Universidad Central del Ecuador.
Facultad de Ingeniería, Ciencias Físicas y Matemática. Carrera de Ingeniería Civil. Hidrología Aplicada. Estudio de la Microcuenca del Río Pisque.
Coral Chicaiza Iván Andrés.
Semestre: Quinto.
Paralelo: Segundo.
Fecha de entrega: 2018 - 07 - 27. Abril 2018 – Agosto Agosto 2018
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Índice de contenido 1. Introducción............................................. ................................................................... ............................................. ............................................. .............................. ....... 1 2. Objetivos........................................... ................................................................ ............................................ ............................................ ...................................... ................ 2 2.1.
Objetivo general .......................................... ................................................................. ............................................. ......................................... ...................2
2.2.
Objetivos específicos............................ específicos.................................................. ............................................ ............................................ ........................... ..... 2
3. Descripción del proyecto. proyecto. ........................................... ................................................................. ............................................ .................................. ............ 2 4. Marco teórico........................................... ................................................................. ............................................. ............................................. .............................. ....... 3 5. Cálculos y presentación de resultados. resultados. ......................................... ............................................................... ...................................... ................ 7 5.1.
Hietograma de diseño.............................................. ................................................................... ............................................ .............................. ........ 7
5.2.
Número de curva ......................................... ............................................................... ............................................. ........................................ .................13
5.3.
Hidrograma de crecida. ........................................... ................................................................. ............................................ ............................ ...... 15
5.4.
Curva de duración general................................... general......................................................... ............................................. ................................ ......... 21
5.5.
Curva de variación estacional. ........................................... .................................................................. ....................................... ................23
6. Análisis de resultados. ............................................ .................................................................. ............................................ .................................... .............. 24 7. Conclusiones. Conclusiones............................................ .................................................................. ............................................. ............................................. ............................ ..... 26 8. Recomendaciones. Recomendaciones. ........................................... ................................................................. ............................................ ........................................... .....................28 9. Anexos .......................................... ................................................................. ............................................. ............................................ ....................................... .................28 9.1.
Anexo 1. Microcuenca Microcuenca del río Pisque. .......................................... ................................................................. ............................ ..... 28
9.2.
Anexo 2. Ubicación y red hídrica de la Microcuenca Microcuenca del del Río Pisque....................... ....................... 28
9.3.
Anexo 3. Curvas de de nivel de la Microcuenca del Río Pisque. .................................. .................................. 28
9.4.
Anexo 4. Número de curva de la Microcuenca Microcuenca del Río Pisque. Pisque................................. ................................ 28
9.5.
Caudales medios diarios de los años 2015 – 1999 1999 de la estación H143 Granobles Aj
Guachalá........................................... .................................................................. ............................................. ............................................ ....................................... .................33 10. Bibliografía ........................... .................................................. ............................................. ............................................ ............................................. ........................... 40
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1. Introducción. Después del análisis previo que se realizó en la microcuenca del Río Pisque con respecto a su morfología, obtención de caudales por medio del método racional, balance hídrico, y caudales máximos, en este apartado se procederá a investigar más a fondo a través de datos más cercanos a la realidad los caudales de escorrentía de la microcuenca. Estos resultados son obtenidos por medio de diagramas como, por ejemplo; hietogramas de diseño, hidrogramas de crecida, curvas de duración general y curvas de variación estacional. Como primera parte se realizará la obtención y análisis de los hietogramas de diseño, que no son más que curvas que permiten ver el comportamiento de una lluvia con respecto a su duración para determinados tiempos de retorno. En esta proyecto se realizará el análisis para 10, 25, 50 y 100 años de periodo de retorno. Posteriormente se procederá a obtener el número de curva de la cuenca, número que depende del tipo y uso de suelo y permite cuantificar la capacidad de infiltración que esta posee. Todos estos datos nos llevarán a calcular a través del modelo computacional HEC – HMS, el hidrograma de crecida, el cual es un gráfico que describe el comportamiento de los caudales con respecto al tiempo. ti empo. Por último, se realizará la obtención y análisis de la curva de duración general y curva de variación estacional, los cuales permiten verificar la garantía de que los caudales del río abastezcan abastezcan los caudales de demanda que un proyecto puede requerir. Además, esta garantía se debe cumplir en todas las épocas del año, es decir, como es de conocimiento, no siempre se tiene las mismas condiciones meteorológicas y de precipitación que permitan mantener la constancia de los caudales requeridos en un río, por lo que dicho análisis permitirá concluir la necesidad de un proyecto de embalse que dote de d e agua en estas épocas de escases, o solamente un canal que transporte el agua a su punto de uso o consumo. Para esta conclusión se procederá
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2. Objetivos. 2.1. Objetivo general -
Determinar el hietograma de diseño de la microcuenca del río Pisque, así como su número de curva, hidrogramas de crecida, curvas de duración general y variación estacional por medio de la ayuda de modelos computacionales como ArcGIS y HEC – HMS.
2.2. Objetivos específicos. -
Obtener los valores de precipitación máxima obtenidos en el hietograma de diseño para 10, 25, 50 y 100 años de periodo de retorno.
-
Obtener los números de curva ponderados para cada subdivisión de la microcuenca del Río Pisque que se obtienen por medio del uso y tipo de suelo.
-
Analizar las curvas de duración general y variación estacional de la microcuenca del Río Pisque y su garantía de satisfacer algún tipo de proyecto de abastecimiento hídrico en la zona ubicada.
3. Descripción del proyecto. La microcuenca del río pisque está ubicada en el norte del país aproximadamente a 11 Km al Noroeste de la ciudad de Quito y pertenece a la cuenca alta del Río Guayllabamba, Guayllabamba, parte integral y subcuenca del Río Esmeraldas. Esta microcuenca abarca los cantones de Pedro Moncayo, parte del cantón Cayambe, Guayllabamba y parte del cantón Quito, como es la parroquia de Guayllabamba. La microcuenca cuenta con un área planimétrica aproximada de 700 Km2. La microcuenca está ubicada en una zonal generalmente templada y cálida. La ubicación de la desembocadura del río pisque al río Guayllabamba es la siguiente:
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Longitud: 78°23'16.08"O La topografía de la microcuenca es prácticamente irregular ya que se encuentra ubicada en plena cordillera de los andes y junto al páramo de Mojanda y al nevado Cayambe, por lo que las aguas provocadas por el deshielo del nevado terminan siendo parte de río Pisque. Afluentes secundarios de esta microcuenca microcuenca son el río Cangahua, el río Guachalá, el río Granobles, el río Blanco y el río Huambi.
4. Marco teórico. -
Hietograma de diseño.
Un Hietograma es una forma gráfica de representar el comportamiento incremental y decremental de una lluvia, el cual se lo presenta por medio de un diagrama de barras. Existe un método que es el más utilizado debido a su facilidad, el cual es el llamado método de los bloques alternos. Este método permite plasmar la precipitación máxima en el intervalo de tiempo más lluvioso de manera que las precipitaciones inferiores se acomodan de manera escalonada, escalonada, alternada de lado y lado y descendente con respecto al valor máximo. (Maidment & Chow, 1994)
-
Número de curva.
El método del número de curva fue f ue desarrollado por el Servicio de Conservación de Recursos Naturales de EE. UU. (Natural Resources Conservation Service – NRCS), originalmente llamado Servicio de Conservación de Suelos (Soil Conservation Service - SCS) para calcular la precipitación efectiva como una función de la lluvia acumulada, la cobertura del suelo, el uso del suelo y las condiciones de humedad. La metodología del número de la curva (CN), es
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distintas condiciones de humedad antecedente. antecedente. La representación gráfica de la profundidad de precipitación y la profundidad profundidad de exceso de precipitación o escorrentía escorrentía directa permitió obtener obtener una familia de curvas que fueron estandarizadas a partir de un número adimensional de curva CN, que varía de 1 a 100, según sea el grado del escurrimiento directo. Así un número de la curva CN = 100, indica que toda la lluvia escurre y un CN = 1, indica que toda la lluvia se infiltra. (Lavao Pastrana, 2014)
-
Hidrograma de crecida.
El hidrograma es una representación gráfica de las variaciones del caudal de una corriente con respecto al tiempo ante el cambio de sus dos componentes básicos; básicos; el flujo base que proviene del agua subterránea y la escorrentía que proviene de las lluvias. Las corrientes en cuencas con suelos con baja permeabilidad, que más bien van a hacer un aporte a los mantos acuíferos presentan relaciones muy bajas o nulas entre crecidas. Las corrientes en cuencas con suelos permeables y que reciben gran aporte de agua subterránea, van a mostrar caudales medios y caudales de crecida. Para realizar el análisis del hidrograma, es necesario separar la escorrentía directa y su flujo base. Esto se se hace hace para para posteriormente posteriormente poder hacer hacer el el análisis análisis del del histograma histograma unitario. Para ello ello existen distintas teorías basadas en la rapidez o lentitud en que se manifiesta el escurrimiento subterráneo al aparecer el escurrimiento directo producto de una precipitación. No existe forma única de hacer la separación, y puesto que las definiciones de las dos componentes son un tanto arbitrarias los métodos de separación son también arbitrarios. (Ferrer, ( Ferrer, 1993).
-
Curva de duración general.
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de forma simple y directa el rango de variación de caudales en un punto específico de una corriente (Searcy, 1963). El comportamiento de los caudales en una corriente se puede representar en el largo plazo mediante la CDC, dado que incorpora la relación entre la frecuencia de ocurrencia y la magnitud de los caudales. Esta curva integra también el efecto combinado que tienen sobre el comportamiento de los caudales de una corriente, corri ente, características de la cuenca como la climatología, la geología, la geomorfología, el tipo de suelo, la vegetación y las intervenciones antrópicas como presas y derivaciones, por lo que son curvas típicamente utilizadas en estudios de similitud hidrológica entre corrientes (Mohamoud, 2008). La construcción de la CDC es un procedimiento sintético de análisis que cumple múltiples propósitos en temas hidrológicos. En la ingeniería de los recursos hídricos, la CDC ha sido ampliamente utilizada para diversos propósitos y para la resolución de problemas prácticos, tales como el análisis de determinantes de calidad de agua, la estimación inicial de la generación de energía hidroeléctrica, la estimación de la sedimentación en ríos y embalses, la planeación del uso del agua, el manejo integrado del recurso hídrico, el suministro de agua y la evaluación de la disponibilidad del recurso para propósitos de asentamientos de población humana, entre muchas otras aplicaciones relacionadas con el aprovechamiento y uso responsable de las fuentes de agua naturales y la conservación del medio ambiente (Vogel & Fennessey, Fennessey, 1995). Debido a esto, desde el punto de vista de la ingeniería hidrológica, h idrológica, se hace
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permiten relacionar el caudal promedio del río en cada mes del año, con la l a probabilidad de tener al menos el caudal promedio mensual señalado. Con estas curvas se puede determinar en cada mes la probabilidad con la que se tendrá un caudal determinado para generar. Se pueden determinar también los caudales remanentes para generar, una vez satisfechos los caudales ecológicos que fije la DGA. Para estimar estas curvas es necesario apoyarse en las estadísticas hidrométricas disponibles para cuencas hidrográficas próximas, y de características climáticas y geomorfológicas geomorfológicas razonablemente razonablemente similares a ésta. Se puede proceder, por ejemplo, a la transposición de caudales específicos (por unidad de área) u otros métodos de síntesis hidrológica. Es importante que la estadística que se usa como base de la transposición corresponda a un régimen hidrológico similar al de la cuenca en estudio. También se pueden usar transposiciones de caudales específicos por unidad de precipitación, si se estima que ésta última es significativamente diferente en las dos cuencas. Para mayor seguridad en las estimaciones de los caudales generables, es conveniente medirlos en el punto de captación; si se hace esto es más útil y conveniente medir sistemáticamente durante al menos un año hidrológico completo. (Mardondes Morales, 2009)
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5. Cálculos y presentación de resultados. 5.1. Hietograma de diseño.
Tiempo de duración. (Kirpich 1942):
. 0,02(√ ) Donde: Tc = tiempo de concentración (horas). Lf = longitud del cauce principal hasta la divisoria (kilómetros). S0 = pendiente promedio del cauce principal (m/m)
. 60, 9 95 km 0,066 066 ( √ 0,0,0352 ) 1,72 ℎ 103,14 Δt = 10,31 min
Ecuaciones.
Zona 8
Tabla No. 1 Ecuaciones de intensidad máxima de la zona 8.
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o
Hietograma de diseño.
Intensidad máxima correspondiente correspondiente al periodo de retorno (mm/h)
, , ∗ −, Donde: IdTR = = Intensidad diaria máxima correspondiente al periodo de retorno (mm/h) tc = Tiempo de concentración (min)
15159,82 ∗ 2 ∗ 10,31−, 111,84 /ℎ Precipitación (mm)
∗ ∆ Donde: ITR = = Intensidad máxima correspondiente correspondiente al periodo de retorno (mm/h) ∆t1 = Primer intervalo de duración (h)
111, 111,84∗ 84 ∗ 0,1717 P = 19,23 mm
Variación de precipitación (mm)
∆ −
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Tabla No.2 Precipitaciones para 10 años de periodo de retorno. Δt
Δt
I
P
ΔP
(min)
(h)
mm/h
mm
Mm
10,31
0,17
111,84
19,23
19,23
20,63
0,34
81,87 81,8 7
14,07
5,15 5 ,15
30,94
0,52
66,27 66,2 7
11,39
2,68 2 ,68
41,26
0,69
51,02
8,77
2,62
51,57
0,86
41,66
7,16
1,61
61,89
1,03
35,29
6,07
1,09
72,20
1,20
30,68
5,27
0,79
82,51
1,38
27,17
4,67
0,60
92,83
1,55
24,41
4,20
0,47
103,14
1,72
22,18
3,81
0,38
Gráfica No.1 Hietograma de diseño para 10 años de periodo de retorno
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Periodo de retorno de 25 años.
Idtr = 2,5 mm/h o
Hietograma de diseño.
Tabla No.3 Precipitaciones para 25 años de periodo de retorno. Δt
Δt
I
P
ΔP
(min)
(h)
mm/h
mm
mm
10,31
0,17
139,81
24,03
24,03
20,63
0,34
102,34
17,59
6,44
30,94
0,52 0 ,52
82,84 8 2,84
14,24
3,35 3 ,35
41,26
0,69 0 ,69
63,78 6 3,78
10,96
3,28 3 ,28
51,57
0,86
52,07
8,95
2,01
61,89
1,03
44,12
7,58
1,37
72,20
1,20
38,35
6,59
0,99
82,51
1,38
33,97
5,84
0,75
92,83
1,55
30,52
5,25
0,59
103,14
1,72
27,73
4,77
0,48
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Periodo de retorno de 50 años.
Idtr = 3 mm/h o
Hietograma de diseño.
Tabla No.4 Precipitaciones para 50 años de periodo de retorno. Δt
Δt
I
P
ΔP
(min)
(h)
mm/h
mm
mm
10,31
0,17
167,77
28,84
28,84
20,63
0,34
122,81
21,11
7,73
30,94
0,52 0 ,52
99,41 9 9,41
17,09
4,02
41,26
0,69 0 ,69
76,53 7 6,53
13,16
3,93
51,57
0,86 0 ,86
62,48 6 2,48
10,74
2,42
61,89
1,03
52,94
9,10
1,64
72,20
1,20
46,02
7,91
1,19
82,51
1,38
40,76
7,01
0,90
92,83
1,55
36,62
6,30
0,71
103,14
1,72
33,28
5,72
0,57
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Periodo de retorno de 100 años.
Idtr = 3,5 mm/h o
Hietograma de diseño.
Tabla No.5 Precipitaciones para 100 años de periodo de retorno. (h)
I mm/h
P mm
mm
10,31
0,17
195,73
33,65
33,65
20,63
0,34 0 ,34
143,28
24,63
9,02
30,94
0,52 0 ,52
115,98
19,94
4,69
41,26
0,69
89,29
15,35
4,59
51,57
0,86
72,90
12,53
2,82
61,89
1,03
61,76
10,62
1,91
72,20
1,20
53,69
9,23
1,39
82,51
1,38
47,55
8,17
1,05
92,83
1,55
42,72
7,34
0,83
103,14
1,72
38,82
6,67
0,67
Δt
Δt
(min)
ΔP
Gráfica No.4 Hietograma de diseño para 100 años de periodo de retorno.
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5.2. Número de curva El número de curva de la microcuenca del Río Pisque se calculó mediante la ayuda del modelo computacional computacional ArcGIS, el cual nos ayudó a obtener el número de curva de cada zona de nuestra microcuenca en estudio con su respectiva área. En anexos podemos encontrar la gráfica que nos ayudará a obtener el número de curva ponderado para cada microcuenca.
-
Número de curva ponderado (Subcuenca 4).
∗ ∑ = ∑= Donde: NCp = Número de de curva ponderado ponderado de cada subcuenca. subcuenca. Ai = Área de cada zona correspondiente correspondiente al número de curva al que pertenece (km 2) Ni = Número de curva de cada cada zona.
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3
6
78
2,915
78
0,755
78
0,018
75
2,941
75
6,257
78
12,125
78
1,240
81
0,058
78
0,072
81
0,112
61
0,173
78
0,558
79
5,222
61
0,698
81
0,005
75
0,047
79
0,112
75
2,268
75
6,408
61
0,044
75
14,429
81
0,070
81
0,077
81
0,077
81
0,019
78
20,366
78
44,665
81
0,002
81
0,077
81
0,077
81
0,985
61
2,605
75
2,358
81
0,077
75
2,679
81
0,313
81
0,077
81
0,672
75
0,153
81
0,072
81
0,077
81
0,112
75
1,162
81
0,468
61
0,738
81
0,402
78
101,900
81
0,112
61
0,002
78
19,373
75
0,138
81
0,050
61
2,586
61
0,012
4
77 5
78
7
70
78
76
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61
6,555
79
3,481
78
63,348
79
22,267
5.3. Hidrograma de crecida. Tabla No.6 Datos de entrada para la elaboración del Hidrograma de crecida en HEC – HMS. Subcuencas 1 2 3 4
Áreas
Longitud del cauce
Pendiente promedio del cauce principal
(km2) 81,589 125,953 71,694 1,426
(Km) 17,737 20,183 15,781 1,109
(%) 5,664 5,958 8,15 3,65
Tiempo de duración (h) 0,553 0,599 0,439 0,077
(min) 33,179 35,942 26,360 4,648
Tiempo de retardo (h) 0,332 0,359 0,264 0,046
(min) 19,908 21,565 15,816 2,789
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Modelación del sistema. Gráfica No.5 Modelación del sistema en HEC - HMS.
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Por lo tanto, según el hidrograma obtenido los resultados son:
Gráfica No.7 Caudal pico para 10 años de periodo de retorno en HEC - HMS.
Periodo de retorno de 25 años.
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Por lo tanto, según el hidrograma obtenido los resultados son:
Gráfica No.9 Caudal pico para 25 años de periodo de retorno en HEC - HMS.
Periodo de retorno de 50 años.
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Por lo tanto, según el hidrograma obtenido los resultados son:
Gráfica No.11 Caudal pico para 50 años de periodo de retorno en HEC - HMS.
Periodo de retorno de 100 años.
Hidrograma de crecida.
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Por lo tanto, según el hidrograma obtenido los resultados son:
Gráfica No.13 Caudal pico para 100 años de periodo de retorno en HEC - HMS.
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5.4. Curva de duración general. Se procede a obtener los datos de caudales medios diarios de la estación H143 Granobles AJ Guachalá desde el año 2013 al año 1999 los cuales serán los 15 años de estudio para la obtención de la curva de duración general. Los datos de anuarios estarán incluidos en anexos.
Tabla No.7 Datos acumulados para la curva de duración general.
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Gráfica No.14 Curva de duración general.
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5.5. Curva de variación estacional. La curva de variación estacional se realizará con respecto al año que contenga la mediana de caudal medio anual.
Tabla No.8 Selección del año medio según los l os caudales medios mensuales. Año
Caudales medios anuales
Mediana
Año medio
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Gráfica No.15 Curva de variación estacional.
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inversamente proporcionales. De manera contraria ocurre con la longitud del cauce
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o estructuras de retención de agua como presas o embalses para abastecer la escasez de
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9.5. Caudales medios diarios de los años 2015 1999 de la estación H143 Granobles
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