Examen de Hidrologia Aplicada
December 4, 2022 | Author: Anonymous | Category: N/A
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EXAMEN DE HIDROLOGIA APLICADA. NOMBRES Y APELLIDOS. CODIGO PROBLEMA 2 Obtener el hidrograma unitario de una tormenta con los siguientes datos Área de la cuenca: A=3077.28Km2 Duraión en exceso: de 12 horas CALCULO DE HIDROGRAMA PATRÓN CALCULO DE HIDROGRAMA UNIT UNITARIO ARIO CALCULO DE HIDROGRAMA BASE
Tiempo Hr (1)
Caudal base Caudal Obs. M3/s estmado m3/s (3) (2)
Caudal direco estmado m3/s (4)=(2)-(3)
HU de 12 hr m3/s (5)=(4)/30
Hidrog
HIDROGRAMA PATRÓN 900
900
800
0 12 24 36 48 60 72 84 96 108
50 150 800 600 400 250 150 120 100 80
50 40 40 50 55 58 60 65 70 75
0 110 760 550 345 192 90 55 30 5
TOTAL=
2137
0.0 3.7 25.3 18.3 11.5 6.4 3.0 1.8 1.0 0.2 m3/s
800
700 ) s / 3 m ( l a d u a C
700
600 500 400
/ s 3 m l a d u a C
300 200 100
600 500 400 300 200 100
0 0
20
40
60
Tiempo (Hrs)
80
100
120
0
0
20
CALCULO DE HIDROGRAMA S A PARTIR DEL H.U. DE 12 HR OBTENCIÓN DEL H.U. 24 HR A PARTIR DEL HIDROGRAMA S CALCULO DE HIDROGRAMA UNITARIO DE 24 HR
Tiempo Hr (1)
CÁLCULO DE
Curva S deducida Diferencia HU de 12 hr a partr de un H.U. Curva S HU 24 horas de Hu acumulada para de = 12hr desplazada 24 Hr. ordenadas m3/s K*(4) m3/s (5)=(4)/30 (m3/s) (3) (4)=(2)-(3) (2)
0 12 24
0.0 3.7 25.3
36 48 60 72 84 96 108
18.3 11.5 6.4 3.0 1.8 1.0 0.2
0.0 3.7
0.0 3.7 29.0
29.0 47.3 58.8 65.2 68.2 70.1 71.1
47.3 58.8 65.2 68.2 70.1 71.1 71.2
0.0
0.0 3.7 29.0
0.0 1.8 14.5
3.7 29.0 47.3 58.8 65.2 68.2 70.1
43.7 29.8 17.9 9.4 4.8 2.8 1.2
21.8 14.9 9.0 4.7 2.4 1.4 0.6
80.0
Relación (HU-12/HU-24)
70.0 60.0
k=
0.5
e l t i T s i x A
50.0 40.0 30.0 20.0 10.0 0.0 0
20
40
Ax Cu rva S
HU d e
ordenadas de la curva S m3/s
Tiempo Hr (1)
HU de 12 hr m3/s (5)=(4)/30
0 12 24 36 48 60 72 84
0.0 3.7 25.3 18.3 11.5 6.4 3.0 1.8
0.0 3.7 25.3 18.3 11.5 6.4 3.0
0.0 3.7 25.3 18.3 11.5 6.4
0. 0 3. 7 25.3 18.3 11.5
0. 0 3. 7 25.3 18.3
0.0 3.7 25.3
0.0 3.7
0.0
96 108
1.0 0.2
1.8 1.0
3.0 1.8
6. 4 3. 0
11.5 6. 4
18.3 11.5
25.3 18.3
3.7 25.3
Desplazamienoss iguales (A=12hr) Desplazamieno
CALCULO DE HIDROGRAMA ADIMENSIONAL DEL SCS TP= 1.97 hr Q p= 110.86 m m3 3/s hpe= 70 m m
0.0 3.7 29.0 47.3 58.8 65.2 68.2 70.1 0.0 3.7
71.1 71.2
0.0
Hidrograma Adimencional 1.200 1.000
T/TP 0.0 0.1 0.2 0.3 0.4 0.5 0.6
Q /QP 0.000 0.015 0.075 0.160 0.280 0.430 0.600
T 0.00 0.20 0.39 0.59 0.79 0.99 1.18
Q 0.00 1.66 8.31 17. 74 31. 04 47. 67 66. 52
0.7 0.8
0.770 0.890
1.38 1.58
85. 36 98. 67
0.800 P 0.600 Q / Q 0.400
0.200 0.000 0.0
1.0
2.0
3.0
/p Hidrogr ama adimencional Hidrograma
4.0
5.0
0.9 1.0 1.1 1.2
0.970 1.000 0.980 0.920
1.77 1.97 2.17 2.36
107.53 110.86 108.64 101.99
1.3 1.4 1.5 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.5 4.0 4.5 5.0
0.840 0.750 0.650 0.570 0.430 0.320 0.240 0.180 0.130 0.098 0.075 0.036 0.018 0.009 0.004
2.56 2.76 2.96 3.15 3.55 3.94 4.33 4.73 5.12 5.52 5.91 6.90 7.88 8.87 9.85
93.12 83.15 72.06 63.19 47.67 35.48 26.61 19.95 14.41 10.86 8.31 3.99 2.00 1.00 0.44
H Adimensional 120.00 100.00 80.00
) s / 3 60.00 m ( Q 40.00
20.00 0.00 0.00
2.00
4.00
6.00
t(horas) H adimensional
8.00
10.00
rama de la tormenta e H. Unitario 30.0 25.0 20.0 15.0 10.0 5.0 40
60
Tiempo (h)
80
100
120
0.0
cauda l obs caudal bas e HU de 12 hr
URVA EN S
60
80
100
is Tit Title le 2 H rs
H U d e 24 h rs
120
6.0
12.00
PROBLEMA 3 A parr de las relaciones I-D-F de la estación Aiquile, que se muestra en la Tabla 9.6, determinar: la expresión Relación I-D-F de la esación Aiquile PERIODO DE RETORNO 5 10 5 92,52 74,34 106,20 85,32 10 20 50 100
20
DURACION (minuos) / Inensidad (mm/h 30 60 90 120
57,51
46,76
33,39
23,25
18,86
65,97
53,64
38,31
26,68
21,64
119,28 136,20
95,82 109,38
74,10 84,60
60,24 68,80
43,03 49,14
29,97 34,22
24,31 27,76
148,92
119,58
92,49
75,20
53,72
37,41
30,34
Para determinar los parámetros a, b y K se aplicara una correlación múlple. Para este fn se adecua la ecuaci Donde: i Intensidad Intensidad máxima en mm./hora a, b y K Parámetros D Duración de la precipitación precipitación en minutos. Donde:
Entonces, la ecuación de la recta es: Para determinar los par parámetros ámetros A, B, C se deben resolver el sistema de ecuaciones mínimo cuadr cuadrác ác
En este caso se adecua los datos para aplicar la r parámetros, como se muestra en la Tabla 9.7
Tabla 9.7. Aplicación del méodo de la regresión múltple por mínimos cuadrados N
T(años)
i(mm/hr)
D(min)
y=logi
x1=logT
X2=logD
Y*X1
1
5
92.5
5
1.96614173
0.69897
0.69897
1.3742741
2
10
106.2
5
2.02612452
1
0.69897
2.02612452
3
20
119.28
5
2.07656763
1.30103
0.69897
2.70167678
4
50
136.2
5
2.13417711
1.69897
0.69897
3.62590289
5
100
148.92
5
2.17295303
2
0.69897
4.34590606
6 7
5 10
74.34 85.32
10 10
1.87122256 1.93105085
0.69897 1
1 1
1.30792844 1.93105085
8
20
95.82
10
1.98145617
1.30103
1
2.57793391
9
50
109.38
10
2.03893792
1.69897
1
3.46409437
10
100
119.58
10
2.07765855
2
1
4.1553171
11
5
57.51
20
1.75974337
0.69897
1.30103
1.23000783
12
10
65.97
20
1.81934648
1
1.30103
1.81934648
13
20
74.1
20
1.86981821
1.30103
1.30103
2.43268958
14 15
50 100
84.6 92.49
20 20
1.92737036 1.96609478
1.69897 2
1.30103 1.30103
3.27454443 3.93218956
16
5
46.76
30
1.6698745
0.69897
1.47712125 1.16719219
17
10
53.64
30
1.72948877
1
1.47712125 1.72948877
18
20
60.24
30
1.77988496
1.30103
1.47712125 2.31568373
19
50
68.8
30
1.83758844
1.69897
1.47712125 3.12200764
20
100
75.2
30
1.87621784
2
1.47712125 3.75243568
21
5
33.39
60
1.52361642
0.69897
1.77815125 1.06496218
22
10
38.31
60
1.58331215
1
1.77815125 1.58331215
23
20
43.03
60
1.63377135
1.30103
1.77815125 2.12558553
24
50
49.14
60
1.69143515
1.69897
1.77815125 2.87369759
25
100
53.72
60
1.730136
2
1.77815125 3.46027201
26
5
23.25
90
1.36642296
0.69897
1.95424251 0.95508866
27 28
10 20
26.68 29.97
90 90
1.42618583 1.47668674
1 1.30103
1.95424251 1.42618583 1.95424251 1.92121375
29
50
34.22
90
1.53428001
1.69897
1.95424251 2.60669571
30
100
37.41
90
1.57298771
2
1.95424251 3.14597542
31
5
18.86
120
1.27554169
0.69897
2.07918125 0.89156538
32
10
21.64
120
1.33525726
1
2.07918125 1.33525726
33
20
24.31
120
1.38578496
1.30103
2.07918125 1.8029478
34
50
27.76
120
1.44341946
1.69897
2.07918125 2.45232637
35
100
30.34
120
1.48201558
2
2.07918125 2.96403115
36
5
13.91
180
1.14332713
0.69897
2.25527251 0.79915137
37
10
15.96
180
1.20303289
1
2.25527251 1.20303289
38
20
17.92
180
1.25333801
1.30103
2.25527251 1.63063034
39
50
20.47
180
1.31111784
1.69897
2.25527251 2.22754989
40
100
22.37
180
1.34966598
2
2.25527251 2.69933197
41
5
8.69
360
0.93901978
0.69897
2.5563025 0.65634666
42
10
9.97
360
0.99869516
1
2.5563025 0.99869516
43
20
11.2
360
1.04921802
1.30103
2.5563025 1.36506412
44
50
12.79
360
1.10687054
1.69897
2 2..5563025 1.88053985
45
100
13.98
360
1.14550717
2
2.5563025 2.29101434
46 47
5 10
4.59 5.27
720 720
0.66181269 0.72181062
0.69897 1
2.8573325 0.46258722 2.8573325 0.72181062
48
20
5.91
720
0.77158748
1.30103
2.8573325 1.00385846
49
50
6.75
720
0.82930377
1.69897
2.8573325 1.40896223
50
100
7.38
720
0.86805636
2
2.8573325 1.73611272
51
5
2.44
1440
0.38738983
0.69897
3.15836249 0.27077387
52
10
2.8
1440
0.44715803
1
3.15836249 0.44715803
53
20
3.15
1440
0.49831055
1.30103
3.15836249 0.64831698
54
50
3.59
1440
0.55509445
1.69897
3.15836249 0.94308882
54
100
3.93
1441
0.59439255
2
3.15866398 1.1887851
∑
78.8072799 73.68867 105.580133 107.477722 ∑y ∑x1 ∑X2 ∑Y*X1
ene: Entonces remplaza remplazando ndo valores en se
78.80=A*50+B*73.68867+C*105.58
107.4777 A 73.68867+B 110.745 132.125877=A*105.58+B*141.4558+C A= 2.440883, B= 0.1801789906, C= 0.6529949478
K= 10 〗 ^="275.983347 a= B= 0.1801789906, " 〖 Se ene la relación:
De est estos os ssee de dete termi rmina na los pa pará rámet metrr
b= -C =0.6529949478
(/ℎ)=("275.983347" ^0.1801789906)/^0.6529949478
que relacione a éstas de la siguiente manera:
ra) 13,91
180
8,69
360
4,59
720
1440
15,96
9,97
5,27
2,80
17,92
11,20
5,91
3,15
20,47
12,79
6,75
3,59
2,44
22,37
13,98
7,38
3,93
n:
as siguientes:
egresión lineal y determinar los
Y * X2
XI*X2
X1*X1
X2*X2
1.3742741 1.3742 741 0.48855 0.48855907 907 0.4885590 0.48855907 7 0.48855907 1.41620026
0.69897
1
0.48855907
1.45145849 1.45145 849 0.90938 0.90938094 094 1.69267 1.69267905 905 0.4885 0.48855907 5907
1.49172578 1.49172 578 1.18752 1.18752907 907 2.88649 2.88649908 908 0.4885 0.48855907 5907 1.51882899 1.39794001
4
0.48855907
1.87122256
0.69897
0.48855907
1
1.93105085
1
1
1
1.98145617
1.30103
1.69267905
1
2.03893792 2.07765855
1.69897 2
2.88649908 4
1 1
2.28947891 0.90938 2.28947891 0.90938094 094 0.48855 0.48855907 907 1.6926 1.69267905 7905 2.36702435 1.30103 1 1.69267905 2.43268958 2.43268 958 1.69267 1.69267905 905 1.69267 1.69267905 905 1.6926 1.69267905 7905 2.50756666 2.50756 666 2.21041 2.21041094 094 2.88649 2.88649908 908 1.6926 1.69267905 7905 2.55794828 2.60205999
4
1.69267905
2.46660712 2.46660 712 1.0324634 1.03246345 5 0.48855907 2.18188 2.1818872 72 2.55466462 1.47712125
1
2.1818872
2.62910591 2.62910 591 1.9217790 1.92177906 6 1.69267905 2.18188 2.1818872 72 2.71434 2.7 1434094 094 2.5 2.5095 095847 847 2.8 2.88649 8649908 908 2.1 2.18188 818872 72 2.77140125 2.95424251
4
2.1818872
2.70922044 2.70922 044 1.24287 1.24287439 439 0.48855 0.48855907 907 3.1618 3.16182187 2187 2.81536848 1.77815125
1
3.16182187
2.90509256 2.90509 256 2.31342 2.31342811 811 1.69267 1.69267905 905 3.1618 3.16182187 2187 3.00762753 3.00762 753 3.02102 3.02102564 564 2.88649 2.88649908 908 3.1618 3.16182187 2187 3.0764435
3.5563025
4
3.16182187
2.67032 2.6 7032183 183 1.3 1.3659 659569 569 0.4 0.48855 8855907 907 3.8190 3.81906379 6379 2.78711297 1.95424251
1
3.81906379
2.88580401 2.88580 401 2.54252 2.54252812 812 1.69267 1.69267905 905 3.8190 3.81906379 6379 2.99835 2.9 9835521 521 3.3 3.3201 201994 994 2.8 2.88649 8649908 908 3.8190 3.81906379 6379 3.07399945 3.90848502 4 3.81906379 2.65208236 2.65208 236 1.45328 1.45328532 532 0.48855 0.48855907 907 4.3229 4.32299465 9465 2.77624185 2.07918125
1
4.32299465
2.8812981 2.8812 981 2.70507 2.70507717 717 1.6926790 1.69267905 5 4.32299465 3.00113068 3.00113 068 3.53246 3.53246657 657 2.88649 2.88649908 908 4.3229 4.32299465 9465 3.08137899 4.15836249
4
4.32299465
2.57851424 2.57851 424 1.57636 1.57636783 783 0.48855 0.48855907 907 5.0862 5.08625407 5407 2.71316699 2.25527251
1
5.08625407
2.82661874 2.82661 874 2.93417 2.93417718 718 1.69267 1.69267905 905 5.0862 5.08625407 5407 2.95692802 2.95692 802 3.83164 3.83164034 034 2.88649 2.88649908 908 5.0862 5.08625407 5407 3.04386459 4.51054501
4
5.08625407
2.4004186 2.4004 186 1.78677 1.78677877 877 0.4885590 0.48855907 7 6.53468248 2.55296693 2.5563025
1
6.53468248
2.68211866 3.32582 2.68211866 3.32582623 623 1.69267 1.69267905 905 6.5346 6.53468248 8248 2.82949594 2.82949 594 4.34308 4.34308127 127 2.88649 2.88649908 908 6.5346 6.53468248 8248 2.92826285
5.112605
4
6.53468248
1.89101 1.8 9101889 889 1.997 1.9971897 18971 1 0.4 0.48855 8855907 907
8.1 8.1643 64349 49
2.06245293 2.8573325
8.164349
1
2.20468 2.2 0468198 198 3.717 3.7174752 47529 9 1.6 1.69267 9267905 905
8.1 8.1643 64349 49
2.36959 2.3 6959662 662 4.8 4.8545 545222 222 2.8 2.88649 8649908 908
8.1 8.1643 64349 49
2.48032565 5.71466499
8.164349
4
1.2235175 1.2235 175 2.20760 2.20760064 064 0.4885590 0.48855907 7 9.97525363 1.41228715 3.15836249
1
9.97525363
1.57384536 1.57384 536 4.10912 4.10912434 434 1.69267 1.69267905 905 9.9752 9.97525363 5363 1.75318949 1.75318 949 5.36596 5.36596314 314 2.88649 2.88649908 908 9.9752 9.97525363 5363
1.87748634 6.31732796
4
9.97715814
13 132. 2.12 12587 5877 7 141.4 141.4558 55828 28 11 110. 0.745 74510 109 9 23 232. 2.13 1396 9629 29 ∑Y*X2
232.1396
s K, a y b.
∑XI*X2
∑X1*X1
∑X2*X2
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