7521.753947.51080531.252.503.7551016204047.51110541.002.253.504.759.7514193847.251140551.002.003.254.59.5121836471170561.002.003.004.259.2511.751635471200571.002.003.004911.5143447571230581.002.003.0048.7511.2513.75334757.251260591.002.003.0048.51113.5324757.559P (mm)368102024304047.557.559t (min)30609012024030036060090012001260imax (mm/h)6.06.05.35.05.04.85.04.03.1672.92.8

1mPN

1Tf

()60(B)ColumnaDColumna

(

)

loglogloglog

ikmTndc

=+-+

1122

o

yaaxax

=++

01122210111212220211222yNaaxaxxyaxaxaxxxyaxaxxax

(

)

11

22

log, log, , xlogT,

, xlog

o

yiakam

andc

====

=-=+

012

012

012

77.3914957.23380.053

93.09357.23380.79193.503

123.02780.05393.503136.289

aaa

aaa

aaa

=++

=++

=++

01201201277.3914957.23380.05393.09357.23380.79193.503123.02780.05393.503136.289aaaaaaaaa

(

)

0.194

0.620

232.011

10

T

i

d

=

+

0.1940.620232.01110Tid

(

)

0.223

0.500

64.447

T

i

d

=

0.2230.50064.447Tid

1

N

T

m

+

=

1NTm

(

)

m

n

kT

i

dc

=

+

mnkTidc

24

24

t

ii

t

=

MBD0059BDC3.unknown

MBD00663A98.unknown

MBD00801C99.unknown

MBD00972F81.unknown

MBD00801785.unknown

MBD005D167A.unknown

MBD00047FFF.unknown

MBD0057A28B.unknown

MBD0056F550.unknown

MBD000375CE.unknown

MBD00047FFE.unknown