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PROBLEMAS DE ESTRUCTURAS HIDRAULICAS
PROBLEMA 01 (examen parcial 1999 -I
Ene !e" Mar A"r Ma# $%n $%l A&'
A' 1 86.1 98.3 64.2 43.1 31.0 13.4 5.2 4.8
A' ) 74.6 80.1 56.3 38.2 24.1 7.3 4.9 5.8
S'l%ci'n
P 30000 kw
H 400 m
* 9+1,
Transformando el caudal a volumen mensual
).+/0/ MMC
Mee * (m. (MMC Ac%m *2 2 2 Ac%m Di3 'l 'l Em"
Enero 86.10 223.17 223.17 9.15 23.71 23.71 199.46
e!rero 98.30 254.79 477.96 9.15 23.71 47.41 430.55
"ar#o 64.20 166.41 644.37 9.15 23.71 71.12 573.25
$!r%l 43.10 111.72 756.09 9.15 23.71 94.83 661.26
"a&o 31.00 80.35 836.44 9.15 23.71 118.54 717.90
'un%o 13.40 34.73 871.17 9.15 23.71 142.24 728.93 29.391
'ul%o 5.20 13.48 884.65 9.15 23.71 165.95 718.70
$(os)o 4.80 12.44 897.09 9.15 23.71 189.66 707.43
*e+)%em!re 6.10 15.81 912.90 9.15 23.71 213.37 699.54
,c)u!re 14.90 38.62 951.52 9.15 23.71 237.07 714.45-ov%em!re 38.70 100.31 1051.83 9.15 23.71 260.78 791.05
/%c%em!re 59.00 152.93 1204.76 9.15 23.71 284.49 920.27
Enero 74.60 193.36 1398.12 9.15 23.71 308.20 1089.93
e!rero 80.10 207.62 1605.74 9.15 23.71 331.90 1273.84
"ar#o 56.30 145.93 1751.67 9.15 23.71 355.61 1396.06
$!r%l 38.20 99.01 1850.69 9.15 23.71 379.32 1471.37
"a&o 24.10 62.47 1913.16 9.15 23.71 403.02 1510.13 26.141
'un%o 7.30 18.92 1932.08 9.15 23.71 426.73 1505.35
'ul%o 4.90 12.70 1944.78 9.15 23.71 450.44 1494.34
$(os)o 5.80 15.03 1959.81 9.15 23.71 474.15 1485.66
*e+)%em!re 8.50 22.03 1981.84 9.15 23.71 497.85 1483.99
,c)u!re 18.30 47.43 2029.28 9.15 23.71 521.56 1507.72
-ov%em!re 46.20 119.75 2149.03 9.15 23.71 545.27 1603.76
*e )%ene el s%(u%en)e re(%s)ro de caudales med%os mensuales en un r%o de)erm%nados duran)e un +er%
der%var a(ua +ara una cen)ral %droelec)r%ca ue (enerara 30 ". on una al)ura de ca%da de 400 m. s
de em!alse reuer%do ue +erm%)a re(ular la descar(a & (aran)%#ar as% la d%s+on%!%l%dad de a(ua +ara
ener(%a.
a ca+ac%dad de una cen)ral se de)erm%na con la s%(u%en)e ecuac%on ue relac%ona la +o)enc%a P co
ca%da H
m.
()/3(2.8)( m H smQkw P =
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/%c%em!re 63.80 165.37 2314.40 9.15 23.71 568.98 1745.42
PROBLEMA 0)
Ene !e" Mar A"r Ma# $%n $%l A&'
A' 19/9 22.1 25.8 18.7 14.2 6.5 3.0 2.6 3.8
A' 1940 23.8 28.4 16.3 10.2 4.8 2.6 2.4 3.5
S'l%ci'n
P 10000 kw
H 250 m
* 5+44
Transformando el caudal a volumen mensual
1)+655 MMC
Mee * (m. (MMC Ac%m *2 2 2 Ac%m Di3 'l 'l Em"
Enero 22.1 57.28 57.28 4.88 12.64 12.64 44.64
e!rero 25.8 66.87 124.16 4.88 12.64 25.29 98.87
"ar#o 18.7 48.47 172.63 4.88 12.64 37.93 134.70
$!r%l 14.2 36.81 209.43 4.88 12.64 50.58 158.86
"a&o 6.5 16.85 226.28 4.88 12.64 63.22 163.06 13.57
'un%o 3.0 7.78 234.06 4.88 12.64 75.86 158.19'ul%o 2.6 6.74 240.80 4.88 12.64 88.51 152.29
En el +ro&ec)o de una cen)ral %droelec)r%ca ue a+roveca las a(uas de un r%o se )%ene
arac)er%s)%cas de la cen)ral H250 m. P10 "w.
! :e(%men de descar(as
a ca+ac%dad de una cen)ral se de)erm%na con la s%(u%en)e ecuac%on ue relac%ona la +o)enc%a P coca%da H
m.
0 5 10 15 20 25
0.00
500.00
1000.00
1500.00
2000.00
CUR-A MASA
TIEMPO (M ESES
- O
L U
M
E 7 (
M
M
C
()/3(2.8)( m H smQkw P =
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$(os)o 3.8 9.85 250.65 4.88 12.64 101.15 149.50
*e+)%em!re 8.5 22.03 272.68 4.88 12.64 113.80 158.88
,c)u!re 12.6 32.66 305.34 4.88 12.64 126.44 178.90
-ov%em!re 18.5 47.95 353.29 4.88 12.64 139.08 214.21
/%c%em!re 20.9 54.17 407.46 4.88 12.64 151.73 255.74
Enero 23.8 61.69 469.15 4.88 12.64 164.37 304.78
e!rero 28.4 73.61 542.76 4.88 12.64 177.01 365.75
"ar#o 16.3 42.25 585.01 4.88 12.64 189.66 395.36
$!r%l 10.2 26.44 611.45 4.88 12.64 202.30 409.15 16.10
"a&o 4.8 12.44 623.89 4.88 12.64 214.95 408.95
'un%o 2.6 6.74 630.63 4.88 12.64 227.59 403.04
'ul%o 2.4 6.22 636.85 4.88 12.64 240.23 396.62
$(os)o 3.5 9.07 645.93 4.88 12.64 252.88 393.05
*e+)%em!re 7.8 20.22 666.14 4.88 12.64 265.52 400.62
,c)u!re 14.5 37.58 703.73 4.88 12.64 278.17 425.56
-ov%em!re 25.9 67.13 770.86 4.88 12.64 290.81 480.05
/%c%em!re 32.7 84.76 855.62 4.88 12.64 303.45 552.17
PROBLEMA 0.
S'l%ci'n
* 4+00
Transformando el caudal a volumen mensual
)0+/.6 MMC
Mee * (m. (MMC Ac%m *2 2 2 Ac%m Di3 'l 'l Em"
'an;84 16.9 43.80 43.80 8.00 20.74 20.74 23.07
e!;84 14.5 37.58 81.39 8.00 20.74 41.47 39.92
"ar;84 13.1 33.96 115.34 8.00 20.74 62.21 53.14
$+r;84 10.6 27.48 142.82 8.00 20.74 82.94 59.88
"a&;84 9.8 25.40 168.22 8.00 20.74 103.68 64.54 14.00'un;84 7.5 19.44 187.66 8.00 20.74 124.42 63.24
as a(uas de un r%o del cual se )%ene un re(%s)ro de caudales de cor)a e<)ens%on 5 a=os seran a+rove%rr%(ac%on s% el caudal de demanda es 8 m3>s se +%de efec)uar un anal%s%s de los reuer%m%en)os de aldemandas.
m.
0 5 10 15 20 250.00
100.00
200.00
300.00
400.00
500.00
600.00
CUR-A MASA
TIEMPO (MESES
- O
L U M
E 7 (
M
M
C
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'ul;84 4.3 11.15 198.81 8.00 20.74 145.15 53.65
$u(;84 6.8 17.63 216.43 8.00 20.74 165.89 50.54
*e+;84 9.8 25.40 241.83 8.00 20.74 186.62 55.21
,c);84 10.6 27.48 269.31 8.00 20.74 207.36 61.95
-ov;84 11.8 30.59 299.89 8.00 20.74 228.10 71.80
/ec;84 12.0 31.10 331.00 8.00 20.74 248.83 82.17
'an;85 18.0 46.66 377.65 8.00 20.74 269.57 108.09
e!;85 21.9 56.76 434.42 8.00 20.74 290.30 144.12
"ar;85 15.6 40.44 474.85 8.00 20.74 311.04 163.81
$+r;85 13.2 34.21 509.07 8.00 20.74 331.78 177.29
"a&;85 10.7 27.73 536.80 8.00 20.74 352.51 184.29
'un;85 9.2 23.85 560.65 8.00 20.74 373.25 187.40 9.85
'ul;85 5.6 14.52 575.16 8.00 20.74 393.98 181.18
$u(;85 6.6 17.11 592.27 8.00 20.74 414.72 177.55
*e+;85 8.5 22.03 614.30 8.00 20.74 435.46 178.85
,c);85 9.8 25.40 639.71 8.00 20.74 456.19 183.51
-ov;85 10.7 27.73 667.44 8.00 20.74 476.93 190.51
/ec;85 11.5 29.81 697.25 8.00 20.74 497.66 199.58'an;86 17.9 46.40 743.64 8.00 20.74 518.40 225.24
e!;86 20.8 53.91 797.56 8.00 20.74 539.14 258.42
"ar;86 14.8 38.36 835.92 8.00 20.74 559.87 276.05
$+r;86 12.6 32.66 868.58 8.00 20.74 580.61 287.97
"a&;86 10.1 26.18 894.76 8.00 20.74 601.34 293.41
'un;86 8.6 22.29 917.05 8.00 20.74 622.08 294.97 13.74
'ul;86 3.7 9.59 926.64 8.00 20.74 642.82 283.82
$u(;86 7.0 18.14 944.78 8.00 20.74 663.55 281.23
*e+;86 10.8 27.99 972.78 8.00 20.74 684.29 288.49
,c);86 11.9 30.84 1003.62 8.00 20.74 705.02 298.60
-ov;86 12.2 31.62 1035.24 8.00 20.74 725.76 309.48
/ec;86 14.0 36.29 1071.53 8.00 20.74 746.50 325.04'an;87 19.0 49.25 1120.78 8.00 20.74 767.23 353.55
e!;87 24.9 64.54 1185.32 8.00 20.74 787.97 397.35
"ar;87 17.6 45.62 1230.94 8.00 20.74 808.70 422.24
$+r;87 14.8 38.36 1269.30 8.00 20.74 829.44 439.86
"a&;87 9.2 23.85 1293.15 8.00 20.74 850.18 442.97 23.59
'un;87 7.9 20.48 1313.63 8.00 20.74 870.91 442.71
'ul;87 2.9 7.52 1321.14 8.00 20.74 891.65 429.49
$u(;87 4.6 11.92 1333.07 8.00 20.74 912.38 420.68
*e+;87 7.5 19.44 1352.51 8.00 20.74 933.12 419.39
,c);87 8.4 21.77 1374.28 8.00 20.74 953.86 420.42
-ov;87 9.3 24.11 1398.38 8.00 20.74 974.59 423.79
/ec;87 9.6 24.88 1423.27 8.00 20.74 995.33 427.94
'an;88 14.3 37.07 1460.33 8.00 20.74 1016.06 444.27
e!;88 15.6 40.44 1500.77 8.00 20.74 1036.80 463.97
"ar;88 12.0 31.10 1531.87 8.00 20.74 1057.54 474.34
$+r;88 11.8 30.59 1562.46 8.00 20.74 1078.27 484.19
"a&;88 8.6 22.29 1584.75 8.00 20.74 1099.01 485.74 19.44
'un;88 7.5 19.44 1604.19 8.00 20.74 1119.74 484.44
'ul;88 3.9 10.11 1614.30 8.00 20.74 1140.48 473.82
$u(;88 5.1 13.22 1627.52 8.00 20.74 1161.22 466.30
*e+;88 8.8 22.81 1650.33 8.00 20.74 1181.95 468.37
,c);88 10.1 26.18 1676.51 8.00 20.74 1202.69 473.82
-ov;88 11.8 30.59 1707.09 8.00 20.74 1223.42 483.67/ec;88 12.6 32.66 1739.75 8.00 20.74 1244.16 495.59
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PROBLEMA 05
Ene !e" Mar A"r Ma# $%n $%l A&'
A' 1 126.2 131.8 143.2 94.9 67.9 50.6 56.3 70.5
n 0.85
30 m
S'l%ci'n
P 7500 kw
* )9+94
Transformando el caudal a volumen mensual
//+/1) MMC
Mee (MMC Ac%m *2 2 2 Ac%m Di3 'l 'l Em"Enero 126.2 126.20 29.98 77.712 77.71 48.49
os volumenes mensuales descar(ados +or un r%o duran)e un a=o seco son las a(uas de d%ca+rovecam%en)o %droelec)r%co ue desarrollara una +o)enc%a ne)a de P7500 ?w. *E +%dealmacenam%en)o reuer%da de un reservor%o de re(ulac%on anual ue (aran)%ce ela almacenam%e
m.
-ov;83 'un;84 'an;85 'ul;85 e!;86 $u(;86 "ar;87 *e+;87 $+r
0.00
100.00
200.00
300.00
400.00
500.00
600.00
C%r8a Maa
Tiemp' (Mee
- ' l % m e n ( M
M C
P(kw)=9.81nQ(m 3/s ) H (m)
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e!rero 131.8 258.00 29.98 77.712 155.42 102.58
"ar#o 143.2 401.20 29.98 77.712 233.14 168.06
$!r%l 94.9 496.10 29.98 77.712 310.85 185.25 65.55
"a&o 67.9 564.00 29.98 77.712 388.56 175.44
'un%o 50.6 614.60 29.98 77.712 466.27 148.33
'ul%o 56.3 670.90 29.98 77.712 543.98 126.92
$(os)o 70.5 741.40 29.98 77.712 621.69 119.71
*e+)%em!re 86.3 827.70 29.98 77.712 699.41 128.29
,c)u!re 93.4 921.10 29.98 77.712 777.12 143.98
-ov%em!re 109.0 1030.10 29.98 77.712 854.83 175.27
/%c%em!re 119.1 1149.20 29.98 77.712 932.54 216.66
PROBLEMA 0, (examen parcial 1994 -I
os caudales med%os mensuales de un r%o son
Ene !e" Mar A"r Ma# $%n $%l A&'
A' 1 185.1 228.6 198.2 124.1 66.4 38.2 16.4 18.2
S'l%ci'n
Mee * (m. (MMC Ac%m *2 2 2 Ac%m Di3 'l 'l Em"
Enero 185.1 479.78 479.78 24.76 64.174 64.17 415.61
e!rero 228.6 592.53 1072.31 24.76 64.174 128.35 943.96
"ar#o 198.2 513.73 1586.04 24.76 64.174 192.52 1393.52
$!r%l 124.1 321.67 1907.71 24.76 64.174 256.69 1651.02
"a&o 66.4 172.11 2079.82 24.76 64.174 320.87 1758.95
'un%o 38.2 99.01 2178.84 24.76 64.174 385.04 1793.79 38.664
'ul%o 16.4 42.51 2221.34 24.76 64.174 449.22 1772.13
$(os)o 18.2 47.17 2268.52 24.76 64.174 513.39 1755.13
*e+)%em!re 40.7 105.49 2374.01 24.76 64.174 577.56 1796.45
,c)u!re 62.8 162.78 2536.79 24.76 64.174 641.74 1895.05
-ov%em!re 85.5 221.62 2758.41 24.76 64.174 705.91 2052.50/%c%em!re 124.2 321.93 3080.33 24.76 64.174 770.08 2310.25
*% se )%ene +rev%s)o desarrollar un a+rovecam%en)o ue )endra como caudal de demanda el 25 @ del cde)erm%ne el volumen de em!alse reuer%do.
0 2 4 6 8 10 12
0.00
50.00
100.00
150.00
200.00
250.00
C%r8a Ma0a
Tiemp' (Me0e0
- ' l % m
e n e 0 ( M M C
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T'al 1144+5
Me2ia 99+0
Ca%2al (),: )5+/6
'l Men%al 65+1/5 MMC
m.
m.
m.
0 2 4 6 8 10 12
0.00
500.00
1000.00
1500.00
2000.00
2500.00
CUR-A MASA
TIEMPO (M ESES
- O
L U M
E 7
( M
M
C
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Sep Oc 7'8 Dic
6.1 14.9 38.7 59.0
8.5 18.3 46.2 63.8
do seco. *% se )%ene +rev%s)o
e +%de de)erm%nar el volumen
+ro+os%)os de (enerac%on de
el caudal & la al)ura de
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Sep Oc 7'8 Dic
8.5 12.6 18.5 20.9
7.8 14.5 25.9 32.7
a
el caudal & la al)ura de
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cadas +ara un +ro&ec)o deacenam%en)o +ara cu!r%r las
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Sep Oc 7'8 Dic
86.3 93.4 109.0 119.1
o r%o se u)%l%#aran +ara une)erm%nar la ca+ac%dad den)o del caudal demandado
;88 -ov;88 "a&;89
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Sep Oc 7'8 Dic
40.7 62.8 85.5 124.2
audal med%o anual del r%o
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PROBLEMA 01
os caudales med%os mensuales son los %nd%cados en la )a!la s%(u%en)e
Ene !e" Mar A"r Ma# $%n $%l A&' Sep
A' 1 68.2 84.3 76.5 48.6 32.3 12.6 8.8 10.9 24.7
*% en d%co 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 ane'
* ),+00
Transformando el caudal a volumen mensual
65+400 MMC
Mee * (m. (MMC Ac%m *2 2 2 Ac%m Di3 'l 'l Em"
Enero 68.2 176.77 176.77 25.00 64.800 64.80 111.97
e!rero 84.3 218.51 395.28 25.00 64.800 129.60 265.68
"ar#o 76.5 198.29 593.57 25.00 64.800 194.40 399.17
$!r%l 48.6 125.97 719.54 25.00 64.800 259.20 460.34
"a&o 32.3 83.72 803.26 25.00 64.800 324.00 479.26 111.46
'un%o 12.6 32.66 835.92 25.00 64.800 388.80 447.12
'ul%o 8.8 22.81 858.73 25.00 64.800 453.60 405.13
$(os)o 10.9 28.25 886.98 25.00 64.800 518.40 368.58
*e+)%em! 24.7 64.02 951.00 25.00 64.800 583.20 367.80,c)u!re 35.1 90.98 1041.98 25.00 64.800 648.00 393.98
-ov%em! 46.8 121.31 1163.29 25.00 64.800 712.80 450.49
/%c%em!r 59.2 153.45 1316.74 25.00 64.800 777.60 539.14
Se&%n2' ane'
* )5+00
Transformando el caudal a volumen mensual
6)+)04 MMC
Mee * (m. (MMC Ac%m *2 2 2 Ac%m Di3 'l 'l Em"
Enero 68.2 176.77 176.77 24.00 62.208 62.21 114.57
e!rero 84.3 218.51 395.28 24.00 62.208 124.42 270.86
"ar#o 76.5 198.29 593.57 24.00 62.208 186.62 406.94
$!r%l 48.6 125.97 719.54 24.00 62.208 248.83 470.71
"a&o 32.3 83.72 803.26 24.00 62.208 311.04 492.22 102.90
'un%o 12.6 32.66 835.92 24.00 62.208 373.25 462.67
'ul%o 8.8 22.81 858.73 24.00 62.208 435.46 423.27
$(os)o 10.9 28.25 886.98 24.00 62.208 497.66 389.32
*e+)%em! 24.7 64.02 951.00 24.00 62.208 559.87 391.13
,c)u!re 35.1 90.98 1041.98 24.00 62.208 622.08 419.90-ov%em! 46.8 121.31 1163.29 24.00 62.208 684.29 479.00
m.
m.
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/%c%em!r 59.2 153.45 1316.74 24.00 62.208 746.50 570.24
Tercer ane' (Uili;an2' <erramiena "%car '"=ei8'
* ).+6.
Transformando el caudal a volumen mensual
61+)51 MMC
Mee * (m. (MMC Ac%m *2 2 2 Ac%m Di3 'l 'l Em"
Enero 68.2 176.77 176.77 23.63 61.241 61.24 115.53
e!rero 84.3 218.51 395.28 23.63 61.241 122.48 272.80
"ar#o 76.5 198.29 593.57 23.63 61.241 183.72 409.85
$!r%l 48.6 125.97 719.54 23.63 61.241 244.96 474.58
"a&o 32.3 83.72 803.26 23.63 61.241 306.20 497.06 100.00
'un%o 12.6 32.66 835.92 23.63 61.241 367.44 468.48
'ul%o 8.8 22.81 858.73 23.63 61.241 428.68 430.05 $(os)o 10.9 28.25 886.98 23.63 61.241 489.92 397.06
*e+)%em! 24.7 64.02 951.00 23.63 61.241 551.16 399.84
,c)u!re 35.1 90.98 1041.98 23.63 61.241 612.41 429.58
-ov%em! 46.8 121.31 1163.29 23.63 61.241 673.65 489.64
/%c%em!r 59.2 153.45 1316.74 23.63 61.241 734.89 581.85
m.
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Oc 7'8 Dic
35.1 46.8 59.2
uede ser a+rovecado
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PROBLEMA 01
Ene !e" Mar A"r Ma# $%n $%l A&' Sep
A' 1 126.2 131.8 143.2 94.9 67.9 50.6 56.3 70.5 86.3
n 0.85
30 m
S'l%ci'n
P 7500 kw* )9+94
Transformando el caudal a volumen mensual
//+/1) MMC
Mee (MMC Ac%m *2 2 2 Ac%m Di3 'l 'l Em"
Enero 126.2 126.20 29.98 77.712 77.71 48.49
e!rero 131.8 258.00 29.98 77.712 155.42 102.58
"ar#o 143.2 401.20 29.98 77.712 233.14 168.06
$!r%l 94.9 496.10 29.98 77.712 310.85 185.25 65.55
"a&o 67.9 564.00 29.98 77.712 388.56 175.44'un%o 50.6 614.60 29.98 77.712 466.27 148.33
'ul%o 56.3 670.90 29.98 77.712 543.98 126.92
$(os)o 70.5 741.40 29.98 77.712 621.69 119.71
*e+)%em! 86.3 827.70 29.98 77.712 699.41 128.29
,c)u!re 93.4 921.10 29.98 77.712 777.12 143.98
-ov%em! 109.0 AAA 29.98 77.712 854.83 175.27
/%c%em!r 119.1 AAA 29.98 77.712 932.54 216.66
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