• Author / Uploaded
• Raul Gandhi Piñas Astete

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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

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

V = 0.0864QT Donde:

V = volumen, en MM3 (millones de m3) T = número de días del mes Q = caudal en m3/s

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

AÑO

Q m3/s 36.03 47.92 38.96 27.31 14.06 11.63 10.09 9.70 10.32 14.10 17.49 21.36

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

DIAS 31 28 31 30 31 30 31 31 30 31 30 31

DIAS ACUM 31 59 90 120 151 181 212 243 273 304 334 365

V mm3 96.501 115.934 104.346 70.797 37.648 30.151 27.035 25.968 26.737 37.776 45.328 57.207

VOL acumulado mm3 96.501 212.434 316.781 387.578 425.226 455.377 482.412 508.381 535.118 572.894 618.222 675.428

CURVA MASA

V ACUM (m m 3)

800

Qs

700 600

capacidad mínima de embalse

500

Colum nI

400 300 200 100 0 0

50

100

150

200

250

300

350

400

TIEMPO

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

QU = 150.00

CONSTRUCCION DE LA CURVA DE DURACION 1º. Ordenar descendentemente los datos mensuales dandole una numeración 2º. Luego calcular el promedio de estos 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

CURVA DE DURACION 60.00

Q (m 3/se g)

50.00 40.00 30.00 20.00 10.00 0.00 0.00

20.00

40.00

60.00 %

80.00

100.00

120.00

91.67 100.00

20.00 10.00 0.00 0.00

20.00

40.00

60.00

80.00

100.00

120.00

%

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

CAUDALES MEDIOS MENSUALES (m3/s) Estacion: ANGASMAYO AÑO

ENE

FEB

MAR

ABR

1980

111.09

172.22 199.59 105.59

53.83

34.03

40.65

38.97

37.67

110.87

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

1984

171.72

370.41 267.30

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

1990

131.56

130.18 102.88

96.06

70.73

88.22

47.43

39.78

55.50

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

211.52

MAY

JUN

JUL

AGO

SET

OCT

NOV 91.98

110.64

77.67 128.47

88.69

110.43 191.38 157.23

CONSTRUCCION DE LA CURVA MASA

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

V = 0.0864QT Donde:

DIC

V = volumen, en MM3 (millones de m3) T = número de días del mes Q = caudal en m3/s

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

AÑO

Q m3/s 168.11 206.38 185.87 144.36 80.56 58.07 47.23 44.68 52.09 86.78 110.71 116.32

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

DIAS 31 28 31 30 31 30 31 31 30 31 30 31

DIAS ACUM 31 59 90 120 151 181 212 243 273 304 334 365

V mm3 450.260 499.278 497.847 374.185 215.784 150.527 126.493 119.679 135.029 232.425 286.954 311.558

VOL acumulado mm3 450.260 949.538 1447.384 1821.570 2037.354 2187.881 2314.374 2434.053 2569.082 2801.508 3088.462 3400.020

CURVA MASA

V ACUM (m m 3)

4000

Qs

3500 3000

capacidad mínima de embalse

2500

Colum nI

2000 1500 1000 500 0 0

50

100

150

200

250

300

350

400

TIEMPO

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

QU = 130.00

CONSTRUCCION DE LA CURVA DE DURACION 1º. Ordenar descendentemente los datos mensuales dandole una numeración 2º. Luego calcular el promedio de estos 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

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

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

58.33

66.67

75.00

83.33

91.67 100.00

8.33

16.67

25.00

33.33

83.83 41.67

50.00

CURVA DE DURACION 250.00

200.00 Q (m 3/se g)

%

88.94

97.20

150.00

100.00

50.00

0.00 0.00

20.00

40.00

60.00 %

80.00

100.00

120.00

50.00

0.00 0.00

20.00

40.00

60.00

80.00

100.00

120.00

%

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

CAUDALES MEDIOS MENSUALES (m3/s) Estacion: LAIVE AÑO

ENE

FEB

MAR

ABR

MAY

JUN

JUL

AGO

SET

OCT

NOV

DIC

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

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

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

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

93.32

93.60

75.79

78.99 104.96

CONSTRUCCION DE LA CURVA MASA

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

V = 0.0864QT Donde:

V = volumen, en MM3 (millones de m3) T = número de días del mes Q = caudal en m3/s

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

AÑO

Q m3/s 116.46 139.52 127.19 101.90 60.80 45.59 38.02 36.19 41.44 65.01 80.50 84.20

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

DIAS 31 28 31 30 31 30 31 31 30 31 30 31

DIAS ACUM 31 59 90 120 151 181 212 243 273 304 334 365

V mm3 311.933 337.531 340.672 264.131 162.851 118.163 101.822 96.923 107.424 174.125 208.662 225.511

VOL acumulado mm3 311.933 649.463 990.135 1254.266 1417.117 1535.280 1637.102 1734.025 1841.450 2015.575 2224.237 2449.748

CURVA MASA

V ACUM (m m 3)

3000

Qs 2500

capacidad mínima de embalse

2000

Colum nI

1500

1000

500

0 0

50

100

150

200

250

300

350

400

TIEMPO

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

QU = 450.00

CONSTRUCCION DE LA CURVA DE DURACION 1º. Ordenar descendentemente los datos mensuales dandole una numeración 2º. Luego calcular el promedio de estos 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

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

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

33.33

41.67

50.00

58.33

66.67

75.00

83.33

91.67 100.00

8.33

16.67

25.00

CURVA DE DURACION 180.00 160.00 140.00 Q (m 3/se g)

%

83.44

93.60

120.00 100.00 80.00 60.00 40.00 20.00 0.00 0.00

20.00

40.00

60.00 %

80.00

100.00

120.00

60.00 40.00 20.00 0.00 0.00

20.00

40.00

60.00

80.00

100.00

120.00

%

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

Q 1 2 3 4 5 6 7 8 9 10 11 12

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

1.-

Ordenar los caudales de mayor a menor: 206.38 185.87 168.11 144.36 116.32 110.71 86.78 80.56 58.07 52.09 47.23 44.68

2.-

Calcular el rango de la muestra R=

3.-

161.70

Seleccionar intervalo de clase NC N = 12 NC = Calculo de amplitud ΔX ΔX = R/NC ΔX =

4.-

5.-

5

32.34

Calculo de los limites de clase de cada uno de los intervalos INTERVALO DE CLASE

1 2 3 4 5 6

LIMITE INFERIOR

FRECUENCIA

No dias Q≥ LI

% DIAS Q≥ LI

174.04

206.38

174.04

2

2

17

141.70

174.04

141.70

2

4

33

109.36

141.70

109.36

2

6

50

77.02

109.36

77.02

2

8

67

44.68

77.02

44.68

4

12

100