Volumen de Embalse

PROBLEMAS DE ESTRUCTURAS HIDRAULICAS PROBLEMA 01 (examen parcial 1999 -I *e )%ene )%ene el s%(u% s%(u%en)e en)e re(%s re(%s)ro )ro de de caudales caudales med%o med%os s mensual mensuales es en un un r%o r%o de)erm%n de)erm%nados ados duran duran)e )e un +er% +er% der%var a(ua a(ua +ara una cen)ral cen)ral %droelec)r%ca %droelec)r%ca ue (enerara (enerara 30 ". on una una al)ura de ca%da de 400 m. s de em!alse reuer%do ue +erm%)a re(ular la descar(a & (aran)%#ar as% la d%s+on%!%l%dad de a(ua +ara ener(%a. Ene A' 1 A' )

!e" 86.1 74.6

Mar 98.3 80.1

A"r Ma# $%n $%l 64.2 43.1 31.0 13.4 56.3 38.2 24.1 7.3

A&' 5.2 4.9

4.8 5.8

S'l%ci'n a ca+ac%dad de una una cen)ral se de)erm%na de)erm%na con la s%(u%en)e s%(u%en)e ecuac%on ue ue relac%ona la +o)enc%a +o)enc%a P co ca%da H

 P ( k w) P H *

=

8.2Q ( m3 /  s ) H ( m

30000 kw kw 400 m 9+1, m. 

Transformando el caudal a volumen mensual  Mee Enero e!rero "ar#o  $!r%l "a&o 'un%o 'ul%o  $(os)o *e+)%em!re ,c)u!re -ov%em!re /%c%em!re Enero e!rero "ar#o  $!r%l "a&o 'un%o 'ul%o  $(os)o *e+)%em!re ,c)u!re -ov%em!re

).+/0/ MMC * (m.  (MMC  Ac%m 86.10 223.17 223.17 98.30 254.79 477.96 64.20 166.41 644.37 43.10 111.72 756.09 31.00 80.35 836.44 13.40 34.73 871.17 5.20 13.48 884.65 4.80 12.44 897.09 6.10 15.81 912.90 14.90 38.62 951.52 38.70 100.31 1051.83 59.00 152.93 1204.76 74.60 193.36 1398.12 80.10 207.62 1605.74 56.30 145.93 1751.67 38.20 99.01 1850.69 24.10 62.47 1913.16 7.30 18.92 1932.08 4.90 12.70 1944.78 5.80 15.03 1959.81 8.50 22.03 1981.84 18.30 47.43 2029.28 46.20 119.75 2149.03

*2 9.15 9.15 9.15 9.15 9.15 9.15 9.15 9.15 9.15 9.15 9.15 9.15 9.15 9.15 9.15 9.15 9.15 9.15 9.15 9.15 9.15 9.15 9.15

2 2 Ac%m 23.71 23.71 23.71 47.41 23.71 71.12 23.71 94.83 23.71 118.54 23.71 142.24 23.71 165.95 23.71 189.66 23.71 213.37 23.71 237.07 23.71 260.78 23.71 284.49 23.71 308.20 23.71 331.90 23.71 355.61 23.71 379.32 23.71 403.02 23.71 426.73 23.71 450.44 23.71 474.15 23.71 497.85 23.71 521.56 23.71 545.27

Di3 'l 'l Em" 199.46 430.55 573.25 661.26 717.90 728.93 29.391 718.70 707.43 699.54 714.45 791.05 920.27 1089.93 1273.84 1396.06 1471.37 1510.13 26.141 1505.35 1494.34 1485.66 1483.99 1507.72 1603.76

/%c%    em!re

63.80

165.37 2314.40

9.15

23.71

568.98

1745.42

   C

   M    M    (    7    E    M    U    L    O    -

CUR-A CU R-A MASA 2000.00 1500.00 1000.00 500.00 0.00 0

5

10

15

20

25

TIEM TIEM PO (M ESES ESES

PROBLEMA 0) En el +ro&ec)o de una cen)ral %droelec)r%ca ue a+roveca las a(uas de un r%o se )%ene arac)er%s)%cas arac)er%s) %cas de la cen)ral H250 m. P10 "w. "w. ! :e(%men de descar(as Ene A' 19/9 A' 1940

!e" 22.1 23.8

Mar 25.8 28.4

A"r Ma# 18.7 14.2 16.3 10.2

$%n 6.5 4.8

$%l 3.0 2.6

A&' 2.6 2.4

3.8 3.5

S'l%ci'n a ca+ac%dad de una una cen)ral se de)erm%na de)erm%na con la s%(u%en)e s%(u%en)e ecuac%on ue ue relac%ona la +o)enc%a +o)enc%a P co ca%da H

 P ( k w) P H *

=

8.2Q ( m3 /  s ) H ( m

10000 kw kw 250 m 5+44 m. 

Transformando el caudal a volumen mensual  Mee Enero e!rero "ar#o  $!r%l "a&o 'un%o 'ul%o

1)+655 MMC * (m.  (MMC  Ac%m 22.1 57.28 57.28 25.8 66.87 124.16 18.7 48.47 172.63 14.2 36.81 209.43 6.5 16.85 226.28 3.0 7.78 234.06 2.6 6.74 240.80

*2 4.88 4.88 4.88 4.88 4.88 4.88 4.88

2 2 Ac%m 12.64 12.64 12.64 25.29 12.64 37.93 12.64 50.58 12.64 63.22 12.64 75.86 12.64 88.51

Di3 'l 'l Em" 44.64 98.87 134.70 158.86 163.06 13.57 158.19 152.29

 $(os)o *e+)%em!re ,c)u!re -ov%em!re /%c%em!re Enero e!rero "ar#o  $!r%l "a&o 'un%o 'ul%o  $(os)o *e+)%em!re ,c)u!re -ov%em!re     /%c%em!re

3.8 8.5 12.6 18.5 20.9 23.8 28.4 16.3 10.2 4.8 2.6 2.4 3.5 7.8 14.5 25.9 32.7

   C

9.85 22.03 32.66 47.95 54.17 61.69 73.61 42.25 26.44 12.44 6.74 6.22 9.07 20.22 37.58 67.13 84.76

250.65 272.68 305.34 353.29 407.46 469.15 542.76 585.01 611.45 623.89 630.63 636.85 645.93 666.14 703.73 770.86 855.62

4.88 4.88 4.88 4.88 4.88 4.88 4.88 4.88 4.88 4.88 4.88 4.88 4.88 4.88 4.88 4.88 4.88

12.64 12.64 12.64 12.64 12.64 12.64 12.64 12.64 12.64 12.64 12.64 12.64 12.64 12.64 12.64 12.64 12.64

101.15 113.80 126.44 139.08 151.73 164.37 177.01 189.66 202.30 214.95 227.59 240.23 252.88 265.52 278.17 290.81 303.45

149.50 158.88 178.90 214.21 255.74 304.78 365.75 395.36 409.15 408.95 403.04 396.62 393.05 400.62 425.56 480.05 552.17

16.10

   M    M    (    7    E    M    U    L    O    -

CUR-A MASA 600.00 500.00 400.00 300.00 200.00 100.00 0.00 0

5

10

15

20

25

TIEM PO (M ESES

PROBLEMA 0. as a(uas de un r%o del cual se )%ene un re(%s)ro de caudales de cor)a es se +%de efec)uar un anal%s%s de los reuer%m%en)os de al demandas. S'l%ci'n *

4+00 m. 

Transformando el caudal a volumen mensual 

)0+/.6 MMC

Mee * (m.  (MMC  Ac%m 'an;84 16.9 43.80 43.80 e!;84 14.5 37.58 81.39 "ar;84 13.1 33.96 115.34  $+r;84 10.6 27.48 142.82 "a&;84 9.8 25.40 168.22 'un;84 7.5 19.44 187.66

*2 8.00 8.00 8.00 8.00 8.00 8.00

2 2 Ac%m 20.74 20.74 20.74 41.47 20.74 62.21 20.74 82.94 20.74 103.68 20.74 124.42

Di3 'l 'l Em" 23.07 39.92 53.14 59.88 64.54 14.00 63.24

'ul;84  $u(;84 *e+;84 ,c);84 -ov;84 /ec;84 'an;85 e!;85 "ar;85  $+r;85 "a&;85 'un;85 'ul;85  $u(;85 *e+;85 ,c);85 -ov;85 /ec;85 'an;86 e!;86 "ar;86  $+r;86 "a&;86 'un;86 'ul;86  $u(;86 *e+;86 ,c);86 -ov;86 /ec;86 'an;87 e!;87 "ar;87  $+r;87 "a&;87 'un;87 'ul;87  $u(;87 *e+;87 ,c);87 -ov;87 /ec;87 'an;88 e!;88 "ar;88  $+r;88 "a&;88 'un;88 'ul;88  $u(;88 *e+;88 ,c);88 -ov;88 /ec;88

4.3 6.8 9.8 10.6 11.8 12.0 18.0 21.9 15.6 13.2 10.7 9.2 5.6 6.6 8.5 9.8 10.7 11.5 17.9 20.8 14.8 12.6 10.1 8.6 3.7 7.0 10.8 11.9 12.2 14.0 19.0 24.9 17.6 14.8 9.2 7.9 2.9 4.6 7.5 8.4 9.3 9.6 14.3 15.6 12.0 11.8 8.6 7.5 3.9 5.1 8.8 10.1 11.8 12.6

11.15 17.63 25.40 27.48 30.59 31.10 46.66 56.76 40.44 34.21 27.73 23.85 14.52 17.11 22.03 25.40 27.73 29.81 46.40 53.91 38.36 32.66 26.18 22.29 9.59 18.14 27.99 30.84 31.62 36.29 49.25 64.54 45.62 38.36 23.85 20.48 7.52 11.92 19.44 21.77 24.11 24.88 37.07 40.44 31.10 30.59 22.29 19.44 10.11 13.22 22.81 26.18 30.59 32.66

198.81 216.43 241.83 269.31 299.89 331.00 377.65 434.42 474.85 509.07 536.80 560.65 575.16 592.27 614.30 639.71 667.44 697.25 743.64 797.56 835.92 868.58 894.76 917.05 926.64 944.78 972.78 1003.62 1035.24 1071.53 1120.78 1185.32 1230.94 1269.30 1293.15 1313.63 1321.14 1333.07 1352.51 1374.28 1398.38 1423.27 1460.33 1500.77 1531.87 1562.46 1584.75 1604.19 1614.30 1627.52 1650.33 1676.51 1707.09 1739.75

8.00 8.00 8.00 8.00 8.00 8.00 8.00 8.00 8.00 8.00 8.00 8.00 8.00 8.00 8.00 8.00 8.00 8.00 8.00 8.00 8.00 8.00 8.00 8.00 8.00 8.00 8.00 8.00 8.00 8.00 8.00 8.00 8.00 8.00 8.00 8.00 8.00 8.00 8.00 8.00 8.00 8.00 8.00 8.00 8.00 8.00 8.00 8.00 8.00 8.00 8.00 8.00 8.00 8.00

20.74 20.74 20.74 20.74 20.74 20.74 20.74 20.74 20.74 20.74 20.74 20.74 20.74 20.74 20.74 20.74 20.74 20.74 20.74 20.74 20.74 20.74 20.74 20.74 20.74 20.74 20.74 20.74 20.74 20.74 20.74 20.74 20.74 20.74 20.74 20.74 20.74 20.74 20.74 20.74 20.74 20.74 20.74 20.74 20.74 20.74 20.74 20.74 20.74 20.74 20.74 20.74 20.74 20.74

145.15 165.89 186.62 207.36 228.10 248.83 269.57 290.30 311.04 331.78 352.51 373.25 393.98 414.72 435.46 456.19 476.93 497.66 518.40 539.14 559.87 580.61 601.34 622.08 642.82 663.55 684.29 705.02 725.76 746.50 767.23 787.97 808.70 829.44 850.18 870.91 891.65 912.38 933.12 953.86 974.59 995.33 1016.06 1036.80 1057.54 1078.27 1099.01 1119.74 1140.48 1161.22 1181.95 1202.69 1223.42 1244.16

53.65 50.54 55.21 61.95 71.80 82.17 108.09 144.12 163.81 177.29 184.29 187.40 181.18 177.55 178.85 183.51 190.51 199.58 225.24 258.42 276.05 287.97 293.41 294.97 283.82 281.23 288.49 298.60 309.48 325.04 353.55 397.35 422.24 439.86 442.97 442.71 429.49 420.68 419.39 420.42 423.79 427.94 444.27 463.97 474.34 484.19 485.74 484.44 473.82 466.30 468.37 473.82 483.67 495.59

9.85

13.74

23.59

19.44

C%r8a Maa        C    M 600.00    M    (   n   e   m 500.00   %    l   '    400.00

300.00

200.00

100.00

0.00 -ov;83

'un;84

'an;85

'ul;85

e!;86

$u(;86

"ar;87

*e+;87

$ +r  

Tiemp' (Mee

PROBLEMA 05 os volumenes mensuales descar(ados +or un r%o duran)e un a=o seco son las a(uas de d%c a+rovecam%en)o %droelec)r%co ue desarrollara una +o)enc%a ne)a de P7500 ?w. *E +%de almacenam%en)o reuer%da de un reservor%o de re(ulac%on anual ue (aran)%ce ela almacenam%e Ene 126.2

A' 1 n 

!e" 131.8

Mar 143.2

A"r 94.9

Ma# 67.9

$%n 50.6

$%l 56.3

0.85 30 m S'l%ci'n

 P ( kw )= 9.81 nQ ( m 3 / s ) H ( m ) P *

7500 kw )9+94 m. 

Transformando el caudal a volumen mensual  Mee Enero

//+/1) MMC  (MMC 126.2

 Ac%m 126.20

*2 2 2 Ac%m 29.98 77.712 77.71

Di3 'l 48.49

'l Em"

A&' 70.5

e!rero "ar#o  $!r%l "a&o 'un%o 'ul%o  $(os)o *e+)%em!re ,c)u!re -ov%em!re /%c%em!re    

131.8 143.2 94.9 67.9 50.6 56.3 70.5 86.3 93.4 109.0 119.1

   C    M    M    (

   0    e    n    e    m    %    l    '    -

258.00 401.20 496.10 564.00 614.60 670.90 741.40 827.70 921.10 1030.10 1149.20

29.98 29.98 29.98 29.98 29.98 29.98 29.98 29.98 29.98 29.98 29.98

77.712 77.712 77.712 77.712 77.712 77.712 77.712 77.712 77.712 77.712 77.712

155.42 233.14 310.85 388.56 466.27 543.98 621.69 699.41 777.12 854.83 932.54

102.58 168.06 185.25 175.44 148.33 126.92 119.71 128.29 143.98 175.27 216.66

65.55

C%r8a Ma0a 250.00 200.00 150.00 100.00 50.00 0.00 0

2

4

6

8

10

12

Tiem p' (Me0e0

PROBLEMA 0, (examen parcial 1994 -I os caudales med%os mensuales de un r%o son

A' 1

Ene !e" Mar A"r Ma# $%n $%l 185.1 228.6 198.2 124.1 66.4 38.2

A&' 16.4

18.2

*% se )%ene +rev%s)o desarrollar un a+rovecam%en)o ue )endra como caudal de demanda el 25 @ del c de)erm%ne el volumen de em!alse reuer%do. S'l%ci'n

Mee Enero e!rero "ar#o  $!r%l "a&o 'un%o 'ul%o  $(os)o *e+)%em!re ,c)u!re -ov%em!re /%c%em!re

* (m.  (MMC  Ac%m 185.1 479.78 479.78 228.6 592.53 1072.31 198.2 513.73 1586.04 124.1 321.67 1907.71 66.4 172.11 2079.82 38.2 99.01 2178.84 16.4 42.51 2221.34 18.2 47.17 2268.52 40.7 105.49 2374.01 62.8 162.78 2536.79 85.5 221.62 2758.41 124.2 321.93 3080.33

*2 24.76 24.76 24.76 24.76 24.76 24.76 24.76 24.76 24.76 24.76 24.76 24.76

2 2 Ac%m 64.174 64.17 64.174 128.35 64.174 192.52 64.174 256.69 64.174 320.87 64.174 385.04 64.174 449.22 64.174 513.39 64.174 577.56 64.174 641.74 64.174 705.91 64.174 770.08

Di3 'l 'l Em" 415.61 943.96 1393.52 1651.02 1758.95 1793.79 38.664 1772.13 1755.13 1796.45 1895.05 2052.50 2310.25

T'al Me2ia Ca%2al (),: 'l Men%al

1144+5 99+0 )5+/6 65+1/5

m.  m.  m.  MMC

       C    M    M    (    7    E    M    U    L    O    -

CUR-A MASA 2500.00 2000.00 1500.00 1000.00 500.00 0.00 0

2

4

6

TIEM PO (M ESES

8

10

12

do seco. *% se )%ene +rev%s)o e +%de de)erm%nar el volumen +ro+os%)os de (enerac%on de

Sep Oc 7'8 Dic 6.1 14.9 38.7 59.0 8.5 18.3 46.2 63.8

el caudal  & la al)ura de

a

Sep Oc 7'8 Dic 8.5 12.6 18.5 20.9 7.8 14.5 25.9 32.7

el caudal  & la al)ura de

cadas +ara un +ro&ec)o de acenam%en)o +ara cu!r%r las

;88

-ov;88

"a&;89

o r%o se u)%l%#aran +ara un e)erm%nar la ca+ac%dad de n)o del caudal demandado Sep Oc 86.3 93.4

7'8 Dic 109.0 119.1

Sep Oc 7'8 Dic 40.7 62.8 85.5 124.2 audal med%o anual del r%o

PROBLEMA 01 os caudales med%os mensuales son los %nd%cados en la )a!la s%(u%en)e Ene 68.2

A' 1

!e" 84.3

Mar 76.5

A"r 48.6

Ma# 32.3

$%n 12.6

$%l 8.8

A&' 10.9

Sep 24.7

*% en d%co curso se cuen)a con un reservor%o de 100 "" de ca+ac%dad cual es el caudal cons)an)e ue + S'l%ci'n *e real%#ara )an)eos asum%endo caudales de d%se=o Primer ane' * ),+00 m.  Transformando el caudal a volumen mensual 

65+400 MMC

Mee * (m.  (MMC  Ac%m Enero 68.2 176.77 176.77 e!rero 84.3 218.51 395.28 "ar#o 76.5 198.29 593.57  $!r%l 48.6 125.97 719.54 "a&o 32.3 83.72 803.26 'un%o 12.6 32.66 835.92 'ul%o 8.8 22.81 858.73  $(os)o 10.9 28.25 886.98 *e+)%em! 24.7 64.02 951.00 ,c)u!re 35.1 90.98 1041.98 -ov%em! 46.8 121.31 1163.29 /%c%em!r 59.2 153.45 1316.74

*2 25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00

2 2 Ac%m 64.800 64.80 64.800 129.60 64.800 194.40 64.800 259.20 64.800 324.00 64.800 388.80 64.800 453.60 64.800 518.40 64.800 583.20 64.800 648.00 64.800 712.80 64.800 777.60

Di3 'l 'l Em" 111.97 265.68 399.17 460.34 479.26 111.46 447.12 405.13 368.58 367.80 393.98 450.49 539.14

*2 24.00 24.00 24.00 24.00 24.00 24.00 24.00 24.00 24.00 24.00 24.00

2 2 Ac%m 62.208 62.21 62.208 124.42 62.208 186.62 62.208 248.83 62.208 311.04 62.208 373.25 62.208 435.46 62.208 497.66 62.208 559.87 62.208 622.08 62.208 684.29

Di3 'l 'l Em" 114.57 270.86 406.94 470.71 492.22 102.90 462.67 423.27 389.32 391.13 419.90 479.00

Se&%n2' ane' * )5+00 m.  Transformando el caudal a volumen mensual 

6)+)04 MMC

Mee * (m.  (MMC  Ac%m Enero 68.2 176.77 176.77 e!rero 84.3 218.51 395.28 "ar#o 76.5 198.29 593.57  $!r%l 48.6 125.97 719.54 "a&o 32.3 83.72 803.26 'un%o 12.6 32.66 835.92 'ul%o 8.8 22.81 858.73  $(os)o 10.9 28.25 886.98 *e+)%em! 24.7 64.02 951.00 ,c)u!re 35.1 90.98 1041.98 -ov%em! 46.8 121.31 1163.29

/%c%em!r

59.2

153.45

1316.74

24.00

62.208

746.50

570.24

Tercer ane' (Uili;an2'