Proyecto Hidrologico Para La Construccion de Una Presa.111

I .- ANALISIS DE CONSISTENCIA

DOBLE MASA:

Teniendo en cuenta la estacion Patron y la Estacion a comparar se realiza la

la Prueba de Doble Masa.

El proceso de Doble masa se realiza con Estaciones con datos completados,

en el eje de las abscisas (X) a los datos acumulados de la Estacion Patron y en eje de

las ordemadas (Y) a los datos acumulados de la precipitacion de la estacion acomparar.

En la recta de doble masa se identifica el quiebre o los quiebres y ver el periodo

inconsistente con el periodo consistente; del analisis grafico se observa que la linea recta

se cumple en lo Dobles masas de la estacion patron versus el acumulado de la

estacion comparada.

ESTACION ESTACION ESTACION PROMEDIO ESTACION ESTACION ESTACION

AO LLAGADEN CONTUMAZA CHILETE (R.S+BELL.)/2LLAG. ACUM CONT. ACUM CHIL. ACUM PROM ACUM

1963 655.720 792.140 210.100 552.653 655.72 792.14 210.10 552.65

1964 696.280 417.730 168.990 427.667 1352.00 1209.87 379.09 980.32

1965 541.840 393.130 247.180 394.050 1893.84 1603.00 626.27 1374.37

1966 428.110 955.490 146.940 510.180 2321.95 2558.49 773.21 1884.55

1967 661.390 344.560 304.220 436.723 2983.34 2903.05 1077.43 2321.27

1968 313.200 669.710 108.320 363.743 3296.54 3572.76 1185.75 2685.02

1969 553.700 452.660 244.050 416.803 3850.24 4025.42 1429.80 3101.82

1970 469.190 623.950 180.990 424.710 4319.43 4649.37 1610.79 3526.53

1971 603.850 1023.240 253.170 626.753 4923.28 5672.61 1863.96 4153.28

1972 509.190 783.660 222.520 505.123 5432.47 6456.27 2086.48 4658.41

1973 726.950 371.000 348.120 482.023 6159.42 6827.27 2434.60 5140.43

1974 457.530 545.230 163.230 388.663 6616.95 7372.50 2597.83 5529.09

1975 688.480 474.500 322.070 495.017 7305.43 7847.00 2919.90 6024.11

1976 436.950 678.360 195.200 436.837 7742.38 8525.36 3115.10 6460.95

1977 662.560 1155.290 353.240 723.697 8404.94 9680.65 3468.34 7184.64

1978 278.480 1576.560 144.890 666.643 8683.42 11257.21 3613.23 7851.29

1979 527.290 567.770 199.150 431.403 9210.71 11824.98 3812.38 8282.69

1980 337.900 1075.390 175.710 529.667 9548.61 12900.37 3988.09 8812.36

1981 629.590 559.490 232.480 473.853 10178.20 13459.86 4220.57 9286.21

1982 467.130 938.040 204.170 536.447 10645.33 14397.90 4424.74 9822.66

1983 581.290 751.650 273.670 535.537 11226.62 15149.55 4698.41 10358.19

1984 545.990 1132.010 272.120 650.040 11772.61 16281.56 4970.53 11008.23

1985 343.860 1170.010 75.180 529.683 12116.47 17451.57 5045.71 11537.92

1986 602.590 1263.010 177.330 680.977 12719.06 18714.58 5223.04 12218.89

1987 497.790 366.800 204.730 356.440 13216.85 19081.38 5427.77 12575.33

1988 492.080 792.700 180.080 488.287 13708.93 19874.08 5607.85 13063.62

1989 637.540 678.700 230.640 515.627 14346.47 20552.78 5838.49 13579.25

1990 556.740 907.730 219.630 561.367 14903.21 21460.51 6058.12 14140.61

1991 537.790 839.760 241.150 539.567 15441.00 22300.27 6299.27 14680.18

1992 553.56 964.19 211.67 576.473 15994.56 23264.46 6510.94 15256.65

1993 620.65 976.2 233.39 610.080 16615.21 24240.66 6744.33 15866.73

1994 596.62 804.68 345.17 582.157 17211.83 25045.34 7089.50 16448.89

1995 587.29 1170.24 255.88 671.137 17799.12 26215.58 7345.38 17120.03

1996 667.7 1586.59 175.54 809.943 18466.82 27802.17 7520.92 17929.97

1997 659.42 1101.4 268.99 676.603 19126.24 28903.57 7789.91 18606.57

DE ESTA CURVA DOBLE MASA SELECIONAMOS NUESTRA ESTACION IDICE - LA ESTACION LLAGADEN

PARA ESTO PRIMERAMENTE HACEMOS NUESTRO ANALISIS DE DIBLE MASA.

0.0

5000.0

10000.0

15000.0

20000.0

25000.0

30000.0

35000.0

0.0 5000.0 10000.0 15000.0 20000.0

ES

TA

CIO

NE

S L

LA

GA

DE

N,

CO

NT

UM

AZ

A,

CH

ILE

TE

PROMEDIO ACUMULADO

CURVA DOBLE MASA

LLAGADEN

CONTUMAZ

CHILETE

EVALUACION Y CUANTIFICACION

Mediante el Anlisis estadistico de las Medias y Desviaciones Estndar, para las Pruebas "T" y "F".

N GRADOS D GRADOS DE

DE DATOS LIBERTAD LIBERTAD

ESTACION CONTUMAZA n n-1 TOTAL MEDIA D. ESTAND

PERIODO CONFIBLE 1979 - 1997 19 18 n1+n2-2 77.400 77.812

PERIODO DUDOSO 1963-1978 16 15 33 58.600 78.784

ESTACION CHILETE n n-1 TOTAL MEDIA D. ESTAND

PERIODO CONFIBLE 1963-1985 23 22 n1+n2-2 18.280 26.095

PERIODO DUDOSO 1986 - 1997 12 11 33 19.060 24.346

HACEMOS LAS PRUEBAS ESTADISTICAS CORRESPONDIENTES

PRUEBA T DE STUDENT (MEDIAS)

HP: HIPOTESIS PLANTEADA, X1=X2. LA MEDIA DE LOS DATOS DEBE SER ESTADISTICAMENTE

IGUALES

Tc=(X1-X2)/Sd

Sd =Sp*(1/n1+1/n2)^0.5

Sp=[(n1-1)*S1^2+(n2-1)*S2^2]^0.5(n1+n2-2)

Reemplazando en las ecuaciones anteriores se tiene:

CONTUMAZA CHILETE

Sp= 3338.38 4.4433

Sd= 1132.75 1.5823

Tc= 0.017 1.105

De donde T teorico a un nivel de significacion del 5%

Tt= 2.036 2.036CONDICION NO SE CORRIGE NO SE CORRIGE

Como el Tc < Tt la informacion hidrometereologica NO SE CORRIGIRA POR SALTOS

PRUEBA F FISHER

HP : HIPOTESIS PLANTEADA, S1^2=S2^2

DONDE: S1^2 Y S2^2 Son las variancias muestra

HA : HIPOTESIS ALTERNA S1^2=S2^2 (ALFA=0.050)

DETERMINACION DEL F CALCULADO (Fc)

Fc=S1^2/S2^2 ; si S1^2>S2^2

Fc=S2^2/S^2 ; si S2^2>S1^2

ESTACION

0.0

5000.0

10000.0

15000.0

20000.0

25000.0

30000.0

35000.0

0.0 5000.0 10000.0 15000.0 20000.0 25000.0

ES

TA

C.

CO

NT

UM

AZ

A Y

CH

ILE

TE

ESTACION LLAGADEN (INDICE)

CONTUMAZA

CHILETE

CONTUMAZA CHILETE

FC 1.025 1.149

Luego: FC 0.9755

DETERMINACION DEL F TABULAR (ft)

Los grados de Libertad y el nivel de significacion son

G.L.N = n1-1 Grados de libertad del numerador

G.L.D = n2-1... Grados de libetrad del denominador

NC ...Nivel de Confianza

Alfa = 0.05(NC=95%)

G.D.L 18-15 22 _ 11

Ft= 2.36 2.63CONDICION NO SE CORRIGE NO SE CORRIGE

Como el Fc < Ft la informacion hidrometereologica no sera corregida por saltos

ESTACION

2. TRANSFERENCIA DE DATOS

Ya habiendo cumplido con las pruebas de consistencia, el siguiente paso es trasferir los datos de precipitaciones

para la microcuenca del ro HUERTAS, tomando como base las estaciones: LLAGADEN, CONTUMAZA Y CHILETE.

ESTACION LLAGADENPRESIPITACION (mm)

CATEGORIA Climatologica ordinaria CAJAMARCA

ALTITUD 2000 CAJAMARCA

LATITUD 7 16 MAGDALENA

LONGITUD 78 35

AO ENE FEB MAR ABR MAY JUN JUL AGOS SET OCT NOV DIC TOTAL

1963 108.2 172.0 88.9 118.6 6.1 11.6 2.9 9.9 5.0 31.2 31.6 69.7 655.72

1964 173.13 136.02 79.88 119.37 4.82 8.07 7.47 8.34 16.01 22.13 51.15 69.89 696.28

1965 43.00 55.00 182.30 67.50 13.87 7.37 12.73 15.55 23.43 42.53 25.54 53.02 541.84

1966 88.90 119.51 74.75 40.40 8.10 2.02 6.93 7.05 9.20 35.35 24.40 11.50 428.11

1967 185.00 223.10 84.30 29.50 19.50 1.00 16.80 2.47 0.70 56.40 22.02 20.60 661.39

1968 52.50 55.10 37.50 25.40 4.10 6.10 18.10 4.40 20.00 33.30 33.00 23.70 313.2

1969 13.10 146.40 111.70 73.70 2.30 6.20 8.50 1.00 24.00 33.70 65.30 67.80 553.7

1970 69.25 74.54 92.20 45.80 13.65 15.10 13.83 17.15 11.27 65.00 34.20 17.20 469.19

1971 48.70 57.20 234.50 118.80 4.05 13.60 1.80 19.20 10.00 46.50 9.00 40.50 603.85

1972 53.40 96.80 175.20 33.50 8.30 1.80 9.39 1.50 19.20 15.20 30.60 64.30 509.19

1973 115.00 107.70 159.90 110.30 19.20 11.70 13.68 16.07 31.80 45.00 26.40 70.20 726.95

1974 85.00 126.70 45.40 40.90 3.41 7.60 15.20 5.40 22.50 21.40 25.50 58.52 457.53

1975 175.52 81.18 144.00 14.50 38.23 18.10 2.38 20.40 40.00 76.50 12.60 65.07 688.48

1976 179.90 16.40 87.26 46.42 5.30 9.70 7.45 16.72 2.10 9.60 14.60 41.50 436.95

1977 161.30 202.20 72.80 62.30 9.64 8.12 14.49 7.21 17.90 7.10 14.60 84.90 662.56

1978 10.88 55.80 51.10 14.40 45.50 6.01 17.22 16.28 2.20 17.49 1.00 40.60 278.48

1979 34.50 94.50 275.60 13.70 6.80 3.74 3.80 5.40 9.70 17.49 59.86 2.20 527.29

1980 29.29 5.60 71.00 23.40 3.83 12.20 9.72 4.65 3.91 77.10 44.70 52.50 337.9

1981 61.20 257.50 119.30 22.60 5.73 7.55 8.18 0.60 13.63 38.90 20.00 74.40 629.59

1982 55.70 79.40 25.50 71.70 16.13 8.04 7.96 9.16 22.24 42.50 35.30 93.50 467.13

1983 50.00 75.70 196.00 77.80 15.00 8.80 13.25 6.00 11.94 0.00 0.00 126.80 581.29

1984 36.90 107.90 110.23 72.32 40.85 9.80 5.40 2.79 37.90 53.50 48.80 19.60 545.99

1985 17.90 73.00 51.60 35.83 31.00 9.47 5.59 5.25 10.20 10.10 60.05 33.87 343.86

1986 64.30 50.60 96.60 187.80 7.70 0.52 10.41 6.80 39.06 2.10 35.80 100.90 602.59

1987 190.20 76.30 25.00 85.60 4.78 6.09 9.69 9.70 20.93 7.60 37.70 24.20 497.79

1988 113.70 112.50 29.30 74.70 4.80 4.40 13.85 14.68 18.65 27.40 62.30 15.80 492.08

1989 128.60 189.20 57.60 79.03 7.04 10.28 8.47 19.78 24.71 51.43 16.51 44.89 637.54

1990 56.30 182.37 102.93 59.38 18.42 5.93 13.60 8.11 25.90 45.94 22.28 15.58 556.74

1991 16.40 182.37 104.38 80.32 7.19 6.75 14.32 3.24 9.92 37.95 24.79 50.16 537.79

1992 53.56 90.28 144.40 49.39 8.46 11.41 2.03 18.43 16.99 37.43 59.27 61.91 553.56

1993 94.66 134.54 154.45 80.72 3.51 9.76 14.69 4.32 26.21 20.12 19.95 57.72 620.65

1994 72.95 153.75 140.50 34.75 3.66 11.10 6.38 15.94 19.37 51.71 27.66 58.85 596.62

1995 86.63 99.81 67.16 124.83 3.64 11.73 5.64 3.26 28.66 55.15 33.56 67.22 587.29

1996 45.99 193.01 217.38 44.82 7.59 11.12 12.16 16.77 28.42 35.44 13.51 41.49 667.70

1997 153.96 51.79 175.20 53.63 4.93 9.12 2.72 5.90 19.70 60.70 52.21 69.56 659.42

TOT. 2925.52 3935.76 3885.82 2233.71 407.17 291.91 336.77 329.39 643.30 1230.98 1095.74 1810.17 19126.24

X 83.59 112.45 111.02 63.82 11.63 8.34 9.62 9.41 18.38 35.17 31.31 51.72 546.46

S 54.39 59.70 62.40 38.54 11.16 3.91 4.74 6.23 10.35 20.34 17.50 27.67 113.52

DEPARTAMENTO

PROVINCIA

DISTRITO

ESTACION CONTUMAZAPRESIPITACION (mm)

CATEGORIA Climatologica Ordinaria DEPARTAMENTOCAJAMARCA

ALTITUD 2330 PROVINCIA CONTUMAZ

LATITUD 7 22 DISTRITO CONTUMAZ

LONGITUD 78 49


1963 217.8 96.2 108.5 153.2 20.2 9.1 6.0 90.1 7.0 31.5 40.0 12.5 792.14

1964 8.50 56.00 163.30 38.00 15.00 5.43 2.00 2.50 4.00 25.50 28.50 69.00 417.73

1965 134.80 67.50 35.50 25.00 6.50 8.88 10.57 26.38 14.00 50.00 4.00 10.00 393.13

1966 171.00 265.20 117.00 3.00 27.00 11.19 3.31 85.35 161.05 85.67 17.72 8.00 955.49

1967 11.70 36.40 90.10 9.70 6.00 6.96 1.50 50.00 13.00 63.80 26.00 29.40 344.56

1968 25.50 99.90 186.90 72.50 6.00 7.50 10.33 92.08 3.00 28.40 63.90 73.70 669.71

1969 60.70 38.80 95.10 89.50 33.60 5.00 7.26 6.50 15.20 68.90 14.90 17.20 452.66

1970 22.70 75.10 283.40 61.70 3.90 4.05 0.40 7.70 26.30 59.40 36.80 42.50 623.95

1971 100.50 140.40 541.00 62.90 3.20 2.00 3.00 86.04 5.20 11.20 23.00 44.80 1023.24

1972 251.60 88.90 132.40 147.80 20.40 10.00 10.00 14.35 38.00 14.00 36.21 20.00 783.66

1973 38.90 113.40 24.80 41.20 13.61 10.40 3.54 17.68 46.00 45.27 5.20 11.00 371

1974 25.80 108.00 71.20 5.00 18.56 8.20 4.42 53.40 17.00 104.20 121.45 8.00 545.23

1975 122.70 94.10 45.60 69.20 8.90 12.00 10.38 1.00 73.22 6.00 6.00 25.40 474.5

1976 110.90 111.30 119.60 50.40 13.20 10.27 5.52 42.47 20.00 10.00 69.00 115.70 678.36

1977 14.50 51.30 100.90 205.00 161.00 7.94 14.00 12.05 188.40 139.20 126.00 135.00 1155.29

1978 87.00 603.00 246.80 231.20 42.00 9.31 5.00 93.00 95.00 95.25 22.00 47.00 1576.56

1979 174.50 111.00 78.60 9.80 20.00 9.35 5.69 13.76 12.77 53.60 19.90 58.80 567.77

1980 242.51 243.95 122.36 91.05 13.60 8.41 3.94 16.01 145.51 76.72 25.35 85.98 1075.39

1981 24.14 4.57 120.05 94.90 14.93 5.64 3.65 58.58 65.96 47.38 108.21 11.48 559.49

1982 251.20 100.67 120.55 9.79 27.36 8.06 1.11 53.98 116.71 71.98 86.86 89.77 938.04

1983 23.78 150.28 132.84 112.64 16.24 5.81 9.75 64.25 46.39 53.62 65.86 70.19 751.65

1984 183.97 366.35 123.00 37.38 30.80 2.66 10.85 41.16 107.14 58.05 103.20 67.45 1132.01

1985 157.05 243.95 131.07 133.21 31.73 4.91 1.67 89.25 13.96 133.25 100.51 129.45 1170.01

1986 246.43 224.92 119.49 198.60 36.72 7.68 9.60 29.49 172.04 135.57 39.26 43.21 1263.01

1987 79.60 74.60 41.70 89.00 14.90 0.00 0.00 0.00 1.90 18.00 38.10 9.00 366.8

1988 105.10 243.00 175.90 168.20 6.60 7.80 0.00 0.00 14.60 49.10 22.40 0.00 792.7

1989 144.26 77.08 122.78 24.90 56.13 8.33 7.27 1.84 71.58 12.95 99.97 51.61 678.7

1990 148.09 188.05 146.76 71.74 56.29 6.65 4.56 20.17 114.31 28.60 76.59 45.92 907.73

1991 221.07 3.82 127.33 7.16 132.96 5.56 7.85 11.93 150.29 58.37 94.91 18.51 839.76

1992 194.26 184.64 147.53 33.76 53.04 5.30 12.57 16.72 179.80 8.07 46.25 82.25 964.19

1993 115.76 145.20 163.59 89.52 97.08 5.79 13.84 91.59 19.14 98.49 44.06 92.14 976.20

1994 133.74 186.42 138.82 7.96 3.47 9.63 2.08 27.25 38.56 98.08 102.37 56.30 804.68

1995 267.04 193.08 138.65 64.34 160.78 6.46 2.04 57.82 101.16 89.27 55.10 34.50 1170.24

1996 246.78 602.89 121.82 181.18 88.59 7.26 13.36 71.31 133.81 77.27 12.10 30.22 1586.59

1997 188.19 143.94 220.21 198.39 68.94 3.35 13.17 3.26 77.19 62.88 48.80 73.08 1101.40

TOT. 4552.11 5533.91 4855.15 2888.82 1329.26 246.89 220.19 1348.97 2309.19 2069.54 1830.48 1719.06 28903.57

X 130.06 158.11 138.72 82.54 37.98 7.05 6.29 38.54 65.98 59.13 52.30 49.12 825.82

S 83.49 136.83 88.43 66.63 42.40 2.68 4.39 32.73 59.68 37.20 36.38 36.10 326.68

ESTACION CHILETEPRESIPITACION (mm)

CATEGORIA Pluvimetrica DEPARTAMENTOCAJAMARCA

ALTITUD 850 PROVINCIA CONTUMAZA

LATITUD 7 13 DISTRITO CHILETE

LONGITUD 78 51


1963 38.43 50.75 57.39 15.44 2.94 6.76 2.92 6.29 2.48 2.00 13.80 10.90 210.1

1964 30.20 19.60 56.00 30.70 1.80 2.21 7.42 4.50 2.86 5.50 2.40 5.80 168.99

1965 10.00 29.30 133.00 29.50 1.70 1.42 2.24 5.22 2.90 9.50 1.20 21.20 247.18

1966 30.40 13.50 43.30 20.10 2.20 3.32 2.73 5.69 2.10 20.00 2.80 0.80 146.94

1967 82.80 123.10 35.40 8.10 8.60 5.40 12.70 3.88 3.00 16.50 2.14 2.60 304.22

1968 3.60 5.30 7.30 42.29 15.40 4.07 1.08 3.43 5.35 12.50 1.60 6.40 108.32

1969 4.00 42.80 89.90 60.20 1.20 2.40 0.77 11.18 0.60 9.60 13.90 7.50 244.05

1970 24.50 3.80 33.10 23.10 11.80 3.80 1.49 2.20 5.90 48.80 11.60 10.90 180.99

1971 6.90 34.80 144.10 31.10 3.00 4.28 6.49 2.40 1.80 4.10 4.80 9.40 253.17

1972 28.10 39.20 87.20 10.20 3.20 7.15 0.80 6.27 2.20 7.80 12.20 18.20 222.52

1973 91.00 30.80 59.10 102.80 6.30 5.63 3.02 8.83 10.10 5.10 9.44 16.00 348.12

1974 28.90 44.40 23.00 14.60 7.01 7.10 2.42 0.80 4.40 8.20 12.00 10.40 163.23

1975 34.10 59.30 127.40 38.30 1.30 7.30 2.64 4.67 8.10 24.70 10.20 4.06 322.07

1976 54.10 57.20 12.60 21.60 5.20 4.00 0.72 8.57 2.48 1.60 9.83 17.30 195.2

1977 50.10 142.00 73.00 36.00 6.70 5.69 2.73 3.92 3.50 0.80 14.40 14.40 353.24

1978 0.30 51.50 40.80 5.10 8.00 6.78 1.81 3.22 3.27 3.66 7.55 12.90 144.89

1979 8.10 43.10 104.00 3.20 14.22 6.36 0.80 7.56 3.90 3.66 1.75 2.50 199.15

1980 2.00 6.10 36.70 52.67 2.80 4.08 1.49 6.82 1.99 20.90 13.36 26.80 175.71

1981 41.60 78.70 34.00 6.50 11.56 7.24 2.64 6.50 3.07 18.77 6.19 15.71 232.48

1982 20.50 49.44 10.10 31.70 2.70 2.21 1.20 11.25 4.77 14.20 16.90 39.20 204.17

1983 95.40 36.10 68.31 27.05 3.26 2.59 3.41 3.41 2.80 13.43 2.29 15.62 273.67

1984 13.27 112.85 54.66 37.54 3.77 2.79 9.18 4.14 4.15 10.04 12.33 7.40 272.12

1985 0.60 18.80 0.90 5.40 10.70 7.06 1.92 7.20 8.00 2.20 0.30 12.10 75.18

1986 12.10 13.60 32.00 76.30 3.00 5.60 0.98 2.60 1.95 5.00 6.80 17.40 177.33

1987 45.00 62.80 12.60 26.90 6.63 0.90 5.60 12.10 1.60 5.24 11.90 13.46 204.73

1988 40.20 32.50 11.80 42.90 3.50 6.19 1.20 5.05 3.85 10.18 9.07 13.64 180.08

1989 25.10 73.65 28.54 50.23 5.19 5.86 7.97 3.46 2.53 2.41 12.09 13.61 230.64

1990 38.71 41.38 31.19 51.73 3.11 4.97 6.43 10.03 4.09 7.18 5.15 15.66 219.63

1991 17.41 46.22 120.77 1.36 2.00 2.61 6.34 1.84 5.42 12.55 8.92 15.71 241.15

1992 38.95 21.41 61.34 33.18 6.60 2.60 2.53 4.63 4.86 9.71 10.26 15.60 211.67

1993 3.58 22.61 104.80 36.44 13.01 7.20 9.03 7.09 5.00 11.50 6.07 7.06 233.39

1994 61.57 22.45 141.30 52.51 4.32 5.50 9.66 9.24 6.31 6.20 12.75 13.36 345.17

1995 13.50 42.99 105.53 35.79 1.30 1.22 5.94 10.20 3.47 20.38 0.17 15.39 255.88

1996 20.79 30.80 50.12 13.37 5.48 4.26 10.65 9.14 6.78 2.55 8.59 13.01 175.54

1997 20.81 86.15 49.69 51.64 6.03 2.86 0.82 4.99 4.17 20.36 11.80 9.67 268.99

TOT. 1036.620 1589.00 2080.94 1125.54 195.53 159.41 139.77 208.32 139.75 376.82 286.55 451.66 7789.91

X 29.6177 45.40 59.46 32.16 5.59 4.55 3.99 5.95 3.99 10.77 8.19 12.90 222.57

Sx 24.75 32.19 41.35 21.88 3.91 1.99 3.34 2.96 2.06 9.28 4.75 7.16 64.29

PROCESAMIENTO DE DATOS

1. En el siguiente cuadro mostramos los promedios de las precipitaciones de las tres estaciones

Altitud media = 2231.00 msnm (SUB CUENCA DEL RIO HUERTAS)

PROMEDIO DE PRECIPITACIONES DE LAS TRES ESTACIONES


1963 121.5 106.3 84.9 95.7 9.8 9.2 3.9 35.4 4.8 21.6 28.5 31.0 552.65

1964 70.6 70.5 99.7 62.7 7.2 5.2 5.6 5.1 7.6 17.7 27.4 48.2 427.67

1965 62.6 50.6 116.9 40.7 7.4 5.9 8.5 15.7 13.4 34.0 10.2 28.1 394.05

1966 96.8 132.7 78.4 21.2 12.4 5.5 4.3 32.7 57.5 47.0 15.0 6.8 510.18

1967 93.2 127.5 69.9 15.8 11.4 4.5 10.3 18.8 5.6 45.6 16.7 17.5 436.72

1968 27.2 53.4 77.2 46.7 8.5 5.9 9.8 33.3 9.5 24.7 32.8 34.6 363.74

1969 25.9 76.0 98.9 74.5 12.4 4.5 5.5 6.2 13.3 37.4 31.4 30.8 416.80

1970 38.8 51.1 136.2 43.5 9.8 7.7 5.2 9.0 14.5 57.7 27.5 23.5 424.71

1971 52.0 77.5 306.5 70.9 3.4 6.6 3.8 35.9 5.7 20.6 12.3 31.6 626.75

1972 111.0 75.0 131.6 63.8 10.6 6.3 6.7 7.4 19.8 12.3 26.3 34.2 505.12

1973 81.6 84.0 81.3 84.8 13.0 9.2 6.7 14.2 29.3 31.8 13.7 32.4 482.02

1974 46.6 93.0 46.5 20.2 9.7 7.6 7.3 19.9 14.6 44.6 53.0 25.6 388.66

1975 110.8 78.2 105.7 40.7 16.1 12.5 5.1 8.7 40.4 35.7 9.6 31.5 495.02

1976 115.0 61.6 73.2 39.5 7.9 8.0 4.6 22.6 8.2 7.1 31.1 58.2 436.84

1977 75.3 131.8 82.2 101.1 59.1 7.3 10.4 7.7 69.9 49.0 51.7 78.1 723.70

1978 32.7 236.8 112.9 83.6 31.8 7.4 8.0 37.5 33.5 38.8 10.2 33.5 666.64

1979 72.4 82.9 152.7 8.9 13.7 6.5 3.4 8.9 8.8 24.9 27.2 21.2 431.40

1980 91.3 85.2 76.7 55.7 6.7 8.2 5.1 9.2 50.5 58.2 27.8 55.1 529.67

1981 42.3 113.6 91.1 41.3 10.7 6.8 4.8 21.9 27.6 35.0 44.8 33.9 473.85

1982 109.1 76.5 52.1 37.7 15.4 6.1 3.4 24.8 47.9 42.9 46.4 74.2 536.45

1983 56.4 87.4 132.4 72.5 11.5 5.7 8.8 24.6 20.4 22.4 22.7 70.9 535.54

1984 78.0 195.7 96.0 49.1 25.1 5.1 8.5 16.0 49.7 40.5 54.8 31.5 650.04

1985 58.5 111.9 61.2 58.1 24.5 7.1 3.1 33.9 10.7 48.5 53.6 58.5 529.68

1986 107.6 96.4 82.7 154.2 15.8 4.6 7.0 13.0 71.0 47.6 27.3 53.8 680.98

1987 104.9 71.2 26.4 67.2 8.8 2.3 5.1 7.3 8.1 10.3 29.2 15.6 356.44

1988 86.3 129.3 72.3 95.3 5.0 6.1 5.0 6.6 12.4 28.9 31.3 9.8 488.29

1989 99.3 113.3 69.6 51.4 22.8 8.2 7.9 8.4 32.9 22.3 42.9 36.7 515.63

1990 81.0 137.3 93.6 61.0 25.9 5.9 8.2 12.8 48.1 27.2 34.7 25.7 561.37

1991 85.0 77.5 117.5 29.6 47.4 5.0 9.5 5.7 55.2 36.3 42.9 28.1 539.57

1992 95.6 98.8 117.8 38.8 22.7 6.4 5.7 13.3 67.2 18.4 38.6 53.3 576.47

1993 71.3 100.8 140.9 68.9 37.9 7.6 12.5 34.3 16.8 43.4 23.4 52.3 610.08

1994 89.4 120.9 140.2 31.7 3.8 8.7 6.0 17.5 21.4 52.0 47.6 42.8 582.16

1995 122.4 112.0 103.8 75.0 55.2 6.5 4.5 23.8 44.4 54.9 29.6 39.0 671.14

1996 104.5 275.6 129.8 79.8 33.9 7.5 12.1 32.4 56.3 38.4 11.4 28.2 809.94

1997 121.0 94.0 148.4 101.2 26.6 5.1 5.6 4.7 33.7 48.0 37.6 50.8 676.60

TOT. 2838.08 3686.22 3607.30 2082.69 643.99 232.74 232.24 628.89 1030.75 1225.78 1070.92 1326.96 18606.57

X 81.09 105.32 103.07 59.51 18.40 6.65 6.64 17.97 29.45 35.02 30.60 37.91 531.62

Sx 28.19 48.00 46.76 29.56 14.13 1.79 2.49 10.79 20.90 13.83 13.42 17.32 108.83

2. seguidamente calculamos el Coeficientes de Correlacin

Para encontrar los coeficientes de correlacion, se formula la ecuacion con las altitudes de las estaciones y su Precipitacion Promedio Mensual

Y con la Prueba de t-Student se comprueba s se puede utilizar o no los datos para cada respectivo mes. Obteniendose los cuadros siguientes:

Altura media de la cuenca 2231.00 m.s.n.m.

Para = 0.05

grados de libertad n = 35 - 2 = 33

ESTACIN ALTITUD ENE FEB MAR ABR MAY JUN JUL AGO SET OCT NOV DIC

LLAGADEN 2000 83.586 112.450 111.023 63.820 11.633 8.340 9.622 9.411 18.380 35.171 31.307 51.719

CONTUMAZA 2330 130.060 158.112 138.719 82.538 37.979 7.054 6.291 38.542 65.977 59.130 52.299 49.116

CHILETE 850 29.618 45.400 59.455 32.158 5.587 4.555 3.993 5.952 3.993 10.766 8.187 12.905

PROM 1726.67 81.09 105.32 103.07 59.51 18.40 6.65 6.64 17.97 29.45 35.02 30.60 37.91

DESV. EST. 776.938 50.268 56.693 40.226 25.465 17.224 1.925 2.830 17.901 32.441 24.182 22.065 21.697

PROM(SUMAPROD) 165129.4 210630.3 198599.4 115762.7 38835.4 12329.3 12432.3 37894.8 64626.7 72421.8 63810.2 76282.5

R 0.643 0.653 0.660 0.658 0.528 0.567 0.443 0.494 0.547 0.636 0.640 0.642

B 0.042 0.048 0.034 0.022 0.012 0.001 0.002 0.011 0.023 0.020 0.018 0.018

A 9.241 23.006 44.029 22.272 -1.811 4.225 3.847 -1.681 -9.957 0.840 -0.804 6.966

Y = BX + A

Tc = 0.84 0.86 0.88 0.87 0.62 0.69 0.49 0.57 0.65 0.82 0.83 0.84

Tt = 2.036 2.036 2.036 2.036 2.036 2.036 2.036 2.036 2.036 2.036 2.036 2.036

EVALUACIN CUMPLE CUMPLE CUMPLE CUMPLE CUMPLE CUMPLE CUMPLE CUMPLE CUMPLE CUMPLE CUMPLE CUMPLE

P (altura de estacin Huertas) 102.073 129.363 120.310 70.381 24.303 7.358 7.450 23.708 40.960 45.006 39.770 46.952

1.2588 1.2283 1.1673 1.1828 1.3208 1.1065 1.1228 1.3194 1.3908 1.2851 1.2998 1.2384COEF. DE CORRELACION

3. Por ultimo se multiplica las Prrecipitaciones Promedio por su Coeficiente para obtener las

precipitaciones para la ESTACIN GENERADA PARA LA SUB CUENCA DEL RIO HUERTAS.

PRECIPITACIONES TOTALES MENSUALES GENERADAS PARA LA ESTACION HUERTAS

ALTURA 2231.00 msnm UTM 736 - 751 Km E

9 184 - 9 202 Km N

AO ENE FEB MAR ABR MAY JUN JUL AGO SET OCT NOV DIC TOTAL

1963 152.93 130.58 99.14 113.25 12.90 10.14 4.42 46.73 6.69 27.72 36.99 38.44 679.94

1964 88.88 86.64 116.41 74.15 9.52 5.79 6.32 6.75 10.60 22.76 35.55 59.73 523.11

1965 78.80 62.15 136.50 48.10 9.72 6.52 9.56 20.74 18.70 43.71 13.32 34.77 482.57

1966 121.81 163.04 91.46 25.04 16.42 6.10 4.85 43.14 79.90 60.41 19.46 8.38 640.01

1967 117.28 156.65 81.63 18.65 15.01 4.93 11.60 24.78 7.74 58.56 21.73 21.71 540.28

1968 34.24 65.63 90.16 55.27 11.23 6.52 11.04 43.94 13.14 31.78 42.68 42.85 448.48

1969 32.64 93.35 115.45 88.08 16.33 5.02 6.19 8.22 18.45 48.06 40.77 38.18 510.74

1970 48.86 62.82 159.03 51.49 12.92 8.46 5.88 11.90 20.15 74.19 35.79 29.14 520.64

1971 65.50 95.15 357.82 83.90 4.51 7.33 4.23 47.34 7.88 26.47 15.94 39.09 755.17

1972 139.77 92.08 153.62 75.50 14.04 6.99 7.56 9.73 27.54 15.85 34.23 42.31 619.22

1973 102.76 103.13 94.86 100.26 17.22 10.23 7.57 18.73 40.75 40.85 17.78 40.12 594.28

1974 58.62 114.27 54.32 23.85 12.76 8.45 8.25 26.21 20.35 57.31 68.87 31.75 485.01

1975 139.44 96.04 123.35 48.10 21.32 13.79 5.76 11.47 56.25 45.92 12.48 39.02 612.94

1976 144.72 75.70 85.39 46.69 10.43 8.84 5.12 29.80 11.40 9.08 40.48 72.03 539.69

1977 94.79 161.93 95.99 119.58 78.08 8.02 11.68 10.19 97.27 63.01 67.15 96.72 904.42

1978 41.20 290.82 131.79 98.84 42.05 8.15 8.99 49.48 46.58 49.86 13.24 41.49 822.47

1979 91.09 101.78 178.29 10.53 18.06 7.17 3.85 11.75 12.23 32.02 35.31 26.21 528.30

1980 114.89 104.67 89.52 65.89 8.91 9.11 5.67 12.09 70.20 74.84 36.14 68.23 660.14

1981 53.26 139.52 106.36 48.89 14.19 7.54 5.42 28.89 38.32 45.00 58.23 41.94 587.54

1982 137.38 93.97 60.76 44.63 20.34 6.75 3.84 32.72 66.63 55.12 60.25 91.84 674.22

1983 70.99 107.30 154.53 85.75 15.19 6.34 9.88 32.40 28.34 28.72 29.53 87.77 656.74

1984 98.24 240.37 112.02 58.05 33.21 5.62 9.52 21.15 69.17 52.08 71.20 38.99 809.62

1985 73.66 137.47 71.43 68.77 32.33 7.91 3.44 44.73 14.91 62.35 69.69 72.41 659.09

1986 135.46 118.37 96.53 182.42 20.88 5.09 7.86 17.10 98.77 61.11 35.47 66.67 845.74

1987 132.09 87.49 30.86 79.44 11.58 2.58 5.72 9.59 11.33 13.21 38.00 19.26 441.15

1988 108.68 158.86 84.44 112.68 6.56 6.78 5.63 8.68 17.20 37.13 40.63 12.15 599.41

1989 125.02 139.18 81.29 60.78 30.10 9.03 8.87 11.03 45.81 28.61 55.70 45.45 640.88

1990 102.00 168.60 109.29 72.09 34.26 6.47 9.20 16.85 66.90 35.01 45.07 31.85 697.60

1991 106.95 95.15 137.15 35.03 62.59 5.50 10.67 7.48 76.79 46.64 55.73 34.83 674.50

1992 120.33 121.33 137.46 45.86 29.98 7.12 6.41 17.50 93.49 23.65 50.16 65.95 719.24

1993 89.79 123.79 164.53 81.48 50.02 8.39 14.06 45.30 23.34 55.73 30.36 64.78 751.58

1994 112.56 148.47 163.66 37.54 5.04 9.67 6.78 23.06 29.78 66.82 61.86 53.05 718.30

1995 154.06 137.52 121.14 88.69 72.96 7.16 5.10 31.35 61.80 70.59 38.49 48.34 837.20

1996 131.57 338.47 151.49 94.37 44.76 8.35 13.54 42.76 78.36 49.37 14.82 34.97 1002.82

1997 152.30 115.41 173.19 119.72 35.18 5.65 6.25 6.22 46.85 61.66 48.88 62.87 834.19

TOT. 3572.57 4527.72 4210.84 2463.33 850.60 257.52 260.75 829.77 1433.60 1575.22 1391.94 1643.34 23017.21

X 102.07 129.36 120.31 70.38 24.30 7.36 7.45 23.71 40.96 45.01 39.77 46.95 657.63

Sx 35.47927812 58.96239539 54.58917317 34.9661574 18.659593 1.9822501 2.7978192 14.2407623 29.0740563 17.7672377 17.4455375 21.4463857 135.895686

657.63

3. BALANCE HIDRICO Y

GENERACION DE CAUDALES MAXIMOS MENSUALES

Para esta ocacion usaremos el METODO DE BALANCE HIDROLOGICO

La Ecuacion General es:

Donde:

Qm= Caudal medio mensual (mm/mes)

Pi= Prec.Total mensual sobre la cuenca (mm/mes)

Di= Deficit de escurrimiento (mm/mes)

Gi= Gasto de la retencion de la cuenca(mm/mes)

Pero:

C:Coeficiente de Escorrentia

Tendriamos:

DATOS PREVIOS:

ALTITUD 2231 msnm

TEMPERATURA MEDIA 15.82 C

657.6

Donde:

L: Coef de Temperatura

T: Temperatura

L = 893.6781

Donde:

D: Dficit de escorrendia

P: Precipitacin mensual anual

L: Coeficiente de temperatura

Reemplazando tenemos:

D = 547.7392

Donde:

Ce: Coeficiente de escorrentia

P: Presipitacin mensual anual

COEFICIENTE DE ESCORRENTIA (Ce)

PR. MENSUAL ANUAL

COEFICIENTE DE TEMPERATURA (L)

DFICIT DE ESCORRENTA

iiiim AGDPQ -+-=

iiim AGPEQ -+=

*i i i iP D C P PE- = =

3300 25L T T= + +

12 2

20.9

PD P

L

-

= +

P DCe

P

-=

D: Dficit de escorrendia

Reemplazando en la formula tenemos:

Ce= 0.167

32.2

CALCULO DE LA PRECIPITACION EFECTIVA

Pe: Precipitacin Efectiva

P: Ptotal mensual

N: Numero de escurrimiento

MES Ene Feb Mar Abr May Jun Jul Agos Sep Oct Nov

P TOTAL 102.07 129.36 120.31 70.38 24.30 7.36 7.45 23.71 40.96 45.01 39.77

P EFEC. P. 57.64 81.80 73.67 31.48 2.76 0.22 0.21 2.55 10.94 13.41 10.24

N. DE ESCURRIMIENTO

P DCe

P

-=

2508

5.08

203220.32

PN

Pe

PN

- +

=

+ -

Dic

46.95

14.65

DATOS

REA DE LA CUENCA: 101.5 km2

PENDIENTE DEL CAUCE PRINCIPAL:10.1 %

TEMPERATURA MEDIA: 15.82

COEFICIENTE DE ESCORRENTA:0.167

COEFICIENTE DE AGOTAMIENTO:

Donde:

a: Coeficiente de agotamiento

AR: rea de la Cueenca

a = 0.0184

RETENCIN EN LA CUENCA ( R )

Donde:

Ca: Coeficiente del Acuifero

Retencin por acufero Donde:

I(%): Pendiente del cauce principal

LA 239.25

Ademas:

15.23

Retencin por lagunas y pantanos

LL = 500

AL = Area de lagunas y pantanos

AL = 0 mm*km2/ao

Retencin por Nevado

LN = 500

AN =

AN = 0 mm*km2/ao

Reemplazando temos que la retencin total es la siguiente

R= 3643.6579 mm*km2/ao

35.8875 mm/ao

Seguidamente llenamos el siguiente cuadro, teniendo como base las formulas respectivas

para obtener calculos

Relacin entre Descargas y Retencin Caudales generados(mm/mes)

Gasto de la Retencin de la cuenca Caudales generados(m3/seg)

Coeficiente de Abastecimiento

Abastecimiento de la Retencin de la cuenca

RETENCION TOTAL

MICROCUENCA de 15% a 18%

Area de nevados

0.00252 ( ) 0.030a Ln AR= - +

( * )* * *aR C AR LA AL LL AN LN= + +

(%)750* 315

100

ILA

=+ - +

*aC A R

R etenciontotalR

AR

=

at

o eb-=

100=T

E

i PE

PEa

Ra

Ai

i = 100

ii AGPE -+

AREAAGPE ii -+ )(R

b

bG

m

o

i =

ABASTECIMIENTO

TOTAL EFECTIVA bi Gi ai Ai VOLUMEN

N Das mm/mes mm/mes mm/mes m3/seg MMC

1 2 3 4 5 6 7 8 9 10 11

ENERO 31 102.07 57.64 19.24 6.91 50.74 8.67 22.46

FEBRERO 28 129.36 81.80 27.31 9.80 72.00 12.30 31.88

MARZO 31 120.31 73.67 24.59 8.83 64.84 11.08 28.71

ABRIL 30 70.38 31.48 10.51 3.77 27.71 4.73 12.27

MAYO 31 24.30 2.76 0.58 16.45 19.21 3.28 8.50

JUNIO 30 7.36 0.22 0.33 9.31 9.53 1.63 4.22

JULIO 31 7.45 0.21 0.19 5.37 5.58 0.95 2.47

AGOSTO 31 23.71 2.55 0.11 3.04 5.58 0.95 2.47

SETIEMBRE 30 40.96 10.94 0.06 1.72 12.66 2.16 5.60

OCTUBRE 31 45.01 13.41 4.48 1.61 11.80 2.02 5.23

NOVIEMBRE 30 39.77 10.24 3.42 1.23 9.01 1.54 3.99

DICIEMBRE 31 46.95 14.65 4.89 1.75 12.89 2.20 5.71

AO 365 657.63 299.56 1.26 35.89 94.43 33.89 301.56 51.51 133.51

CALCULO DE PARAMETROS DE CORRELACIN MULTIPLE: Qt, Qt-1,PE

0.00 B C D E F G H

Qt Qt-1 PE (Qt-1)^2 (PE)^2 Qt-1*PE Qt*PE Qt-1*QT

8.67 2.20 57.64 4.85 3322.44 126.94 499.52 19.09 75.10

12.30 8.67 81.80 75.10 6691.31 708.89 1006.02 106.58 151.25

11.08 12.30 73.67 151.25 5427.13 906.02 815.96 136.22 122.68

4.73 11.08 31.48 122.68 990.85 348.65 148.97 52.42 22.40

3.28 4.73 2.76 22.40 7.61 13.06 9.05 15.53 10.77

1.63 3.28 0.22 10.77 0.05 0.73 0.36 5.34 2.65

0.95 1.63 0.21 2.65 0.04 0.34 0.20 1.55 0.91

0.95 0.95 2.55 0.91 6.48 2.43 2.43 0.91 0.91

2.16 0.95 10.94 0.91 119.61 10.43 23.64 2.06 4.67

2.02 2.16 13.41 4.67 179.79 28.99 27.03 4.36 4.06

1.54 2.02 10.24 4.06 104.83 20.64 15.76 3.10 2.37

2.20 1.54 14.65 2.37 214.57 22.55 32.26 3.39 4.85

51.51 51.51 299.56 402.62 17064.7 2189.7 2581.2 350.55 2653.17

A B C D E F G H 3055.79

PRECIPITACIN

mm/mes

CAUDALES

MENS. GENER.

GASTO

Parametros de generacin sintetica de caudales

B1 1.5

B2 0.13

B3 0.13

S 1.43

R^2 0.95

R 0.98

ECUACION DEL CAUDAL MEDIO MENSUAL PARA PERIODOS EXTENDIDOS

Es necesario correlacionar el caudal actual en funcion del caudala anterior,

combinandolo con la precipitacion efectiva, que se convierte con nuestra variable de impulso

Para mantener el rango de los valores generados y obtener una aproximacion mayor a la realidad,

se utiliza ademas una variable aleatoria.

NUMEROS ALEATORIOS

AO ENE FEB MAR ABR MAY JUN JUL AGO SEP OCT NOV

1963 -0.30 -1.28 0.24 1.28 1.20 1.73 -2.18 -0.23 1.10 -1.09 -0.69

1964 -1.85 -0.98 -0.77 -2.12 -0.57 -0.40 0.13 -0.37 -0.33 -0.37 1.34

1965 -0.19 -0.51 1.97 0.87 2.38 -0.65 1.66 -1.61 0.54 0.90 1.92

1966 -0.52 0.68 -0.38 0.76 -1.44 -0.85 -1.52 -0.36 -0.03 0.03 -0.32

1967 -1.74 -0.74 -2.58 1.45 -1.28 -0.65 0.76 0.47 0.87 0.60 -1.37

1968 0.69 0.32 -0.94 -0.24 0.13 0.56 0.14 -0.91 1.88 0.49 0.07

1969 0.86 -0.64 -0.92 1.11 -1.20 -1.56 0.71 0.64 2.21 1.44 1.30

1970 0.00 0.45 -0.03 -1.05 -1.77 0.83 0.44 0.62 0.21 -1.03 1.24

1971 -0.84 -0.82 -0.43 -0.45 -0.52 0.85 0.51 -0.61 1.30 -1.76 0.55

1972 0.04 -0.65 -0.55 0.85 0.80 0.46 0.69 1.63 0.30 0.59 1.85

1973 1.04 0.14 1.14 -0.15 -0.78 1.08 -0.58 0.53 0.55 -0.32 -0.44

1974 1.99 -0.57 0.09 -0.23 2.84 1.25 0.88 1.33 0.19 0.54 -0.25

1975 1.27 -0.29 -1.31 0.76 0.78 0.43 0.40 -0.65 0.72 0.53 1.08

1976 0.46 1.47 -1.72 0.05 1.35 1.69 0.24 0.15 1.85 -0.04 -0.66

1977 -0.01 1.04 0.43 1.45 -0.12 -0.96 -1.54 -2.57 0.10 0.30 -0.02

1978 0.26 1.48 0.09 -1.12 -1.39 0.19 0.95 -1.51 -0.61 0.52 -0.22

1979 -0.16 -0.44 -0.80 0.64 0.06 1.26 0.26 0.06 0.23 0.21 -0.01

1980 0.24 0.15 0.75 -0.74 0.62 0.22 0.11 0.87 1.80 -1.31 -1.23

1981 1.19 -0.88 -2.15 -0.90 0.20 0.43 -0.98 -0.86 0.46 0.12 -0.54

1982 -0.94 -0.90 1.05 1.63 -0.67 -0.17 0.11 1.84 0.60 1.65 0.18

1983 -0.64 -0.97 1.19 0.92 -1.73 1.27 -0.20 -1.13 -1.88 -0.82 0.47

1984 -0.07 -0.05 0.21 -0.35 0.93 -0.49 2.34 0.74 0.61 -0.98 0.87

2

1

2

3121 )1( rSZPEBQBBQ iii -+++= -

1 1

2

1 1 2 1

23

1

22 1 1

2 1 3

1

2 1 3

12

( )( ) ( )

12 12 12

9

( ) (12

i i i

i i i i i

i ii i i i

i i i i

i i i i i

i i

i i i

Q PE B Q

Q Q PE B Q Q

B Q PEPE Q PE PE

Q Q Q Q PEQ B Q Q B Q PE

S

Q QB Q Q B Q P

r

-

- - -

-

-

-

-

-

=

- - - - -

=

- -

=

1

22

)12

( )

12

i

i

i

i

Q PEE

QQ

-

-

1985 -0.73 -0.30 -1.34 1.35 1.05 0.18 -2.19 0.51 0.53 1.22 -0.96

1986 -0.56 -0.73 -1.72 1.37 -0.97 1.55 -1.17 -0.41 -1.31 1.59 0.03

1987 0.98 1.95 -0.06 -1.03 -0.57 0.85 0.87 0.51 -1.49 -1.40 -0.14

1988 -0.63 0.88 -0.84 -0.11 -0.23 1.52 -1.32 -0.94 -0.17 -1.06 -1.43

1989 0.58 -0.34 0.41 -2.05 1.17 -1.95 -0.52 -0.98 -0.10 0.13 1.74

1990 -0.79 -0.75 -0.76 1.28 -1.44 0.97 -0.65 -0.67 0.08 -0.83 0.70

1991 -0.79 0.42 -0.87 -0.23 -0.26 0.38 -0.72 -0.76 -0.51 -0.06 0.33

1992 -0.79 0.53 -0.99 -0.31 -0.26 0.38 -0.78 -0.87 -0.57 0.23 0.37

1993 -0.79 0.63 -1.10 -0.39 -0.27 0.37 -0.84 -0.97 -0.63 0.52 0.40

1994 -0.79 0.74 -1.21 -0.47 -0.27 0.37 -0.91 -1.07 -0.69 0.81 0.44

1995 -0.79 0.85 -1.33 -0.55 -0.28 0.36 -0.97 -1.18 -0.75 1.10 0.47

1996 -0.79 0.96 -1.44 -0.63 -0.28 0.35 -1.03 -1.28 -0.81 1.39 0.50

1997 -0.79 1.07 -1.55 -0.71 -0.29 0.35 -1.10 -1.39 -0.87 1.68 0.54

PRECIPITACIONES EFECTIVAS MENSUALES DE LA SUB CUENCA DEL RIO HUERTAS


1963 103.37 82.90 55.11 67.40 0.09 0.01 0.83 14.51 0.32 4.11 8.67

1964 46.43 44.56 70.20 34.43 0.03 0.49 0.39 0.31 0.00 2.22 7.88

1965 38.15 25.23 88.27 15.39 0.02 0.35 0.02 1.59 1.04 12.60 0.12

1966 75.01 112.76 48.59 3.03 0.55 0.43 0.72 12.25 39.04 23.95 1.23

1967 70.97 106.81 40.44 1.03 0.32 0.70 0.02 2.94 0.17 22.60 1.89

1968 7.20 27.84 47.49 20.26 0.01 0.35 0.00 12.74 0.11 5.96 11.97

1969 6.39 50.18 69.35 45.76 0.54 0.67 0.42 0.12 0.98 15.37 10.82

1970 15.89 25.73 109.02 17.65 0.09 0.10 0.48 0.03 1.42 34.47 8.01

1971 27.74 51.71 300.78 42.30 0.81 0.23 0.89 14.90 0.16 3.59 0.47

1972 91.26 49.11 104.00 35.50 0.20 0.28 0.20 0.02 4.03 0.45 7.19

1973 58.23 58.56 51.46 56.08 0.71 0.00 0.19 1.05 10.81 10.87 0.83

1974 22.65 68.30 19.60 2.60 0.08 0.10 0.12 3.49 1.48 21.71 30.31

1975 90.96 52.47 76.38 15.39 1.76 0.17 0.50 0.01 20.95 13.99 0.06

1976 95.80 35.66 43.53 14.48 0.00 0.07 0.65 5.03 0.01 0.05 10.65

1977 51.40 111.72 52.42 73.02 37.57 0.14 0.02 0.00 53.51 25.87 28.99

1978 11.08 235.21 84.00 54.86 11.59 0.13 0.06 16.30 14.41 16.56 0.12

1979 48.28 57.39 127.05 0.00 0.89 0.25 1.00 0.02 0.04 6.08 7.76

1980 68.85 59.89 46.96 28.03 0.06 0.05 0.52 0.04 31.33 34.98 8.20

1981 18.87 91.03 61.36 15.91 0.21 0.20 0.58 4.62 9.41 13.40 22.37

1982 89.07 50.71 24.20 13.17 1.47 0.31 1.01 6.42 28.59 20.16 23.83

1983 31.95 62.18 104.85 43.82 0.35 0.39 0.01 6.26 4.38 4.54 4.90

1984 54.35 186.30 66.32 22.24 6.67 0.53 0.03 1.71 30.54 18.06 32.11

1985 34.05 89.16 32.29 30.23 6.23 0.15 1.14 13.23 0.31 25.38 30.94

1986 87.33 71.94 52.89 130.94 1.63 0.66 0.16 0.69 54.80 24.47 7.84

1987 84.27 45.27 5.52 38.67 0.01 1.45 0.51 0.02 0.01 0.11 9.23

1988 63.38 108.86 42.74 66.90 0.35 0.31 0.53 0.08 0.71 8.74 10.74

1989 77.89 90.72 40.17 24.22 5.16 0.05 0.06 0.00 13.92 4.49 20.57

1990 57.58 117.95 63.92 32.81 7.21 0.36 0.04 0.63 28.80 7.60 13.45

1991 61.87 51.71 88.87 7.61 25.55 0.56 0.00 0.21 36.53 14.44 20.58

1992 73.69 74.58 89.15 13.95 5.11 0.26 0.37 0.77 50.30 2.53 16.76

1993 47.19 76.78 114.15 40.32 16.66 0.10 0.20 13.59 2.42 20.59 5.29

1994 66.80 99.24 113.34 8.97 0.67 0.02 0.31 2.32 5.02 28.74 25.02

1995 104.42 89.20 74.41 46.27 33.50 0.25 0.65 5.75 24.97 31.64 9.50

1996 83.80 281.80 102.03 51.05 13.25 0.11 0.14 12.02 37.79 16.23 0.29

1997 102.78 69.31 122.26 73.14 7.69 0.52 0.40 0.41 14.58 24.87 15.90

Ahora remplazamos los datos en la ecuacin anterior para tener los datos de los caudales medios mensuales

CUADRO DE CAUDALES MEDIOS GENERADOS PARA LA SUB CUENCA DEL RIO HUERTAS


1963 15.13 13.00 10.34 12.11 2.51 2.48 1.12 3.43 2.02 1.97 2.67

1964 7.23 8.11 11.98 6.74 1.94 1.86 1.81 1.55 1.52 1.95 3.22

1965 6.69 5.74 15.20 5.22 2.88 1.76 2.25 1.31 1.93 3.71 2.39

1966 11.37 17.50 9.29 3.58 1.73 1.71 1.32 3.10 6.69 4.90 1.82

1967 10.46 16.28 7.53 3.54 1.75 1.81 1.96 2.15 1.93 4.91 1.57

1968 2.94 6.35 8.97 5.50 2.16 2.15 1.76 2.99 2.24 2.71 3.34

1969 2.89 8.95 11.82 9.24 1.80 1.52 1.99 1.84 2.46 4.24 3.59

1970 3.85 6.12 17.26 4.90 1.56 2.20 1.92 1.82 1.88 5.93 3.20

1971 5.12 9.09 42.06 8.29 2.05 2.23 1.99 3.37 2.06 1.69 2.00

1972 13.66 8.80 16.44 7.83 2.40 2.11 1.96 2.15 2.25 2.03 3.29

1973 9.69 10.29 10.15 10.18 1.96 2.27 1.55 1.93 3.20 3.09 1.73

1974 5.37 11.33 5.67 3.20 3.03 2.34 2.01 2.50 1.88 4.78 5.62

1975 14.02 9.36 12.61 5.19 2.59 2.09 1.91 1.42 4.58 3.77 2.11

1976 14.39 7.73 8.21 4.84 2.55 2.48 1.87 2.32 2.22 1.77 2.94

1977 8.47 17.48 10.05 12.90 6.96 1.64 1.22 0.80 8.61 5.24 5.53

1978 3.31 33.68 14.05 9.71 3.18 2.00 2.02 3.26 3.30 4.10 1.71

1979 8.01 9.95 19.36 3.15 2.25 2.36 1.93 1.64 1.70 2.64 2.77

1980 10.81 10.46 9.44 6.35 2.32 2.00 1.82 1.91 6.27 5.91 2.43

1981 4.62 14.18 10.39 4.72 2.21 2.09 1.47 1.95 2.99 3.56 4.50

1982 13.06 8.93 6.58 5.17 2.09 1.91 1.88 3.05 5.53 4.93 4.92

1983 5.73 10.40 17.11 8.93 1.61 2.38 1.65 2.08 1.59 2.11 2.55

1984 8.83 26.83 11.79 5.72 3.28 1.84 2.46 2.08 5.79 3.81 6.22

1985 5.98 14.12 6.87 7.30 3.26 2.01 1.16 3.51 1.83 5.47 5.48

1986 12.96 11.74 9.42 20.40 2.02 2.51 1.36 1.58 8.33 5.47 2.79

1987 13.05 9.14 3.80 7.64 1.94 2.39 2.06 1.79 1.15 1.35 2.92

1988 9.83 17.06 8.39 11.60 2.09 2.45 1.36 1.34 1.66 2.58 2.70

1989 12.10 14.31 8.45 5.43 3.16 1.31 1.55 1.31 3.40 2.41 4.99

1990 9.02 17.72 11.17 7.62 2.59 2.28 1.51 1.49 5.39 2.50 3.73

1991 9.58 9.48 14.37 3.85 5.36 2.12 1.48 1.41 6.21 3.64 4.54

1992 11.11 12.49 14.37 4.65 2.70 2.08 1.51 1.45 7.98 2.18 4.06

1993 7.67 12.81 17.59 8.06 4.20 2.06 1.47 3.08 1.74 4.62 2.58

1994 10.22 15.77 17.45 3.96 2.12 2.05 1.46 1.58 2.06 5.78 5.15

1995 15.11 14.50 12.35 8.78 6.38 2.07 1.49 1.99 4.63 6.25 3.15

1996 12.43 39.57 15.90 9.37 3.75 2.05 1.40 2.78 6.28 4.33 1.96

1997 14.89 11.98 18.50 12.22 3.02 2.11 1.41 1.23 3.24 5.55 4.00

DIC

-1.69

-0.09

-0.08

2.19

-1.12

0.83

0.11

-0.31

-0.12

-0.34

-1.37

-1.22

-2.77

0.91

0.20

-0.34

-1.22

0.56

0.10

1.56

0.92

1.45

1.21

0.33

-0.63

-2.16

-0.51

0.24

-1.28

-1.59

-1.90

-2.21

-2.53

-2.84

-3.15

DIC

9.48

23.45

7.47

0.10

1.88

12.07

9.33

4.73

9.85

11.75

10.45

5.95

9.81

32.77

53.05

11.25

3.49

29.82

11.52

48.91

45.50

9.79

33.07

28.63

1.18

0.04

13.69

6.00

7.51

28.08

27.19

18.72

15.55

7.58

25.77

DIC

2.39

4.72

2.64

2.42

1.59

3.53

2.95

2.22

2.94

3.12

2.62

2.08

2.09

6.25

8.66

3.05

1.76

5.76

3.23

8.56

7.91

3.44

6.38

5.53

1.65

1.01

3.32

2.56

2.27

4.84

4.63

3.43

2.91

1.78

4.04

4 CURVAS DE PERSISTENCIA PARA CADA MES DE LOS CAUDALES GENERADOS

Utilizando la ecuacin (09) se procedi a ordenar lo datos en forma decreciente y a calcular los valores de la probabilidad emprica , P(x > X) , que se muestra en el CUADRO 01

Probilidad de Weibull f(x) : Probalidad de Weibull

m : El numero de orden asignado

N : Numero de aos (muestra)

CUADRO 01: ORDENAMIENTO DE LOS DATOS DE CAUDALES MEDIOS GENERADOS Y CLCULO DE LA PROBABILIDAD EMPIRICA

m P(X>X) ENE FEB MAR. ABR. MAY. JUN. JUL. AGOS. SET. OCT. NOV. DIC. TOTAL

1 2.778 15.1 39.6 42.1 20.4 7.0 2.5 2.5 3.5 8.6 6.2 6.2 8.7 1002.8

2 5.556 15.1 33.7 19.4 12.9 6.4 2.5 2.2 3.4 8.3 5.9 5.6 8.6 904.4

3 8.333 14.9 26.8 18.5 12.2 5.4 2.5 2.1 3.4 8.0 5.9 5.5 7.9 845.7

4 11.111 14.4 17.7 17.6 12.1 4.2 2.5 2.0 3.3 6.7 5.8 5.5 6.4 837.2

5 13.889 14.0 17.5 17.4 11.6 3.7 2.4 2.0 3.1 6.3 5.5 5.2 6.3 834.2

6 16.667 13.7 17.5 17.3 10.2 3.3 2.4 2.0 3.1 6.3 5.5 5.0 5.8 822.5

7 19.444 13.1 17.1 17.1 9.7 3.3 2.4 2.0 3.0 6.2 5.5 4.9 5.5 809.6

8 22.222 13.1 16.3 16.4 9.4 3.2 2.3 2.0 3.0 5.8 5.2 4.5 4.8 755.2

9 25.000 13.0 15.8 15.9 9.2 3.2 2.3 2.0 2.8 5.5 4.9 4.5 4.7 751.6

10 27.778 12.4 14.5 15.2 8.9 3.0 2.3 1.9 2.5 5.4 4.9 4.1 4.6 719.2

11 30.556 12.1 14.3 14.4 8.8 3.0 2.2 1.9 2.3 4.6 4.9 4.0 4.0 718.3

12 33.333 11.4 14.2 14.4 8.3 2.9 2.2 1.9 2.2 4.6 4.8 3.7 3.5 697.6

13 36.111 11.1 14.1 14.0 8.1 2.7 2.2 1.9 2.1 3.4 4.6 3.6 3.4 679.9

14 38.889 10.8 13.0 12.6 7.8 2.6 2.1 1.9 2.1 3.3 4.3 3.3 3.4 674.5

15 41.667 10.5 12.8 12.3 7.6 2.6 2.1 1.8 2.1 3.2 4.2 3.3 3.3 674.2

16 44.444 10.2 12.5 12.0 7.6 2.5 2.1 1.8 2.0 3.2 4.1 3.2 3.2 660.1

17 47.222 9.8 12.0 11.8 7.3 2.5 2.1 1.8 1.9 3.0 3.8 3.2 3.1 659.1

18 50.000 9.7 11.7 11.8 6.7 2.4 2.1 1.6 1.9 2.5 3.8 3.1 3.1 656.7

19 52.778 9.6 11.3 11.2 6.3 2.3 2.1 1.6 1.9 2.2 3.7 2.9 2.9 640.9

20 55.556 9.0 10.5 10.4 5.7 2.2 2.1 1.6 1.8 2.2 3.6 2.9 2.9 640.0

21 58.333 8.8 10.4 10.3 5.5 2.2 2.1 1.5 1.8 2.2 3.6 2.8 2.9 619.2

22 61.111 8.5 10.3 10.2 5.4 2.2 2.1 1.5 1.8 2.1 3.1 2.8 2.6 612.9

23 63.889 8.0 9.9 10.1 5.2 2.1 2.0 1.5 1.6 2.1 2.7 2.7 2.6 599.4

24 66.667 7.7 9.5 9.4 5.2 2.1 2.0 1.5 1.6 2.0 2.6 2.7 2.6 594.3

25 69.444 7.2 9.4 9.4 5.2 2.1 2.0 1.5 1.6 1.9 2.6 2.6 2.4 587.5

26 72.222 6.7 9.1 9.3 4.9 2.1 2.0 1.5 1.5 1.9 2.5 2.6 2.4 540.3

27 75.000 6.0 9.1 9.0 4.8 2.0 1.9 1.5 1.5 1.9 2.4 2.4 2.3 539.7

28 77.778 5.7 8.9 8.5 4.7 2.0 1.9 1.4 1.4 1.9 2.2 2.4 2.2 528.3

29 80.556 5.4 8.9 8.4 4.7 1.9 1.8 1.4 1.4 1.8 2.1 2.1 2.1 523.1

30 83.333 5.1 8.8 8.2 4.0 1.9 1.8 1.4 1.4 1.7 2.0 2.0 2.1 520.6

31 86.111 4.6 8.1 7.5 3.9 1.8 1.8 1.4 1.3 1.7 2.0 2.0 1.8 510.7

32 88.889 3.9 7.7 6.9 3.6 1.7 1.7 1.3 1.3 1.7 2.0 1.8 1.8 485.0

33 91.667 3.3 6.3 6.6 3.5 1.7 1.6 1.2 1.3 1.6 1.8 1.7 1.7 482.6

34 94.444 2.9 6.1 5.7 3.2 1.6 1.5 1.2 1.2 1.5 1.7 1.7 1.6 448.5

35 97.222 2.9 5.7 3.8 3.1 1.6 1.3 1.1 0.8 1.1 1.3 1.6 1.0 441.1

n 35 35 35 35 35 35 35 35 35 35 35 35 35

X 9.4 13.5 12.7 7.4 2.8 2.1 1.7 2.1 3.6 3.8 3.4 3.7 657.6

S 3.8 7.2 6.5 3.6 1.2 0.3 0.3 0.7 2.2 1.5 1.3 2.0 135.9

R 0.984 0.982 0.993 0.981 0.943 0.982 0.990 0.984 0.988 0.990 0.960 0.959 0.987

Tc 32.24 30.41 48.64 29.61 17.26 30.41 40.72 32.24 37.19 40.72 20.52 20.27 35.74

Tt 2.048 2.048 2.048 2.048 2.048 2.048 2.048 2.048 2.048 2.048 2.048 2.048 2.048

HA si / no SI SI SI SI SI SI SI SI SI SI SI SI SI

Seguidamente se presentan las curvas de persistencia correspondiente al acumulado y a cada mes de la estacin problema.

( ) 1001

mf x

N

= +

HP: R = 0 ( = 0.05)

HA: R 0

Tc = 35.74

Tt = 0.987

Tc > Tt Aceptar HA

(Prueba significativa puede utilizarce la ecuacin)

RESUMEN DE CURVAS DE PERSISTENCIA

DISPN

AL 95%

ENERO EXPONENCIALy = 19.202e(-0.0162*x) 1.891

FEBRERO LOGARITMICA y = -8.0266Ln(x) + 42.7936.24

MARZO LOGARITMICA y = -6.8674Ln(x) + 37.8076.53

ABRIL LOGARITMICA y = -4.0468Ln(x) + 22.1553.73

MAYO LOGARITMICA y = -1.4088Ln(x) + 7.92971.51

JUNIO LOGARITMICA y = -0.2787Ln(x) + 3.0961.83

JULIO LOGARITMICA y = -0.348Ln(x) + 2.95961.37

AGOSTO LOGARITMICA y = -0.8146Ln(x) + 5.06851.36

SETIEMBRE LOGARITMICA y = -2.4938Ln(x) + 12.7291.37

OCTUBRE LINEAL y = -0.0515x + 6.3436 1.45

NOVIEMBRE LOGARITMICA y = -1.442Ln(x) + 8.645 2.08

DICIEMBRE LOGARITMICA y = -2.2673Ln(x) + 11.951.62

HP: R = 0

HA: R 0

Tc =

Tt =

ECUACIONTIPOMES

y = -152.3ln(x) + 1214.1 R = 0.9354

0

200

400

600

800

1000

1200

0.0 20.0 40.0 60.0 80.0 100.0 120.0

PR

EC

IPIT

AC

IN

(m

m)

P(x>X) (%)

CURVA DE PERSISTENCIA - ACUMULADO

(Prueba significativa puede utilizarce la ecuacin)

Utilizando la ecuacin (09) se procedi a ordenar lo datos en forma decreciente y a calcular los valores de la

HP: R = 0 ( = 0.05) HP: R = 0 ( = 0.05)

HA: R 0 HA: R 0

Tc = 32.2423097 Tc = 30.41367441

Tt = 2.048 Tt = 2.048

Tc > Tt Aceptar HA Tc > Tt Aceptar HA

(Prueba significativa puede utilizarce la ecuacin) (Prueba significativa puede utilizarce la ecuacin)

HP: R = 0 ( = 0.05) HP: R = 0 ( = 0.05)

HA: R 0 HA: R 0

Tc = 48.64 Tc = 29.61

Tt = 2.048 Tt = 2.048


y = 19.202e-0.016x R = 0.9154

0

2

4

6

8

10

12

14

16

18

20

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

PR

EC

IPIT

AC

IN

(m

m)

P(x>X) (%)

CURVA DE PERSISTENCIA - ENERO

y = -8.027ln(x) + 42.793 R = 0.9275

0

5

10

15

20

25

30

35

40

45

0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0 90.0 100.0110.0

PR

EC

IPIT

AC

IN

(m

m)

P(x>X) (%)

CURVA DE PERSISTENCIA - FEBRERO

y = -6.867ln(x) + 37.807 R = 0.8387

0

5

10

15

20

25

30

35

40

45

0.0 20.0 40.0 60.0 80.0 100.0 120.0

PR

EC

IPIT

AC

IN

(m

m)

P(x>X) (%)

CURVA DE PERSISTENCIA - MARZO

y = -4.047ln(x) + 22.155 R = 0.9598

0

5

10

15

20

25

0.0 20.0 40.0 60.0 80.0 100.0 120.0

PR

EC

IPIT

AC

IN

(m

m)

P(x>X) (%)

CURVA DE PERSISTENCIA - ABRIL

y = -1.409ln(x) + 7.9297 R = 0.9469

0

1

2

3

4

5

6

7

8

0.0 20.0 40.0 60.0 80.0 100.0 120.0

PR

EC

IPIT

AC

IN

(m

m)

P(x>X) (%)

CURVA DE PERSISTENCIA - MAYO

y = -0.279ln(x) + 3.096 R = 0.7382

0

0.5

1

1.5

2

2.5

3

0.0 20.0 40.0 60.0 80.0 100.0 120.0

PR

EC

IPIT

AC

IN

(m

m)

P(x>X) (%)

CURVA DE PERSISTENCIA -JUNIO

HP: R = 0 ( = 0.05) HP: R = 0 ( = 0.05)

HA: R 0 HA: R 0

Tc = 17.26 Tc = 30.41

Tt = 2.048 Tt = 2.048



HP: R = 0 ( = 0.05) HP: R = 0 ( = 0.05)

HA: R 0 HA: R 0

Tc = 40.72 Tc = 32.24

Tt = 2.048 Tt = 2.048



HP: R = 0 ( = 0.05) HP: R = 0 ( = 0.05)

HA: R 0 HA: R 0

Tc = 37.19 Tc = 40.72

Tt = 2.048 Tt = 2.048



HP: R = 0 ( = 0.05) HP: R = 0 ( = 0.05)

HA: R 0 HA: R 0

Tc = 20.52 Tc = 20.27

Tt = 2.048 Tt = 2.048

y = -0.348ln(x) + 2.9596 R = 0.8726

0

0.5

1

1.5

2

2.5

3

0.0 20.0 40.0 60.0 80.0 100.0 120.0

PR

EC

IPIT

AC

IN

(m

m)

P(x>X) (%)

CURVA DE PERSISTENCIA - JULIO

y = -0.815ln(x) + 5.0685 R = 0.9128

0

5

10

15

20

25

30

0.0 20.0 40.0 60.0 80.0 100.0 120.0

PR

EC

IPIT

AC

IN

(m

m)

P(x>X) (%)

CURVA DE PERSISTENCIA - AGOSTO

y = -2.494ln(x) + 12.729 R = 0.9494

0

2

4

6

8

10

12

0.0 20.0 40.0 60.0 80.0 100.0 120.0

PR

EC

IPIT

AC

IN

(m

m)

P(x>X) (%)

CURVA DE PERSISTENCIA - SETIEMBRE

y = -0.0515x + 6.3436 R = 0.9918

0

1

2

3

4

5

6

7

0.0 20.0 40.0 60.0 80.0 100.0 120.0

PR

EC

IPIT

AC

IN

(m

m)

P(x>X) (%)

CURVA DE PERSISTENCIA - OCTUBRE

y = -1.442ln(x) + 8.645 R = 0.9409

0

1

2

3

4

5

6

7

8

0.0 20.0 40.0 60.0 80.0 100.0 120.0

PR

EC

IPIT

AC

IN

(m

m)

P(x>X) (%)

CURVA DE PERSISTENCIA - NOVIEMBRE

y = -2.267ln(x) + 11.95 R = 0.9773

0

2

4

6

8

10

12

0.0 20.0 40.0 60.0 80.0 100.0 120.0

PR

EC

IPIT

AC

IN

(m

m)

P(x>X) (%)

CURVA DE PERSISTENCIA -DICIEMBRE

5. CALCULO DEL CAUDAL MAXIMO

A.- METODO RACIONAL

INTENSIDADES MXIMAS (mm/hr)

ESTACIN : WEBERBAWER DEPARTAMENTO : CAJAMARCA

ALTITUD : 2536 msnm PROVINCIA : CAJAMARCA

LATITUD : 07 10 SUR LONGITUD : 78 30 W

m Ao 5 min. 10 min. 30 min. 60 min. 120 min.

1 1973 101 71 24 14 11

2 1974 73 58 34 18 19

3 1975 90 50 24 16 10

4 1976 68 63 37 19 9

5 1977 65 53 37 21 11

6 1978 26 24 21 12 6

7 1979 60 60 38 23 14

8 1980 73.02 61 33.8 21.08 9.28

9 1981 67.2 54.8 29.13 15.54 13.02

10 1982 88.29 75.15 37.2 23.1 13.27

11 1983 75.3 50.4 31.4 23.71 13.99

12 1984 112.8 71.8 27.6 15.63 9.8

13 1985 59.31 54.4 25.56 14.7 8.05

14 1986 84.6 65.4 30.11 15.6 8.23

15 1987 76 49.2 21.6 13.2 7.95

16 1988 70.4 52.8 23 13.79 7.85

17 1989 73.6 47.8 28 16 9.6

18 1990 111.6 75 37.94 23 12

19 1991 83 73 41 26 14

20 1992 56 39 19 10 5

21 1993 58 51 28 18 10

22 1994 91.49 64.18 36.22 19.04 12.91

23 1995 71.11 56.25 28.66 16.72 9.32

24 1996 81.3 60.21 22.44 17.88 11.12

25 1997 82.2 68.1 35.04 17.86 8.94

26 1998 92 66.34 40.6 27.1 13.5

27 1999 70.8 42.85 20.05 11 4.44

Prom. 76.33 57.69 30.05 17.85 10.45

Desv. Est. 17.98 11.85 6.77 4.47 3.18

TRANSPOSICION DE INTENSIDADES (mm/hr)

Al no contarse con intensidades para la microcuenca del Ro Huertas, se transpone los datos de las intensida de la estacin

WEBERBAWER

SUB CUENCA : DEPARTAMENTO : CAJAMARCA

Altitud Media: 2231 msnm PROVINCIA: CONTUMAZA

Aplicando la siguiente ecuacin

Donde: I2 : Intensidad de la sub cuenca

I1 : Intensidad de la est. Weberbawer

HMEDIA : Altura media de la sub cuenca

H1 : Altura de la est. Weberbawer

RIO HUERTAS

1

12H

HII media=

CUADRO DE INTENSIDADES MAXIMAS

m Ao 5 min. 10 min. 30 min. 60 min. 120 min.

1 1973 88.85 62.46 21.11 12.32 9.68

2 1974 64.22 51.02 29.91 15.84 16.71

3 1975 79.18 43.99 21.11 14.08 8.80

4 1976 59.82 55.42 32.55 16.71 7.92

5 1977 57.18 46.63 32.55 18.47 9.68

6 1978 22.87 21.11 18.47 10.56 5.28

7 1979 52.78 52.78 33.43 20.23 12.32

8 1980 64.24 53.66 29.73 18.54 8.16

9 1981 59.12 48.21 25.63 13.67 11.45

10 1982 77.67 66.11 32.73 20.32 11.67

11 1983 66.24 44.34 27.62 20.86 12.31

12 1984 99.23 63.16 24.28 13.75 8.62

13 1985 52.18 47.86 22.49 12.93 7.08

14 1986 74.43 57.53 26.49 13.72 7.24

15 1987 66.86 43.28 19.00 11.61 6.99

16 1988 61.93 46.45 20.23 12.13 6.91

17 1989 64.75 42.05 24.63 14.08 8.45

18 1990 98.18 65.98 33.38 20.23 10.56

19 1991 73.02 64.22 36.07 22.87 12.32

20 1992 49.26 34.31 16.71 8.80 4.40

21 1993 51.02 44.87 24.63 15.84 8.80

22 1994 80.49 56.46 31.86 16.75 11.36

23 1995 62.56 49.48 25.21 14.71 8.20

24 1996 71.52 52.97 19.74 15.73 9.78

25 1997 72.31 59.91 30.83 15.71 7.86

26 1998 80.94 58.36 35.72 23.84 11.88

27 1999 62.29 37.70 17.64 9.68 3.91

Prom. 67.15 50.75 26.44 15.70 9.20

Desv. Est. 15.82 10.42 5.96 3.93 2.79

INTENSIDADES TRANSPUESTAS ORDENADOS EN FORMA DESCENDENTE

5 min. 10 min. 30 min. 60 min. 120 min.

138.46 92.25 50.33 33.27 23.32

136.99 92.06 49.84 31.92 17.19

123.98 89.61 46.65 29.10 17.19

112.93 88.14 46.57 28.36 17.17

112.31 87.15 45.66 28.23 16.57

110.48 83.59 45.42 28.23 16.29

108.38 81.43 45.42 25.88 15.98

103.85 80.28 44.46 25.78 15.85

101.88 78.78 43.01 23.37 14.73

100.90 77.33 41.74 23.32 13.65

99.80 74.88 41.49 22.10 13.50

93.29 73.91 38.54 22.10 13.50

92.43 73.65 36.96 21.95 12.28

90.35 71.20 35.76 21.92 12.28

89.63 69.05 35.18 20.52 12.03

89.61 67.27 34.37 19.64 11.78

87.29 66.78 34.37 19.64 11.44

86.91 65.06 33.88 19.19 11.39

86.42 64.81 31.38 19.15 11.05

83.47 62.60 29.46 19.08 10.97

82.49 61.87 29.46 18.04 10.10

79.79 61.38 28.23 17.19 9.88

73.65 60.39 27.55 16.93 9.76

72.80 58.68 26.51 16.20 9.64

71.20 52.60 25.78 14.73 7.37

68.74 47.87 24.61 13.50 6.14

31.92 29.46 23.32 12.28 5.45

AHORA SELECCIONAMOS EL MODELO MATEMATICO

Ao m

1973 1

1974 2

1975 3

1976 4

1977 5

1978 6

1979 7

1980 8

1981 9

1982 10

1983 11

1984 12

1985 13

1986 14

1987 15

1988 16

1989 17

1990 18

1991 19

1992 20

1993 21

1994 22

1995 23

1996 24

1997 25

1998 26

1999 27

PRUEBA DE BONDAD DE AJUSTE (SMIRNOV - KOLMOGOROV)

(T = 5 min)

Estimacin de los parametros:

Estimacin de u:

los valores : y y uy , se obtienen de tabla en la cual se ingresa con el nmero de datos con los que se esta

trabajando.

los valores : x y s, es el promedio y desviacin estandar de los valores correspondientes a las intensidades

transpuestas correspondientes al tiempo que se esta trabajando ( I 5 min ).

los valores : y u , se calculan con las ecuaciones :

Donde:

y = 1.0998 X = 67.15 = 14.38

uy = 0.53443 S = 15.82 u = 59.47

t se cacula en la tabla de valores extremos de Kolmogorov-Smirnov, ingresando el numero de datos ( 27 ).

t = 0.258

P(X>X) Weibull P(X>X) Blom P(X>X) G-P

0.036 0.023 0.026

0.071 0.060 0.062

0.107 0.096 0.099

0.143 0.133 0.135

0.179 0.170 0.172

0.214 0.206 0.208

0.250 0.243 0.245

0.286 0.280 0.281

0.321 0.317 0.318

0.357 0.353 0.354

0.393 0.390 0.391

0.429 0.427 0.427

0.464 0.463 0.464

0.500 0.500 0.500

0.536 0.537 0.536

0.571 0.573 0.573

0.607 0.610 0.609

0.643 0.647 0.646

0.679 0.683 0.682

0.714 0.720 0.719

0.750 0.757 0.755

0.786 0.794 0.792

0.938

0.821 0.830 0.828

0.857 0.867 0.865

0.964 0.977 0.974

0.893 0.904 0.901

0.929 0.940

-

--

=

ux

e

xeF

yuxU -=

_

S

y

=

1

Obteniendo el siguiente cuadro para I 5 min

m I5 min. 1- P(X>X) F(X < X)

1 138.46 0.96 0.9959

2 136.99 0.93 0.9955

3 123.98 0.89 0.9888

4 112.93 0.86 0.9760

5 112.31 0.82 0.9750

6 110.48 0.79 0.9716

7 108.38 0.75 0.9672

8 103.85 0.71 0.9553

9 101.88 0.68 0.9490

10 100.90 0.64 0.9455

11 99.80 0.61 0.9413

12 93.29 0.57 0.9092

13 92.43 0.54 0.9039

14 90.35 0.50 0.8897

15 89.63 0.46 0.8845

16 89.61 0.43 0.8843

17 87.29 0.39 0.8655

18 86.91 0.36 0.8621

19 86.42 0.32 0.8577

20 83.47 0.29 0.8283

21 82.49 0.25 0.8173

22 79.79 0.21 0.7840

23 73.65 0.18 0.6887

24 72.80 0.14 0.6733

25 71.20 0.11 0.6425

26 68.74 0.07 0.5917

27 31.92 0.04 0.0011

c = 0.57

Por lo tanto como t > 0 los datos se ajustan al modelo WEIBULL (Para t = 5 mins.)

P(X>X) Weibull /P(X


(T = 10 min)



trabajando.




Donde:

y = 1.0998 X = 50.75 = 9.48

uy = 0.53443 S = 10.42 u = 45.69

t = 0.258

luego se elbora el siguiente cuadro para: I 10 min

m I10 min. 1- P(X>X) F(X < X)

1 92.25 0.96 0.9927

2 92.06 0.93 0.9925

3 89.61 0.89 0.9903

4 88.14 0.86 0.9887

5 87.15 0.82 0.9875

6 83.59 0.79 0.9818

7 81.43 0.75 0.9773

8 80.28 0.71 0.9743

9 78.78 0.68 0.9700

10 77.33 0.64 0.9652

11 74.88 0.61 0.9551

12 73.91 0.57 0.9504

13 73.65 0.54 0.9490

14 71.20 0.50 0.9345

15 69.05 0.46 0.9185

16 67.27 0.43 0.9025

17 66.78 0.39 0.8976

18 65.06 0.36 0.8785

19 64.81 0.32 0.8755

20 62.60 0.29 0.8455

21 61.87 0.25 0.8341

22 61.38 0.21 0.8261

23 60.39 0.18 0.8091

24 58.68 0.14 0.7757

25 52.60 0.11 0.6174

26 47.87 0.07 0.4520

27 29.46 0.04 0.0039

c = 0.63


0.071 0.06

0.107 0.10

P(X>X) Weibull /P(X

Por lo tanto como t > c los datos se ajustan al modelo WEIBULL (Para t = 10 mins.)


(T = 30 min)



trabajando.




Donde:

y = 1.0998 X = 26.44 = 5.42

uy = 0.53443 S = 5.96 u = 23.54

t = 0.258

luego se elbora el siguiente cuadro para I 30 min

m I30 min. 1- P(X>X) F(X < X)

1 50.33 0.96 0.9929

2 49.84 0.93 0.9922

3 46.65 0.89 0.9860

4 46.57 0.86 0.9859

5 45.66 0.82 0.9833

6 45.42 0.79 0.9825

7 45.42 0.75 0.9825

8 44.46 0.71 0.9792

9 43.01 0.68 0.9729

10 41.74 0.64 0.9658

11 41.49 0.61 0.9643

12 38.54 0.57 0.9392

13 36.96 0.54 0.9195

14 35.76 0.50 0.9005

15 35.18 0.46 0.8899

16 34.37 0.43 0.8733

17 34.37 0.39 0.8733

18 33.88 0.36 0.8622

19 31.38 0.32 0.7902

20 29.46 0.29 0.7151

21 29.46 0.25 0.7151

22 28.23 0.21 0.6567

23 27.55 0.18 0.6204

24 26.51 0.14 0.5613

25 25.78 0.11 0.5160

26 24.61 0.07 0.4402

27 23.32 0.04 0.3531

0.071 0.06

0.107 0.09


P(X>X) Weibull /P(X

c = 0.51



(T = 60 min)


los valores : y y uy , se obtienen de tabla en la cual se ingresa con el nmero de datos con los que se esta trabajando.

los valores : x y s , es el promedio y desviacin estandar de los valores correspondientes a las intensidades

transpuestas correspondientes al tiempo que se esta trabajando ( I60 min ).


Donde:

y = 1.0998 X = 15.70 = 3.57

uy = 0.53443 S = 3.93 u = 13.79

t = 0.258

m I60 min. 1- P(X>X) F(X < X)

1 33.27 0.96 0.9957

2 31.92 0.93 0.9937

3 29.10 0.89 0.9863

4 28.36 0.86 0.9831

5 28.23 0.82 0.9826

6 28.23 0.79 0.9826

7 25.88 0.75 0.9665

8 25.78 0.71 0.9656

9 23.37 0.68 0.9337

10 23.32 0.64 0.9328

11 22.10 0.61 0.9067

12 22.10 0.57 0.9067

13 21.95 0.54 0.9029

14 21.92 0.50 0.9023

15 20.52 0.46 0.8589

16 19.64 0.43 0.8230

17 19.64 0.39 0.8230

18 19.19 0.36 0.8016

19 19.15 0.32 0.7998

20 19.08 0.29 0.7960

21 18.04 0.25 0.7376

22 17.19 0.21 0.6790

23 16.93 0.18 0.6597

24 16.20 0.14 0.6008

25 14.73 0.11 0.4633

26 13.50 0.07 0.3380

27 12.28 0.04 0.2167

0.071 0.07

0.107 0.09


P(X>X) Weibull /P(X

c = 0.51



(T = 120 min)



trabajando.




Donde:

y = 1.0998 X = 9.20 = 2.54

uy = 0.53443 S = 2.79 u = 7.84

t = 0.258

m I120 min. 1- P(X>X) F(X < X)

1 23.32 0.96 0.9978

2 17.19 0.93 0.9751

3 17.19 0.89 0.9751

4 17.17 0.86 0.9750

5 16.57 0.82 0.9684

6 16.29 0.79 0.9647

7 15.98 0.75 0.9603

8 15.85 0.71 0.9582

9 14.73 0.68 0.9358

10 13.65 0.64 0.9035

11 13.50 0.61 0.8980

12 13.50 0.57 0.8980

13 12.28 0.54 0.8400

14 12.28 0.50 0.8400

15 12.03 0.46 0.8252

16 11.78 0.43 0.8093

17 11.44 0.39 0.7849

18 11.39 0.36 0.7812

19 11.05 0.32 0.7537

20 10.97 0.29 0.7474

21 10.10 0.25 0.6635

22 9.88 0.21 0.6392

23 9.76 0.18 0.6252

24 9.64 0.14 0.6108

25 7.37 0.11 0.2995

0.071 0.05

0.107 0.08


P(X>X) Weibull /P(X

26 6.14 0.07 0.1416

27 5.45 0.04 0.0771

c 0.47


Ahora, para una VIDA UTIL DE 25 AOS SE TIENE LOS SIGUIENTES DATOS

SUB CUENCA : Ro Huertas DEPARTAMENTO : CAJAMARCA

Altitud Media: PROVINCIA : CHILETE

VIDA UTIL (N). Tiempo de Retorno (T) Riesgo de falla(J)

Aos (Aos) J (%) 5 10 30 60 120

25 390.41 5 145.3 102.2 55.9 35.1 23.0

25 190.32 10 134.9 95.4 52.0 32.5 21.2

25 90.13 20 124.1 88.3 47.9 29.9 19.3

25 56.57 30 117.4 83.8 45.4 28.2 18.125 29.36 50 107.8 77.6 41.8 25.8 16.4

Para calcular el Tr se utilizo las siguientes formulas:

siendo u y varibles segn el tiempo (5.10,30,60,120 min.), que se este trabajando.

se estimo una vida util de 25 aos y un periodo de retorno de 56 aos

DE LA GRAFICA DEL AJUSTE POR REGRESION ( POTENCIAL),PARA UNA VIDA UTIL DE 25 AOS Y UN TIEMPO DE RETORNO 56 AOS

SE AJUSTA A LA ECUACION DE MONTANA, OBTENEMOS LA ECUACION :

0.929 0.07

0.964 0.04

2231 m.s.n.m.

Valores extremos de variable

y = 296.63x-0.596

R = 0.9958

0

20

40

60

80

100

120

140

160

180

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

INT

EN

SID

AD

ES

MA

XIM

AS

TIEMPO (mintos)

CURVA MODELADA DE INTENSIDAD-DURACIN -FRECUENCIA

INTENSIDADES PARA UNA VIDA UTIL DE 25 AOS Y UN TIEMPODE RETORNO DE 56 AOS

Potencial (INTENSIDADES PARA UNA VIDA UTIL DE 25 AOS YUN TIEMPO DE RETORNO DE 56 AOS )

Y=444.92 X-0.5917

0.00

0.20

0.40

0.60

0.80

1.00

4.0 8.0 12.0 16.0 20.0 24.0

Pro

bab

ilid

ad

Intensidades(mm/hr)

HISTOGRAMA (t=120 min)

Modelo Terico

Modelo Emprico(Weibull)

NJ

Tr1

)1(1

1

--

=

---=

TLnLnuX

11

Y=444.92 X-0.5917

Donde x representa el valor del tc, en nuestro caso igual a 1.03 horas que es 61.8 minutos, entonces:

Entonces Y representa el valor de la intensidad maxima correspondiente a nuestro tiempo de concentracin de nuestra sub cuenca.

I MAX = 38.775 mm/h (intensidad maxima para el tiempo de concentracion del area)

AREA TOTAL= 101.53 km2 (Area de la cuenca del primer trabajo)

CLCULO DEL CAUDAL Qmx.

DESCRIPCIN AREA C C*A

Pastos 35.45 0.29 10.2805

Bosques 9 0.22 1.98

Cultivos 82.36 0.38 31.2968

Desnudos 12.26 0.14 1.7164

Asfalto 3.28 0.12 0.3936

Sumatoria 142.35 45.6673

C PROMEDIO = ( AI * CI + AII *CII + AIII* CIII+AIV*CIV+AV*CV ) / AREA TOTAL

C PROMEDIO = 0.321 (coeficiente de escorrentia varia de 0-1)

PARA CALCULAR EL CAUDAL MAXIMO DE LA MICRO CUENCA UTILIZAMOS LA SIGUIENTE FORMULA

Q=C*I*Areemplazando

Q=(0.511*24.5*159.4*103)/3600

tenemos:

Qmax= 350.828 m3/s

Pendiente 48.72%

Y=444.92x61.8- 0.5917

Y=38.775

6. CLCULO DEL HIDROGRAMA TRIANGULAR

Datos previos:

Area de la Cuenca : Ac = 101.53 Km^2

Longitud de Mximo Recorrido : L.m.r = 23.72 Km

Longitud del Cauce Principal : L.c.p = 23.22 Km

Pendiente del Cauce Principal : S = 9.78 %

Pendiente de la cuenca: So = 49.12 %

Empleando la ecuacin (06.1) se obtiene el valor del Tc, para una pendiente del cauce

principal > de 8% el valor de V = 1.5m/s ontenido de la tabla (01)

Tc empleando la ecuacin (06.2) Tc = 1.9 h

Tiempo de Concentracin Tc = 1.9 h

Mediante la ecuacin (05) se obtiene el (tr)

Tiempo de retardo. tr = 1.14 h

Empleando la ecuacin (04.1) se calcula el (te)

Duracin de la lluvia efectiva te = 2.76 h

Mediante la ecuacin (03) se obtiene el valor del (tp)

Tiempo Pico : tp = 2.518 h

Mediante la ecuacin (02) se estima el valor del (tb)

Tiempo Base : tb = 6.724 h

Empleando la ecuacin (01) se calcula el (qp)

Caudal Pico qp = 8.38 m^3/s*mm

x y

0.00 0.00

2.52 8.38

6.72 0.00

2). CLCULO DEL HIDROGRAMA CURVILINEO

Teniendo en cuenta la Nota 01 se obtiene las coordenadas del

hidrograma unitario curvilineo

ORDENADAS ABSCISAS ORDENADAS ABSCISAS

0 0 1.0 1.0

0.012 0.1 0.918 1.2

0.076 0.2 0.753 1.4

0.158 0.3 0.532 1.6

0.278 0.4 0.418 1.8

0.43 0.5 0.323 2.0

0.601 0.6 0.24 2.2

0.892 0.8 0.177 2.4

1.0 1.0 0.133 2.6

0.095 2.8

0.076 3.0

0.038 3.5

0.019 4.0

0.006 4.5

0 5.0

Hidrograma unitario

RAMA ASCENDENTE RAMA DESCENDENTE

01

23456789

0 1 2 3 4 5 6 7 8

Cau

dal (m

^3/s

/mm

)

Tiempo (h)

HIDROGRAMA UNITARIO TRIANGULAR Grafico (a)

COORDENADAS DEL HIDROGRAMA UNITARIO CURVILINEO

RAMA ASCENDENTE RAMA DESCENDENTE

ORDENADAS ABSCISAS ORDENADAS ABSCISAS

0.00 0.00 8.38 2.52

0.10 0.25 7.69 3.02

0.64 0.50 6.31 3.53 X Y X*tp Y*qp1.32 0.76 4.46 4.03 0 0 0.000 0.000

2.33 1.01 3.50 4.53 0.1 0.012 0.252 0.101

3.60 1.26 2.71 5.04 0.2 0.076 0.504 0.637

5.04 1.51 2.01 5.54 0.3 0.158 0.756 1.324

7.48 2.01 1.48 6.04 0.4 0.278 1.007 2.330

8.38 2.52 1.11 6.55 0.5 0.43 1.259 3.603

0.00 0.00 0.80 7.05 0.6 0.601 1.511 5.036

0.00 0.00 0.64 7.56 0.8 0.892 2.015 7.475

0.00 0.00 0.32 8.81 1.0 1.0 2.518 8.380

0.00 0.00 0.16 10.07 1.0 1.0 2.518 8.380

0.00 0.00 0.05 11.33 1.2 0.918 3.022 7.693

0.00 0.00 0.00 12.59 1.4 0.753 3.526 6.310

1.6 0.532 4.029 4.458

1.8 0.418 4.533 3.503

2.0 0.323 5.037 2.707

2.2 0.24 5.540 2.011

2.4 0.177 6.044 1.483

2.6 0.133 6.548 1.115

2.8 0.095 7.052 0.796

3.0 0.076 7.555 0.637

3.5 0.038 8.814 0.318

4.0 0.019 10.074 0.159

4.5 0.006 11.333 0.050

5.0 0 11.500 0.0000

Precipitacion efectiva, obtenida del balance hidrologico

ENE FEB MAR ABR MAY JUN JUL AGO SET OCT NOV

TOTAL 102.07 129.36 120.31 70.38 24.30 7.36 7.45 23.71 40.96 45.01 39.77

MEDIA 57.64 81.80 73.67 31.48 2.76 0.22 0.21 2.55 10.94 13.41 10.24

PROMEDIO= 24.963 mm

MAXIMO= 81.80 mm

CAUDAL MAXIMO (Qmax) = gasto pico x precipitacion efectiva promedio maximo.

Qmax= 209.19 m3/seg

t (min) 0 1 2 3 4 5 6 7

Q (m3/seg) 0.000 3.200 6.800 7.450 5.500 3.430 1.400 -1.408

3. TRANSITO DE AVENIDAS

Para nuestro caso, analizaremops en embalses. El calculo de la variacion del nivel de agua es esencial en el diseo del aliviadero

y a la vez garantizar la seguridad del conjunto. Considremos las siguientes ecuaciones fundamentales:

La ecuacion de continuidad :

De la grfica (a) obtenemos los siguientes caudales:

0

0.2

0.4

0.6

0.8

1

1.2

0 1 2 3 4 5 6

Cau

dal (m

^3/s

/m)

Tiempo (h)

HIDROGRAMA UNITARIO ADIMENSIONAL CURVILINEO Grfico (b)

( ) ( )dS

I t Q tdt

- =

CUADRO DE TRANSITO DE AVENIDAS

Int Tiempo Tiemp Transc. Q entrada Q ent medio Qsal instant Qsal medio Qneto ent med elev. nivel Cota instan

durante interv durante interv durante int dur. interv h

(hr) (hr) (m3/seg) (m3/seg) (m3/seg) (m3/seg) Dh (m) (m)

1 2 2' 3 4 5 6 7 8

0 0.000 - 0.000 0 - - 0.00000

0 -.5 0.5 0.101 0.05 0.000 0.000 0.05 0.000 0.000411

.5 - 1 1 0.637 0.37 0.004 0.000 0.37 0.003 0.003427

1 - 1.5 1.5 1.324 0.98 0.024 0.004 0.98 0.008 0.011416

1.5 - 2 2 2.330 1.83 0.085 0.024 1.80 0.015 0.026164

2 - 2.5 2.5 3.603 2.97 0.222 0.085 2.88 0.024 0.049743

2.5 - 3 3 5.036 4.32 0.481 0.222 4.10 0.034 0.083273

3 -3.5 3.5 7.475 6.26 0.943 0.481 5.78 0.047 0.130524

3.5 - 4 4 8.380 7.93 1.626 0.943 6.98 0.057 0.187670

4- 4.5 4.5 8.380 8.38 2.395 1.626 6.75 0.055 0.242931

4.5 - 5 5 7.693 8.04 3.109 2.395 5.64 0.046 0.289091

5 - 5.5 5.5 6.310 7.00 3.636 3.109 3.89 0.032 0.320942

5.5 - 6 6 4.458 5.38 3.882 3.636 1.75 0.014 0.335242

6 - 6.5 6.5 3.503 3.98 3.896 3.882 0.10 0.001 0.336048

6.5 - 7 7 2.707 3.10 3.784 3.896 -0.79 -0.006 0.329574

7. - 7.5 7.5 2.011 2.36 3.585 3.784 -1.43 -0.012 0.317914

7.5 - 8 8 1.483 1.75 3.334 3.585 -1.84 -0.015 0.302878

8 - 8.5 8.5 1.115 1.30 3.063 3.334 -2.03 -0.017 0.286229

8.5 - 9 9 0.796 0.96 2.790 3.063 -2.11 -0.017 0.268987

9 - 9.5 9.5 0.637 0.72 2.530 2.790 -2.07 -0.017 0.252021

9.5 - 10 10 0.318 0.48 2.282 2.530 -2.05 -0.017 0.235226

10 - 10.50 10.5 0.159 0.24 2.043 2.282 -2.04 -0.017 0.218512

10.5-11 11 0.050 0.10 1.825 2.043 -1.94 -0.016 0.202654

11-11.5 11.5 0.000 0.03 1.629 1.825 -1.80 -0.015 0.187932

10 m C = 2.0

Intervalo 30 min

AREA 17.2ha 220000 m2 (Area de embalse se saca de la curvas caracteristicas)

Por lo tanto el Caudal Mx en el vertedero es: 3.896 6.5 horas

0.3 mAltura de Vertedero =

m3/seg y tiene lugar a

Longuitud de la cresta: L =

despues del comienzo de la crecida.

Y en consecuencia el efecto del embalse es reducir el caudal

Para la elaboracion del cadro anterior se ha asumido una longuitud de cresta L= 40 m. y un coeficiente C=2.0

0

2

4

6

8

10

12

14

16

18

20

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 10.5

Cau

dal

(m3/s

eg

)

Tiempo (horas)

VOLUMEN DE SUPER ALMACENAMIENTO

Q ent medio Qsal medio

DIC

46.95

14.65

ALMACENAMIENTO Y TRANSITO DE AVENIDAS PARA LA MICROCUENCA DEL RIO HUERTAS

Para encontrar los volumenes de oferta de cada mes, se ha graficado las uarvas de persistencia de los caudales

medios generados mediante el balance hidrologico (2 avance), se ajusta a una curva y se encuentra su ecuacin

Luego se dentra con un 95% (segn el proyecto: ABASTECIMIENTO), en la ecuacion de cada mes para salir con un

caudal disponible al 95%, para convertir a volumenes por segundo se multiplica por el area de la sub cuenca

y se divide entre el # de das de cada mes por 24 horas y 3600 segundos.

CALCULO DEL VOLUMEN UTIL

Para este calculo se tendra que hacer el diagrama RIPPL, a partir del siguiente cuadro de volumenes de oferta y demanda

que se muestra a continuacion: (el Vol. de demanda para este caso nos hemos asumido que es de 0.38 m3/seg, es el maximo)

Qmedio Vol Acumul Qdemanda Vol Acum Diferencia

MES Of demanda

m3/seg m3 MMC m3/seg m3 MMC

31 ENERO 1.89 5064781.6 5.06 5.06 0.40 1071360 1.07 1.07 3.99 31

28 FEBRERO 6.24 15097869 15.10 20.16 0.40 967680 0.97 2.04 18.12 59

31 MARZO 6.53 17499878 17.50 37.66 0.40 1071360 1.07 3.11 34.55 90

30 ABRIL 3.73 9658753.6 9.66 47.32 0.50 1296000 1.30 4.41 42.91 120

31 MAYO 1.51 4055628.6 4.06 51.38 0.60 1607040 1.61 6.01 45.36 151

30 JUNIO 1.83 4735155.1 4.74 56.11 0.70 1814400 1.81 7.83 48.28 181

31 JULIO 1.37 3682400.5 3.68 59.79 0.80 2142720 2.14 9.97 49.82 212

31 AGOSTO 1.36 3639709.6 3.64 63.43 0.80 2142720 2.14 12.11 51.32 243

30 SEPTIEMBRE 1.37 3557628.4 3.56 66.99 0.60 1555200 1.56 13.67 53.32 273

31 OCTUBRE 1.45 3886626.2 3.89 70.88 0.50 1339200 1.34 15.01 55.87 304

30 NOVIEMBRE 2.08 5386978.3 5.39 76.27 0.40 1036800 1.04 16.04 60.22 334

31 DICIEMBRE 1.62 4352386.4 4.35 80.62 0.40 1071360 1.07 17.12 63.50 365

max 63.5020

min 3.9934

67.495 MMCVOLUMEN TIL

VOLUMEN VOLUMEN

Oferta demanda

0

2

4

6

8

10

12

14

16

18

0 100 200 300 400

VO

LU

ME

N A

CU

MU

LA

DO

MM

C

TIEMPO

Diagrama RIPPL

Oferta

demanda

Proyecto Hidrologico Para La Construccion de Una Presa.111

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