• Author / Uploaded
• Edinson Robert Berru Davila

Citation preview

HIDROLOGIA

Distribución de Gumbel Caudales Medios Orden m 1

Caudal (m3/s) 360

P (x)

Y=(X-u)/a

F(y)

F(y)-P(x)

0.0333

-0.5455

0.178100

0.1448

2

367

0.0667

-0.5323

0.182161

0.1155

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29

418 520 522 557 563 581 610 618 658 683 740 779 818 824 824 876 917 921 934 1030 1120 1150 1230 1410 1660 2280 3800

0.1000 0.1333 0.1667 0.2000 0.2333 0.2667 0.3000 0.3333 0.3667 0.4000 0.4333 0.4667 0.5000 0.5333 0.5667 0.6000 0.6333 0.6667 0.7000 0.7333 0.7667 0.8000 0.8333 0.8667 0.9000 0.9333 0.9667

-0.4365 -0.2449 -0.2411 -0.1754 -0.1641 -0.1303 -0.0758 -0.0608 0.0144 0.0613 0.1684 0.2417 0.3149 0.3262 0.3262 0.4239 0.5009 0.5084 0.5328 0.7132 0.8823 0.9386 1.0889 1.4270 1.8967 3.0614 5.9168

0.212824 0.278738 0.280077 0.303703 0.307787 0.320085 0.340014 0.345530 0.373159 0.390423 0.429549 0.455972 0.481984 0.485943 0.485943 0.519701 0.545538 0.548018 0.556028 0.612576 0.661101 0.676265 0.714203 0.786614 0.860652 0.954257 0.997310

0.1128 0.1454 0.1134 0.1037 0.0745 0.0534 0.0400 0.0122 0.0065 0.0096 0.0038 0.0107 0.0180 0.0474 0.0807 0.0803 0.0878 0.1186 0.1440 0.1208 0.1056 0.1237 0.1191 0.0801 0.0393 0.0209 0.0306

957.586 682.725 532.318 650.360

m3/s m3/s m3/s m3/s

𝑋 𝑆 𝛼 𝜇

INGENIERIA CIVIL

∆𝑚𝑎𝑥

0.1454

HIDROLOGIA

Método de Gumbel Precipitaciones Máximas Orden m

Precipit. (mm)

P (x)

Y=(X-u)/a

F(y)

F(y)-P(x)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

20.70 25.40 26.40 27.10 28.60 30.00 32.00 33.10 33.90 33.90 34.60 35.10 35.30 41.10 41.10 43.70 47.40 51.70 51.80 74.10

0.04762 0.09524 0.14286 0.19048 0.23810 0.28571 0.33333 0.38095 0.42857 0.47619 0.52381 0.57143 0.61905 0.66667 0.71429 0.76190 0.80952 0.85714 0.90476 0.95238

-1.18268 -0.68591 -0.58022 -0.50623 -0.34769 -0.19971 0.01168 0.12794 0.21250 0.21250 0.28649 0.33933 0.36047 0.97351 0.97351 1.24831 1.63939 2.09388 2.10445 4.46145

0.03827 0.13730 0.16756 0.19032 0.24273 0.29492 0.37218 0.41482 0.44550 0.44550 0.47194 0.49054 0.49790 0.68540 0.68540 0.75052 0.82358 0.88408 0.88523 0.98852

0.00935 0.04206 0.02470 0.00015 0.00464 0.00921 0.03884 0.03387 0.01693 0.03069 0.05187 0.08089 0.12114 0.01873 0.02889 0.01138 0.01405 0.02694 0.01954 0.03614

37.350 12.134 9.461 31.890

mm mm mm mm

∆𝑚𝑎𝑥

0.1211

𝑋 𝑆 𝛼 𝜇

PRECIPITACIONES PARA CADA TIEMPO DE RETORNO - CUEVA

TR - Años 5 10 20 25

F(z) 0.80000 0.90000 0.95000 0.96000

Z 0.84164 1.28155 1.64485 1.75070

INGENIERIA CIVIL

Y 1.49994 2.25037 2.97020 3.19853

PRECIPITACIÓN - CUEVA BL NORMAL 47.563 52.901 57.309 58.594

GUMBEL 50.090 59.196 67.931 70.702

HIDROLOGIA 50 100

0.98000 0.99000

2.05375 2.32630

3.90194 4.60015

1 2 4 6 8 10 12 14 18 24

5 15.61716 28.57994 38.79233 45.63993 50.93698 65.37947 82.55460 94.07084 102.97937 110.34436 116.67457 122.25645 131.83079 143.55509

10 18.26668 33.42867 45.37364 53.38297 59.57869 76.47143 96.56039 110.03042 120.45034 129.06483 136.46899 142.99787 154.19654 167.90992

20 20.91621 38.27740 51.95495 61.12601 68.22040 87.56338 110.56619 125.99001 137.92130 147.78530 156.26341 163.73928 176.56229 192.26476

Dt min 5 15 30 45 60 120 240 360 480 600 720 840 1080 1440

62.271 65.578 TR, Años 25 21.76917 39.83834 54.07366 63.61871 71.00241 91.13419 115.07505 131.12785 143.54569 153.81194 162.63579 170.41653 183.76245 200.10526

Grafico de Precipitacion y Periodo de Duración

PRECIPITACIÓN - CUEVA BLANCA 250

P (mm)

200 5 AÑOS 150

10 AÑOS

100

20 AÑOS

50

25 AÑOS 50 AÑOS

0 0

200

400

600

800

1000

1200

Dt (min) ESTACION CUEVA BLANCA AÑO 1990 - 2011 Orden Precipit. .3862 Pmax 24 m (mm) Hr 1 20.7 7.99434 2 25.4 9.80948 INGENIERIA CIVIL

1400

100 AÑOS

79.237 87.710

50 24.41870 44.68707 60.65498 71.36175 79.64412 102.22615 129.08085 147.08743 161.01666 172.53241 182.43021 191.15794 206.12820 224.46010

HIDROLOGIA 3 4 5 6 7 8 9 10 11 12 13

26.4 27.1 28.6 30 32 33.1 33.9 33.9 34.6 35.1 35.3

10.19568 10.46602 11.04532 11.586 12.3584 12.78322 13.09218 13.09218 13.36252 13.55562 13.63286

14

41.1

15.87282

15 16 17 18 19 20

41.1 43.7 47.4 51.7 51.8 74.1

15.87282 16.87694 18.30588 19.96654 20.00516 28.61742

INGENIERIA CIVIL

Curso: Hidrología Docente:

Dr. Walter Morales U Alumno:

Edwin Jabe Pare

HIDROLOGIA

DISTRIBUCION DE GUMBEL TR - Años 5 10 20 25 50 100

DISTRIBUCIÓN GUMBEL

F(z)

Y

0.80000 0.90000 0.95000 0.96000 0.98000 0.99000

5 1448.81

INGENIERIA CIVIL

1.49994 2.25037 2.97020 3.19853 3.90194 4.60015

10 1848.27

QAUDAL MEDIO 1448.81 1848.27 2231.45 2353.00 2727.43 3099.10

TR - Años 20 2231.45

HIDROLOGIA

Distribución normal Precipitaciones Máximas Orden m

Precipit. (mm)

P (x)

z

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

20.70 25.40 26.40 27.10 28.60 30.00 32.00 33.10 33.90 33.90 34.60 35.10 35.30 41.10 41.10 43.70 47.40 51.70 51.80 74.10

0.047619 0.095238 0.142857 0.190476 0.238095 0.285714 0.333333 0.380952 0.428571 0.476190 0.523810 0.571429 0.619048 0.666667 0.714286 0.761905 0.809524 0.857143 0.904762 0.952381

-1.372132 -0.984803 -0.902393 -0.844706 -0.721090 -0.605716 -0.440895 -0.350244 -0.284316 -0.284316 -0.226628 -0.185423 -0.168941 0.309039 0.309039 0.523306 0.828224 1.182588 1.190829 3.028580

37.350 12.134

mm mm

𝑋 𝑆

RETORNO - CUEVA BLANCA

TACIÓN - CUEVA BLANCA LOG. NORMAL 46.375 53.310 59.812 61.851

ESTACION CUEVA BLANCA AÑO 1990 - 2011 DISTRIBUCIÓN NORMAL GUMBEL LOG NORMAL

INGENIERIA CIVIL

TR 5 47.563 50.090 46.375

HIDROLOGIA 68.083 74.222 Dt 100 27.06823 49.53580 67.23629 79.10479 88.28583 113.31810 143.08665 163.04702 178.48762 191.25288 202.22463 211.89936 228.49395 248.81493

min 5 15 30 45 60 120 240 360 480 600 720 840 1080 1440

I 5 187.40587 114.31977 77.58466 60.85324 50.93698 32.68974 20.63865 15.67847 12.87242 11.03444 9.72288 8.73260 7.32393 5.98146

1 2 4 6 8 10 12 14 18 24

Grafico Intensidad – Periodo de Duración – Tiempo Retorno

INTENSIDAD - CUEVA BLANCA I (mm/hr)

300 250 200 150 100 50 0 0

20

40

60

Dt (min)

INGENIERIA CIVIL

80

100

120

HIDROLOGIA

Hidrología Dr. Walter Morales Uchofen Edwin Jabe Paredes

INGENIERIA CIVIL

HIDROLOGIA

TR - Años 25 2353.00

50 2727.43

100 3099.10

INGENIERIA CIVIL

HIDROLOGIA

Distribución log - normal de 2 Parámetros Precipitacione Máximas

ximas F(z)

F(z)-P(x)

Orden m

Precipit. (mm)

P (x)

0.085011 0.162360 0.183424 0.199138 0.235427 0.272352 0.329644 0.363078 0.388084 0.388084 0.410356 0.426449 0.432921 0.621354 0.621354 0.699619 0.796228 0.881514 0.883140 0.998771

0.037392 0.067122 0.040567 0.008661 0.002668 0.013363 0.003689 0.017875 0.040487 0.088106 0.113453 0.144980 0.186126 0.045313 0.092932 0.062286 0.013296 0.024371 0.021622 0.046391

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

20.70 25.40 26.40 27.10 28.60 30.00 32.00 33.10 33.90 33.90 34.60 35.10 35.30 41.10 41.10 43.70 47.40 51.70 51.80 74.10

0.04762 0.09524 0.14286 0.19048 0.23810 0.28571 0.33333 0.38095 0.42857 0.47619 0.52381 0.57143 0.61905 0.66667 0.71429 0.76190 0.80952 0.85714 0.90476 0.95238

𝑋 𝑆

37.350 12.134 0.325 0.317 3.570

∆𝑚𝑎𝑥

0.1861

C

𝜎𝑦 𝑢𝑦

10 52.901 59.196 53.310

TR - Años 20 25 57.309 58.594 67.931 70.702 59.812 61.851

50 62.271 79.237 68.083

100 65.578 87.710 74.222

INGENIERIA CIVIL

10 219.20021 133.71469 90.74729 71.17729 59.57869 38.23571 24.14010 18.33840 15.05629 12.90648 11.37242 10.21413 8.56647 6.99625

I (mm/h) 20 25 250.99455 261.23004 153.10960 159.35337 103.90991 108.14733 81.50135 84.82495 68.22040 71.00241 43.78169 45.56710 27.64155 28.76876 20.99833 21.85464 17.24016 17.94321 14.77853 15.38119 13.02195 13.55298 11.69566 12.17261 9.80902 10.20903 8.01103 8.33772

50 293.02438 178.74829 121.30995 95.14900 79.64412 51.11307 32.27021 24.51457 20.12708 17.25324 15.20252 13.65414 11.45157 9.35250

100 324.81872 198.14321 134.47258 105.47306 88.28583 56.65905 35.77166 27.17450 22.31095 19.12529 16.85205 15.13567 12.69411 10.36729

n – Tiempo Retorno

TR = 5 AÑOS TR = 10 AÑOS TR = 20 AÑOS TR = 25 AÑOS TR = 50 AÑOS TR = 10 AÑOS

INGENIERIA CIVIL

PRECIPITACION (mm)

HIDROLOGIA

HIDROLOGIA

INGENIERIA CIVIL

HIDROLOGIA

INGENIERIA CIVIL

HIDROLOGIA

de 2 Parámetros Precipitaciones Máximas y

z

F(z)

F(z)-P(x)

3.03013 3.23475 3.27336 3.29953 3.35341 3.40120 3.46574 3.49953 3.52342 3.52342 3.54385 3.55820 3.56388 3.71601 3.71601 3.77735 3.85862 3.94546 3.94739 4.30542

-1.70480 -1.05886 -0.93695 -0.85434 -0.68427 -0.53340 -0.32966 -0.22297 -0.14757 -0.14757 -0.08305 -0.03776 -0.01982 0.46042 0.46042 0.65406 0.91063 1.18476 1.19086 2.32111

0.04412 0.14483 0.17439 0.19646 0.24690 0.29688 0.37083 0.41178 0.44134 0.44134 0.46691 0.48494 0.49209 0.67739 0.67739 0.74346 0.81876 0.88194 0.88315 0.98986

0.00350 0.04959 0.03153 0.00598 0.00881 0.01116 0.03750 0.03083 0.01277 0.03485 0.05690 0.08649 0.12695 0.01073 0.03689 0.01844 0.00923 0.02480 0.02162 0.03748

∆𝑚𝑎𝑥

0.1270

mm mm mm mm mm

TR, AÑOS 90

85 INGENIERIA CIVIL

HIDROLOGIA

85

Dist. Normal Dist. gumbel

80

PRECIPITACION (mm)

Dist. Log - Nomal

75

70

65

60

55

50

45 1

10

PROBABILIDAD (%)

INGENIERIA CIVIL

100

HIDROLOGIA

INGENIERIA CIVIL

HIDROLOGIA

INGENIERIA CIVIL

HIDROLOGIA

INGENIERIA CIVIL

HIDROLOGIA

Dist. Normal Dist. gumbel Dist. Log - Nomal 2 P.

INGENIERIA CIVIL