Curva Masa - Curva Duracion

CAUDALES MEDIOS MENSUALES (m3/s)

Estacion: HUAYAO

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

1980 18.09 34.43 42.75 16.79 10.62 7.87 8.84 8.60 8.41 17.06 15.09 17.99

1981 25.37 64.97 44.78 24.82 12.27 9.30 8.12 10.12 9.60 17.72 19.90 38.59

1982 46.84 52.33 36.84 24.47 13.35 12.06 10.62 10.57 12.17 17.59 22.09 25.47

1983 31.56 30.45 36.10 31.72 12.84 11.44 9.58 9.24 11.96 13.05 13.51 22.39

1984 34.28 105.93 65.63 46.55 14.30 11.80 10.53 11.19 10.16 13.67 18.37 24.65

1985 20.56 45.10 43.72 37.72 19.45 11.70 9.98 9.30 11.95 13.34 16.70 25.21

1986 47.98 71.32 75.60 36.83 18.11 11.19 10.96 11.02 11.58 12.41 14.70 13.81

1987 60.30 41.13 22.95 16.85 12.33 11.24 11.68 9.63 9.91 12.52 15.62 14.19

1988 67.70 49.95 27.67 28.34 13.90 10.29 9.20 7.20 9.42 11.11 13.62 11.19

1989 20.74 38.74 43.31 32.55 18.66 12.55 10.21 9.83 9.96 15.01 15.77 14.88

1990 27.82 22.38 15.64 20.82 12.38 17.70 12.36 10.42 12.13 17.29 44.66 51.68

1991 53.33 55.17 37.55 27.34 15.02 13.51 8.81 8.82 7.78 9.85 10.93 11.24

1992 13.81 11.09 13.92 10.28 9.50 10.57 10.33 10.10 9.07 12.73 6.38 6.37

PROM 36.03 47.92 38.96 27.31 14.06 11.63 10.09 9.70 10.32 14.10 17.49 21.36

CONSTRUCCION DE LA CURVA MASA

V = 0.0864QT

Donde: V = volumen, en MM3 (millones de m3)

T = número de días del mes

Q = caudal en m3/s

1º. Transformar los Q (mm3/s), a volumenes V(millones de m3)

2º. Acumular los volumenes y obtener la columna de vvolumenes acumulados

AÑO Q DIAS DIAS V VOL acumulado

m3/s ACUM mm3 mm3

ENE 36.03 31 31 96.501 96.501

FEB 47.92 28 59 115.934 212.434

MAR 38.96 31 90 104.346 316.781

ABR 27.31 30 120 70.797 387.578

MAY 14.06 31 151 37.648 425.226

JUN 11.63 30 181 30.151 455.377

JUL 10.09 31 212 27.035 482.412

AGO 9.70 31 243 25.968 508.381

SET 10.32 30 273 26.737 535.118

OCT 14.10 31 304 37.776 572.894

NOV 17.49 30 334 45.328 618.222

DIC 21.36 31 365 57.207 675.428

Al unir las tangentes con una linea vertical tenemos la capacidad mínima del embalse para satisfacer el caudal seguro Qs

0 50 100 150 200 250 300 350 400

0

100

200

300

400

500

600

700

800

CURVA MASA

Column I

TIEMPO

V A

CU

M (

mm

3)

capacidad mínima de embalse

Qs

QU = 150.00

CONSTRUCCION DE LA CURVA DE DURACION

AÑO 1 2 3 4 5 6 7 8 9 10 11 12

1980 42.75 34.43 18.09 17.99 17.06 16.79 15.09 10.62 8.84 8.60 8.41 7.87

1981 64.97 44.78 38.59 25.37 24.82 19.90 17.72 12.27 10.12 9.60 9.30 8.12

1982 52.33 46.84 36.84 25.47 24.47 22.09 17.59 13.35 12.17 12.06 10.62 10.57

1983 36.10 31.72 31.56 30.45 22.39 13.51 13.05 12.84 11.96 11.44 9.58 9.24

1984 105.93 65.63 46.55 34.28 24.65 18.37 14.30 13.67 11.80 11.19 10.53 10.16

1985 45.10 43.72 37.72 25.21 20.56 19.45 16.70 13.34 11.95 11.70 9.98 9.30

1986 75.60 71.32 47.98 36.83 18.11 14.70 13.81 12.41 11.58 11.19 11.02 10.96

1987 60.30 41.13 22.95 16.85 15.62 14.19 12.52 12.33 11.68 11.24 9.91 9.63

1988 67.70 49.95 28.34 27.67 13.90 13.62 11.19 11.11 10.29 9.42 9.20 7.20

1989 43.31 38.74 32.55 20.74 18.66 15.77 15.01 14.88 12.55 10.21 9.96 9.83

1990 51.68 44.66 27.82 22.38 20.82 17.70 17.29 15.64 12.38 12.36 12.13 10.42

1991 55.17 53.33 37.55 27.34 15.02 13.51 11.24 10.93 9.85 8.82 8.81 7.78

1992 13.92 13.81 12.73 11.09 10.57 10.33 10.28 10.10 9.50 9.07 6.38 6.37

PROM 54.99 44.62 32.25 24.74 18.97 16.15 14.29 12.58 11.13 10.53 9.68 9.03

% 8.33 16.67 25.00 33.33 41.67 50.00 58.33 66.67 75.00 83.33 91.67 100.00

1º. Ordenar descendentemente los datos mensuales dandole una numeración2º. Luego calcular el promedio de estos

0.00 20.00 40.00 60.00 80.00 100.00 120.00

0.00

10.00

20.00

30.00

40.00

50.00

60.00

CURVA DE DURACION

Row 107

%

Q (

m3

/se

g)

Indica el % de tiempo durante el cual los caudales han sido igualados o excedidos

0.00 20.00 40.00 60.00 80.00 100.00 120.00

0.00

10.00

20.00

30.00

40.00

50.00

60.00

CURVA DE DURACION

Row 107

%

Q (

m3

/se

g)


Estacion: ANGASMAYO


1980 111.09 172.22 199.59 105.59 53.83 34.03 40.65 38.97 37.67 110.87 91.98 110.64

1981 139.86 265.47 206.00 137.80 67.04 43.92 35.75 49.97 46.10 117.51 140.31 184.14

1982 212.43 229.09 180.35 136.48 76.30 65.30 53.77 53.45 66.24 116.16 164.52 140.26

1983 162.30 158.40 175.88 162.85 71.85 60.29 46.01 43.48 64.54 73.68 77.67 128.47

1984 171.72 370.41 267.30 211.52 84.71 63.19 53.08 58.24 50.30 79.13 124.20 137.15

1985 121.20 206.99 202.68 183.26 135.47 62.36 48.94 43.95 64.42 76.19 107.37 139.25

1986 215.93 282.88 294.35 180.32 121.53 58.30 56.46 56.95 61.44 68.27 88.40 92.41

1987 252.32 194.42 130.63 105.82 67.58 58.70 62.18 46.36 48.39 69.13 96.94 94.14

1988 273.03 221.93 148.39 150.82 81.18 51.26 43.24 29.76 44.82 57.61 78.67 101.66

1989 144.08 145.43 176.93 175.16 78.89 61.29 48.48 47.95 56.74 97.20 96.60 88.69

1990 131.56 130.18 102.88 96.06 70.73 88.22 47.43 39.78 55.50 110.43 191.38 157.23

1991 135.17 197.74 182.70 147.19 91.36 67.12 45.10 37.77 43.89 62.99 106.74 84.41

1992 114.71 107.80 148.69 83.83 46.87 40.98 32.86 34.25 37.18 88.94 74.42 53.74

PROM 168.11 206.38 185.87 144.36 80.56 58.07 47.23 44.68 52.09 86.78 110.71 116.32


V = 0.0864QT



Q = caudal en m3/s




m3/s ACUM mm3 mm3

ENE 168.11 31 31 450.260 450.260

FEB 206.38 28 59 499.278 949.538

MAR 185.87 31 90 497.847 1447.384

ABR 144.36 30 120 374.185 1821.570

MAY 80.56 31 151 215.784 2037.354

JUN 58.07 30 181 150.527 2187.881

JUL 47.23 31 212 126.493 2314.374

AGO 44.68 31 243 119.679 2434.053

SET 52.09 30 273 135.029 2569.082

OCT 86.78 31 304 232.425 2801.508

NOV 110.71 30 334 286.954 3088.462

DIC 116.32 31 365 311.558 3400.020


0 50 100 150 200 250 300 350 400

0

500

1000

1500

2000

2500

3000

3500

4000

CURVA MASA

Column I

TIEMPO

V A

CU

M (

mm

3)


Qs

QU = 130.00



AÑO 1 2 3 4 5 6 7 8 9 10 11 12

1980 199.59 172.22 111.09 110.87 110.64 105.59 91.98 53.83 40.65 38.97 37.67 34.03

1981 265.47 206.00 184.14 140.31 139.86 137.80 117.51 67.04 49.97 46.10 43.92 35.75

1982 229.09 212.43 180.35 164.52 140.26 136.48 116.16 76.30 66.24 65.30 53.77 53.45

1983 175.88 162.85 162.30 158.40 128.47 77.67 73.68 71.85 64.54 60.29 46.01 43.48

1984 370.41 267.30 211.52 171.72 137.15 124.20 84.71 79.13 63.19 58.24 53.08 50.30

1985 206.99 202.68 183.26 139.25 135.47 121.20 107.37 76.19 64.42 62.36 48.94 43.95

1986 294.35 282.88 215.93 180.32 121.53 92.41 88.40 68.27 61.44 58.30 56.95 56.46

1987 252.32 194.42 130.63 105.82 96.94 94.14 69.13 67.58 62.18 58.70 48.39 46.36

1988 273.03 221.93 150.82 148.39 101.66 81.18 78.67 57.61 51.26 44.82 43.24 29.76

1989 176.93 175.16 145.43 144.08 97.20 96.60 88.69 78.89 61.29 56.74 48.48 47.95

1990 191.38 157.23 131.56 130.18 110.43 102.88 96.06 88.22 70.73 55.50 47.43 39.78

1991 197.74 182.70 147.19 135.17 106.74 91.36 84.41 67.12 62.99 45.10 43.89 37.77

1992 148.69 114.71 107.80 88.94 83.83 74.42 53.74 46.87 40.98 37.18 34.25 32.86

PROM 229.37 196.35 158.62 139.84 116.17 102.76 88.50 69.15 58.45 52.89 46.62 42.45

% 8.33 16.67 25.00 33.33 41.67 50.00 58.33 66.67 75.00 83.33 91.67 100.00

0.00 20.00 40.00 60.00 80.00 100.00 120.00

0.00

50.00

100.00

150.00

200.00

250.00

CURVA DE DURACION

Row 107

%

Q (

m3

/se

g)


0.00 20.00 40.00 60.00 80.00 100.00 120.00

0.00

50.00

100.00

150.00

200.00

250.00

CURVA DE DURACION

Row 107

%

Q (

m3

/se

g)


Estacion: LAIVE


1980 81.11 119.52 132.17 77.55 42.74 28.49 33.34 32.12 31.17 80.97 68.64 80.82

1981 99.43 175.24 140.04 98.13 51.89 35.70 29.76 40.02 37.26 85.24 99.72 128.03

1982 143.89 153.83 124.50 97.30 58.19 50.70 42.70 42.48 51.35 84.38 114.79 99.68

1983 113.41 111.00 122.99 113.76 55.17 47.25 37.20 35.39 50.18 56.41 59.11 92.23

1984 119.22 235.27 176.31 143.34 63.82 49.25 42.21 45.82 40.25 60.09 89.52 97.73

1985 87.60 140.63 138.04 126.27 96.67 48.68 39.29 35.72 50.10 58.11 78.70 99.05

1986 145.98 185.37 191.99 124.48 87.82 45.86 44.58 44.92 48.04 52.74 66.28 68.92

1987 167.54 133.05 93.60 77.70 52.26 46.15 48.56 37.45 38.90 53.32 71.90 70.06

1988 179.64 149.57 104.77 106.29 61.46 40.93 35.22 25.31 36.35 45.38 59.78 75.00

1989 102.08 102.93 122.41 121.33 59.93 47.94 38.96 38.59 44.78 72.07 71.68 66.46

1990 94.20 93.32 75.79 71.33 54.41 66.16 38.22 32.71 43.91 80.69 131.21 110.27

1991 96.47 135.06 125.93 104.02 68.24 51.95 36.55 31.24 35.68 49.11 78.29 63.62

1992 83.44 78.99 104.96 63.23 37.82 33.58 27.62 28.66 30.81 66.63 56.91 42.68

PROM 116.46 139.52 127.19 101.90 60.80 45.59 38.02 36.19 41.44 65.01 80.50 84.20


V = 0.0864QT



Q = caudal en m3/s




m3/s ACUM mm3 mm3

ENE 116.46 31 31 311.933 311.933

FEB 139.52 28 59 337.531 649.463

MAR 127.19 31 90 340.672 990.135

ABR 101.90 30 120 264.131 1254.266

MAY 60.80 31 151 162.851 1417.117

JUN 45.59 30 181 118.163 1535.280

JUL 38.02 31 212 101.822 1637.102

AGO 36.19 31 243 96.923 1734.025

SET 41.44 30 273 107.424 1841.450

OCT 65.01 31 304 174.125 2015.575

NOV 80.50 30 334 208.662 2224.237

DIC 84.20 31 365 225.511 2449.748


0 50 100 150 200 250 300 350 400

0

500

1000

1500

2000

2500

3000

CURVA MASA

Column I

TIEMPO

V A

CU

M (

mm

3)


Qs

QU = 450.00



AÑO 1 2 3 4 5 6 7 8 9 10 11 12

1980 132.17 119.52 81.11 80.97 80.82 77.55 68.64 42.74 33.34 32.12 31.17 28.49

1981 175.24 140.04 128.03 99.72 99.43 98.13 85.24 51.89 40.02 37.26 35.70 29.76

1982 153.83 143.89 124.50 114.79 99.68 97.30 84.38 58.19 51.35 50.70 42.70 42.48

1983 122.99 113.76 113.41 111.00 92.23 59.11 56.41 55.17 50.18 47.25 37.20 35.39

1984 235.27 176.31 143.34 119.22 97.73 89.52 63.82 60.09 49.25 45.82 42.21 40.25

1985 140.63 138.04 126.27 99.05 96.67 87.60 78.70 58.11 50.10 48.68 39.29 35.72

1986 191.99 185.37 145.98 124.48 87.82 68.92 66.28 52.74 48.04 45.86 44.92 44.58

1987 167.54 133.05 93.60 77.70 71.90 70.06 53.32 52.26 48.56 46.15 38.90 37.45

1988 179.64 149.57 106.29 104.77 75.00 61.46 59.78 45.38 40.93 36.35 35.22 25.31

1989 122.41 121.33 102.93 102.08 72.07 71.68 66.46 59.93 47.94 44.78 38.96 38.59

1990 131.21 110.27 94.20 93.32 80.69 75.79 71.33 66.16 54.41 43.91 38.22 32.71

1991 135.06 125.93 104.02 96.47 78.29 68.24 63.62 51.95 49.11 36.55 35.68 31.24

1992 104.96 83.44 78.99 66.63 63.23 56.91 42.68 37.82 33.58 30.81 28.66 27.62

PROM 153.30 133.89 110.97 99.25 84.27 75.56 66.20 53.26 45.91 42.02 37.60 34.58

% 8.33 16.67 25.00 33.33 41.67 50.00 58.33 66.67 75.00 83.33 91.67 100.00

0.00 20.00 40.00 60.00 80.00 100.00 120.00

0.00

20.00

40.00

60.00

80.00

100.00

120.00

140.00

160.00

180.00

CURVA DE DURACION

Row 107

%

Q (

m3

/se

g)


0.00 20.00 40.00 60.00 80.00 100.00 120.00

0.00

20.00

40.00

60.00

80.00

100.00

120.00

140.00

160.00

180.00

CURVA DE DURACION

Row 107

%

Q (

m3

/se

g)

Q1 206.382 185.873 168.114 144.365 116.326 110.717 86.788 80.569 58.07

10 52.0911 47.2312 44.68

1.- Ordenar los caudales de mayor a menor:206.38185.87168.11144.36116.32110.71

86.7880.5658.0752.0947.2344.68

2.- Calcular el rango de la muestraR = 161.70

3.- Seleccionar intervalo de clase NCN = 12NC = 5

4.-ΔX = R/NCΔX = 32.34

5.- Calculo de los limites de clase de cada uno de los intervalos

INTERVALO DE CLASE FRECUENCIA

1 174.04 206.38 174.04 2 2 17

2 141.70 174.04 141.70 2 4 33

3 109.36 141.70 109.36 2 6 50

4 77.02 109.36 77.02 2 8 67

5 44.68 77.02 44.68 4 12 100

6

Calculo de amplitud ΔX

LIMITE INFERIOR

No dias Q≥ LI % DIAS Q≥ LI

Documents

Curva Masa - Curva Duracion