Hidrograma Unitario...Final..

July 6, 2019 | Author: zoly104 | Category: Precipitación, Curva, Lluvia, Desembocar (Hidrología), Escorrentía superficial
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HIDROGRAMA UNITARIO

I.

OBJETIVOS 

Analizar y comprender la teoría de hidrograma Unitario



Comparar los métodos para obtener diagramas unitarios



Aplicar el método método de diagrama diagrama unitario unitario para obtener obtener el caudal de una cuenca.

II.

MARCO TEÓRICO. 1. HIDROGRAMA 1.1. DEFINICIÓN: Es DEFINICIÓN: Es la representación gráfica de las variaciones del caudal con respecto al

tiempo, en orden orden cronológico, cronológico, en en un lugar dado de la corriente.

Figura 1. Hidrograma de tormenta Aislada

Figura 2. Hidrograma Anual

En la siguiente figura observa en el hietograma la precipitación que produce infiltración, y la que produce escorrentía directa, ésta última se denomina precipitación neta o efectiva. El área bajo el

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hidrograma, es el volumen de agua que ha pasado por el punto de aforo, en el intervalo de tiempo expresado en el hidrograma. También se puede observar las partes de un hidrograma.

Figura 3. Partes o componentes del hidrograma

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a) Punto de levantamiento (A). En este punto, el agua proveniente de la tormenta bajo análisis comienza a llegar a la salida de la cuenca y se produce después de iniciada la tormenta, durante la misma o incluso cuando ha transcurrido ya algún tiempo después que cesó de llover, dependiendo de varios factores, entre los que se pueden mencionar el área de la cuenca, su sistema de drenaje y suelo, la intensidad y duración de la lluvia, etc. b) Pico del hidrograma (B). Es el caudal máximo que se produce por la tormenta. Con frecuencia es el punto más importante de un hidrograma para fines de diseño. c) Punto de Inflexión (C). En este punto es aproximadamente donde termina el flujo sobre el terreno, y de aquí en adelante, lo que queda de agua en la cuenca escurre por los canales y como escurrimiento subterráneo. d) Fin del escurrimiento directo (D). De este punto en adelante el escurrimiento es solo de origen subterráneo. Normalmente se acepta como el punto de mayor curvatura de la curva de recesión, aunque pocas veces se distingue de fácil manera. e) Curva de concentración o rama ascendente, es la parte que corresponde al ascenso del hidrograma, que va desde el punto de d e levantamiento hasta el pico. f) Curva de recesión o rama descendente, es la zona correspondiente a la disminución progresiva del caudal, que va desde el pico (B) hasta el final del escurrimiento directo (D). Tomada a partir del punto de inflexión (C), es una curva de vaciado de la cuenca (agotamiento). g) Curva de agotamiento, es la parte del hidrograma en que el caudal procede solamente de la escorrentía básica. Es importante notar que la curva de agotamiento, comienza más alto que el punto de inicio del escurrimiento directo (punto de agotamiento antes de la crecida), debido a que parte de la precipitación que se infiltro esta ahora alimentando el cauce. En hidrología, es muy útil ubicar el punto de inicio de la curva de agotamiento (punto D en la Figura 3), a fin de determinar el caudal base y el caudal directo. h) Tiempo de pico (tp), que a veces se denomina tiempo de demora, es el intervalo entre el inicio del período de precipitación neta y el caudal máximo. Es decir es el tiempo que transcurre desde que inicia el escurrimiento directo hasta el pico del hidrograma (Figura 3).

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 j)

Tiempo de retraso (tr), es el intervalo del tiempo comprendido entre los instantes que corresponden, al centro de gravedad del hietograma de la tormenta, y al centro de gravedad del hidrograma (Figura 6). Algunos autores reemplazan el centro de gravedad por el máximo, ambas definiciones serian equivalentes si los diagramas correspondientes correspondientes fueran simétricos.

Figura 5. Intervalos de tiempo asociados con los hidrogramas.

Figura 6. Tiempo de retraso

El área bajo el hidrograma, es el volumen total escurrido; el área bajo el hidrograma y arriba de la línea de separación entre caudal base y directo, es el volumen de escurrimiento directo.

1.3. ANÁLISIS DE UN HIDROGRAMA:

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Donde: Q = escurrimiento total Qd = escurrimiento directo, producido por la precipitación Qb = flujo base, producido por aporte del agua subterránea (incluye el flujo subsuperficial) No todas las corrientes reciben aporte de agua subterránea, ni todas las precipitaciones provocan escurrimiento directo. Solo las precipitaciones importantes, es decir, precipitaciones intensas y prolongadas, producen un aumento significativo en el escurrimiento de las corrientes.

Figura 7. Escurrimiento base y directo

Las características del escurrimiento directo y del flujo base, difieren tanto, que deben tratarse separadamente en los problemas que involucran períodos cortos de tiempo.

1.4. SEPARACIÓN DEL FLUJO BASE DE UN HIDROGRAMA: Se  Se  conoce varias técnicas para separar el flujo base del escurrimiento directo de un hidrograma, éstos se pueden agrupar en métodos simplificados y métodos aproximados. 1.4.1. Métodos simplificados para la separación del flujo base A). Un método simple, consiste en admitir como límite del escurrimiento base, la línea recta AA’ (Figura 8.1), que une el punto de origen del escurrimiento directo y sigue en forma paralela al eje X. Este método da buenos resultados especialmente en tormentas pequeñas donde los niveles freáticos no se alteran. En general sobrestima el tiempo base y el volumen de escurrimiento directo.

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Figura 8.1 Separación 8.1 Separación del flujo base

B). Como variante, se puede asignar al hidrograma del flujo base, un trazado siguiendo la línea recta AD, donde A es el punto de levantamiento y el punto D es el punto de inicio de la curva de agotamiento o donde termina el punto final del escurrimiento directo.(Figura 8.2).

Figura 8.2 Separación 8.2 Separación del flujo base

C). Otra fórmula también subjetiva, es la de admitir para el hidrograma antes citado, la línea ACD (Figura 8.3); el segmento AC esquematiza la porción de la curva de descenso partiendo del caudal correspondiente al comienzo de la subida, y extendiéndose hasta el instante del pico del hidrograma, el segmento CD es una recta, que une el punto C con el punto D, escogido igual que en el proceso anterior.

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1.4.2. MÉTODO APROXIMADO: Este método consiste en dibujar en papel semilogarítmico la curva de descenso. La curva de descenso se puede representar en forma matemática por una ecuación del tipo:

Donde: Q = ordenada del hidrograma de descenso para el tiempo t Q o = ordenada del hidrograma de descenso para el tiempo t o K = constante que depende de la cuenca De la ecuación (7.15) se tiene:

1.5. CLASIFICACIÓN: Según la Clasificación de hidrogramas por D. por  D. Snyder Clasifica a los hidrogramas en: a) b) c) d)

Hidrogramas naturales. Hidrogramas sintéticos. Hidrogramas unitarios. Hidrogramas adimensionales.

2. METODO DEL HIDROGRAMA UNITARIO 2.1. DEFINICIÓN: El método del hidrograma unitario se define como el escurrimiento directo, producido por un

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2.2. HIPOTESIS EN LA QUE SE BASA Distribución uniforme: La precipitación efectiva (lluvia neta) esta uniformemente distribuida en toda el área de la cuenca. Intensidad uniforme: La precipitación precipitación efectiva es de intensidad uniforme en en el periodo T horas Tiempo base constante: Los hidrogramas generados por tormentas de la misma duración tienen el mismo tiempo base (Tb) a pesar de ser diferentes las láminas de precipitación efectiva, independientemente independientemente del volumen total escurrido. Tb=Tc+d

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Superposición de causas y efectos,Es el hidrograma resultante de un periodo de lluvia dado, puede superponerse a hidrogramas resultantes de periodos lluviosos precedentes .como los hidrogramas producidos por las diferentes partes de la tormenta se asume que ocurren independientemente, el hidrograma de escurrimiento total es simplemente la suma de los hidrogramas individuales.

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Para la obtención de un hidrograma unitario es necesario contar con una precipitación uniforme, el área de la cuenca, cuenca, altura de la precipitación promediada promediada sobre la cuenca y periodo a lo largo del cual ocurrió la precipitación efectiva.  

2.3.1. PASOS PARA LA OBTENCIÓN DEL HIDROGRAMA UNITARIO: Seleccionar Seleccionar el episodio de precipitación adecuada para la cuenca en estudio. Separar el caudal base de la escorrentía directa

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Obtener la altura de la precipitación en exceso o efectiva (hp), dividiendo el volumen de escurrimiento directo, directo, entre el área ár ea de la cuenca

ℎ= 

   



Obtener las ordenadas del hidrograma unitario, dividiendo las ordenadas del escurrimiento directo entre la altura de precipitación efectiva (lluvia en exceso).



Determinar la duración efectiva separando lluvia efectiva e infiltración y viendo la duración de la lluvia efectiva (hacerlo con el índice de infiltración media, ᶲ).

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  

compuesta de varios periodos de igual duración y láminas cualesquiera de precipitación efectiva. Predecir el impacto de la precipitación sobre el caudal Predecir crecidas proporcionando estimaciones de caudales del rio a partir de la precipitación. Calcular el caudal que se producirá en determinado período de tiempo en base a una cantidad de precipitación efectiva

EJEMPLO 1: Obtener el hidrograma unitario de una tormenta, con los siguientes datos:

Área de la cuenca: A =3077.28km2=3077.28x106 m 2 Duración en exceso: de 12 horas Hidrograma de la tormenta fila 2 de la tabla

GRUPO AMC

Lluvia antecedente antecedente total de de 5 días (pulg) Estación inactiva(seca) inactiva(seca) Estación activa (de crecimiento)

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1. Calculo del volumen de escurrimiento directo 

Sabiendo que 12horas 12horas es igual 4.32x10 4

   Ve =   Ve =   Ve =

= 9231.84x104 m3 2. Determinamos Determinamos la altura de precipitación precipitación en exceso exceso hpe =

 

    = 

= 30mm

3. Determinamos las ordenadas del H.U.

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Tiempo (h)

hpe = 30mm

Hidrograma de la tormenta o H.U. 900

30

800 H. de la tormenta

700    s     / 600    3    m500     l    a     d 400    u    a    C 300

Escurrimiento base H.U. de 12 Hrs

25    s 20     /

15 10

200

5

100 0

0 0

10

20

30

40

50

60

70

80

90

100 110 120

Tiempo (Hrs)

MÈTODO HIDROGRAMAS UNITARIOS SINTÉTICOS

   3    m     l    a     d    u    a    C

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Figura 01 Hidrograma unitario sintetico triangular

Ecuación 01 --------->

V =hp∗A

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Donde: Qp = caudal punta, en m3/s hp = altura de precipitación en exceso, en mm. A = área de la cuenca, en Km2 tb = tiempo base, en hrs.

Del análisis de varios hidrogramas, Mockus concluye que el tiempo base y el tiempo pico se relacionan mediante la expresión: Ecuación 04 ---------

b =∗

A su vez el tiempo pico se expresa como: (Figura 02):

Ecuación 05 ----------



=+   



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Ecuación 07 --------

Donde: L= longitud del cauce principal, en m S= pendiente del cauce, en %

El tiempo de concentración tc, se puede estimar con la ecuación de Kirpich. Además, la duración de exceso con la que se tiene mayor gasto de pico, a falta de datos, se puede calcular aproximadamente para cuencas grandes, como:

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Determinar el hidrograma sintético triangular para una cuenca con las s iguientes características: características: Área = 15 Km2 Longitud del cauce principal = 5 Km Pendiente del cauce principal = 1 % Precipitación en exceso de hpe=70 mm. Solución: 1. Cálculo del tiempo de concentración, (ecuación de Kirpich), se tiene:

0  =∗ 0

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5. El caudal pico se calcula con la ecuación (7.28):

 =∗ ℎ∗   =∗ ∗ 

=  

6. La Figura 02b muestra muestra el hidrograma triangular triangular calculado

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La lluvia continua puede considerarse formada de una serie infinita de lluvias de período p tal que cada lluvia individual tenga una lámina hpe. La lluvia continua se halla sumando las ordenadas de una serie infinita de hidrogramas unitarios de (de) horas según el principio de superposición. La curva S de una cuenca, se dibuja a partir del HU para una duración de y sirve para obtener el HU para una duración de'. En el esquema que se muestra a continuación, el tiempo base del HU es igual a 6 períodos. La suma máxima de ordenadas se alcanza en este ejemplo después de 5 períodos. Ese valor máximo se estabiliza y permanece constante en el tiempo. Es decir, que se requiere solamente de tb/de hidrogramas unitarios para conformar una curva S, siendo tb el tiempo base del hidrograma unitario. La curva S puede construirse gráficamente, sumando una serie de HU iguales, desplazados un intervalo de tiempo, igual a la duración de la precipitación en exceso (de), para la que fueron deducidos (ver la siguiente figura).

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2. Desplazando las ordenadas un tiempo de=2 horas, se obtienen las siguientes columnas de la Tabla. 3. Sumando las ordenadas de los HU desplazados, se obtiene la última columna. 4. Para graficar la curva S, se plotean la primera y última columna, el resultado se muestra en la figura. 5. Para graficar el hidrograma unitario, se plotean la primera y la última columna

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de'=duración en exceso para el HU que se desea obtener a partir p artir de dicha curva S 4. Las ordenadas del nuevo HU se obtienen multiplicando la diferencia de ordenadas entre curvas S (paso 2), por la constante K (paso 3).

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http://www.miliarium.com/Proyec http://www.miliarium.com/Proyectos/EstudiosHidrogeologic tos/EstudiosHidrogeologicos/Anejos/Me os/Anejos/Metodos_Determin todos_Determin acion_Evaporacion/Unidade acion_Evaporacion/Unidades_Medidas_Evaporac s_Medidas_Evaporacion.asp ion.asp



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