TALLER N°2 CUENCAS HIDROGRÁFICAS Y PRECIPITACIÓN
NESTOR IVAN ARIAS MONTAÑES HERNÁN FELIPE BECERRA BARÓN CRISTIAN JAVIER CASTELBLANCO BAYONA JURY AYLIN GARCÍA ZÁRATE LUIS FERNANDO BLANCO RIAÑO WILLIAM CAMILO JOYA CÁRDENAS
UNIVERSIDAD PEDAGÓGICA Y TECNOLÓGICA DE COLOMBIA FACULTAD DE INGENIERÍA ESCUELA DE TRANSPORTE Y VÍAS HIDROLOGÍA Y DRENAJE VIAL TUNJA 2018
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TALLER N°2 CUENCAS HIDROGRÁFICAS Y PRECIPITACIÓN
GRUPO N° 4 RIO CHIQUINQUIRÁ (PROVINCIA DE OCCIDENTE)
NESTOR IVAN ARIAS MONTAÑES COD. 201520208 HERNÁN FELIPE BECERRA BARÓN COD. 201520264 CRISTIAN JAVIER CASTELBLANCO BAYONA COD. 201322431 JURY AYLIN GARCÍA ZÁRATE COD. 201110584 LUIS FERNANDO BLANCO RIAÑO COD. 201420968 WILLIAM CAMILO JOYA CÁRDENAS COD. 201320531
Trabajo presentado a: Ing. Msc. JOSE RODRIGO ALARCON DALLOS Docente de la asignatura Hidrología y Drenaje Vial
UNIVERSIDAD PEDAGÓGICA Y TECNOLÓGICA DE COLOMBIA FACULTAD DE INGENIERÍA ESCUELA DE TRANSPORTE Y VÍAS HIDROLOGIA Y DRENAJE VIAL TUNJA 2018
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TABLA DE CONTENIDO ......................................................................... ................................................... ............................... ..... 4 1. OBJETIVOS ................................................ 1.1. OBJETIVO GENERAL ........................................ .................................................................. ........................................... ................. 4 1.2. OBJETIVOS ESPECIFICOS .............................. ........................................................ ............................................ .................. 4 ............................................................................ ............................................... ...................... 5 2. METODOLOGIA ................................................... ............................................................................ ............................ 6 3. DESARROLLO DEL TALLER .................................................. 3.1.PRECIPITACIÓN MEDIA DE LA CUENCA ................................................... ................................................... 6 3.1.1. METODO DEL PROMEDIO ARITMETICO ........................................... ........................................... 8 3.1.2. METODO DE LOS L OS POLIGONOS DE THIESSEN T HIESSEN ................................. ................................. 8 3.1.3. METODO DE LAS ISOYETAS................................................ ............................................................ ............ 10 3.2. INTENSIDADES MAXIMAS ...................... ............................................... .................................................. ......................... 10 3.3. PRECIPITACIÓN DE DISEÑO ................................................... ................................................................... ................ 23 3.3.1. DISTRIBUCIÓN NORMAL ...................................................... .................................................................. ............ 26 3.3.2. DISTRIBUCIÓN LOG-NORMAL ......................................................... ......................................................... 27 3.3.3. DISTRIBUCIÓN DE GUMBEL ........................................................ ............................................................ .... 27 3.3.4. DISTRIBUCIÓN LOG-GUMBEL .................................................. ......................................................... ....... 28 3.3.4. DISTRIBUCIÓN DE PEARSON III ................................................... ...................................................... ... 28 3.3.6. DISTRIBUCIÓN LOG-PEARSON III ............................................ ................................................... ....... 29 ......................................... 34 4. ANALISIS DE RESULTADOS Y CONCLUSIONES ......................................... ............................................ ....... 36 5. POSIBLES ERRORES Y RECOMENDACIONES ...................................... ........................................................................ ................................................... ............................. ... 37 BIBLIOGRAFIA ...............................................
ANEXOS
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LISTA DE TABLAS Tabla 1. Resumen Taller n° 1 Cuencas Hidrográficas ........................................ ............................................. .....8 Tabla 2. Localización Loca lización de estaciones pluviométrica. ........................................ ............................................... .......13 Tabla 3. Áreas de los polígonos de d e Thiessen. ................................................ ....................................................... .......17 Tabla 4. Áreas entre isoyetas. ............................................................... ............................................................................... ................18 Tabla 5. Datos principales de pluviogramas. ...................................................... ......................................................... ... 19 Tabla 6. Datos obtenidos del pluviograma ................................................. ............................................................. ............19 Tabla 7. Datos obtenidos del pluviograma N° 1. 1 . ................................................. .................................................... ... 20 Tabla 8.Datos obtenidos o btenidos del pluviograma N° 2. .................................................. ..................................................... ... 21 Tabla 9. Intensidades máximas para cada periodo de duración dur ación ............................ ............................ 22 Tabla 10. Intensidades máximas, Calculo de Frecuencia Frec uencia y Tr. .............................. ..............................24 Tabla 11. Precipitaciones máximas en 24 hrs h rs (1970-2014). (197 0-2014). .............................. .................................. .... 26 Tabla 12. Calculo de F, Tr y log para las precipitaciones máximas. ...................... ......................27 Tabla 13. Calculo de precipitación promedio, desviación estándar y coeficiente asimétrico................................................ asimétrico.......................................................................... .................................................... ..................................... ...........28 Tabla 14. Precipitación de diseño-Distribución Normal.......................................... .........................................29 Tabla 15 . Precipitación de diseño-Distribución diseño -Distribución Log-Normal. Log-Norma l. ................................ ................................ 30 Tabla 16. Precipitación de diseño-Distribución Gumbel......................................... ........................................30 Tabla 17. Precipitación de diseño-Distribución diseñ o-Distribución Log-Gumbel. Lo g-Gumbel. ................................31 Tabla 18. Precipitación de diseño-Distribución Pearson Pea rson lll. ................................... 32 Tabla 19. Precipitación de diseño-Distribución Pearson lll. .................................. ..................................33
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LISTA DE FIGURAS Figura 1. Mapa de estaciones meteorológicas de categoría pluviométricas ..........14 Figura 2. Toma de d e areas de poligonos p oligonos de Thiessen ............................................. .............................................14
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LISTA DE GRAFICAS Grafica 1. Hietograma-Pluviograma N°1. ............................................... ............................................................... ................22 Grafica 2. Curva masa de precipitación-Pluviograma N°1. ................................... ...................................23 Grafica 3. Hietograma-Pluviograma N°2. ............................................... ............................................................... ................23 Grafica 4. Curva masa de precipitación-Pluviograma N°2 ..................................... .....................................24 Grafica 5. Curvas I-D-F. ................................... ............................................................ ................................................... ............................. ... 25
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1. OBJETIVOS
1.1 OBJETIVO GENERAL Calcular la precipitación media de la cuenca y la precipitación de diseño, con base en datos de estaciones pluviométricas de la zona de estudio e identificar intensidades máximas por medio de un pluviograma.
1.2 OBJETIVOS ESPECIFICOS
Emplear los métodos correspondientes (Trazado de Isoyetas, Polígonos de de Thiessen y promedio aritmético) para el cálculo de la precipitación media de la cuenca, teniendo en cuenta las estaciones pluviométricas ubicadas dentro y cerca de esta. Analizar un pluviograma para tomar esta información información y aplicarla en el cálculo de intensidades máximas. Realizar las gráficas respectivas (hietograma, curva masa precipitación y curvas IDF) para analizar de manera adecuada los datos obtenidos por medio del pluviograma. Determinar la precipitación de diseño para una obra de drenaje localizada en una de las corrientes hídricas ubicadas dentro de la cuenca del Rio Surba.
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RESUMEN TALLER N° 1 CUENCAS HIDROGRAFICAS Tabla 1. Resumen Taller n° 1 Cuencas Hidrográficas cur vas de nivel 2450 Delimitación de la El parteaguas se encuentra entre las curvas y 3950, se realizan las divisiones respectivas para cuenca identificar cuencas, subcuencas, microcuencas. Parte alta o recepción: Corresponde a la zona donde nace el río se encuentra entre las curvas de nivel correspondiente a la 3950 a 3600. Garganta: Esta zona se encuentra entre la cota 3600 y la 3000. Lecho o cono de deyección: En esta zona se encuentra el punto de interés (rio Chicamocha) allí se deposita el material extraído en la parte alta, se encuentra en las curvas de nivel de cota 3000 y 2450. Características físicas de la cuenca del Rio Surba. 73.45 km² Área 56,33 Km. Perímetro La cuenca delimitada tiene un tamaño pequeño debido a Tamaño que su área no sobrepasa los 1000 km². Forma de la cuenca Mediante el coeficiente de compacidad de gravelius:
√ 53,33 1.75 2 3,1416∗73,45² 3,1416∗73,45²
Curva Hipsométrica
Se determina la forma de la cuenca, con la ayuda de la tabla, lo cual nos indica para este valor una forma do oval oblonga a rectangular y tendencias a crecidas baja. Esta grafica se realiza con datos en las abscisas de área y en las ordenadas de altitud. Es importante extraer de la gráfica la relación
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CURVA HIPSOMÉTRICA % de la superficie total de la cuenca
0
1
2
3
4
5
6
7
8
9 10 1 0 11 12 13 14 15
3950 3850 3750 ) 3650 m 3550 m 3450 n 3350 s 3250 m ( 3150 D 3050 U 2950 T I 2850 2750 T L 2650 A 2550 2450
0
10
20
30
40
50
60
70
80
Curva de frecuencia y de frecuencua de altitudes Fuente: elaboración propia.
ndice o factor de Indica la oportunidad de tener una tormenta intensa forma sobre la cuenca, se puede realizar de dos formas.
ℎ 11.75 19 0.618
()² 73.45² (21.2)² 0.16
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ndice de pendiente global
28.41 74.71 0.3803∗100 . Mediante esta se puede caracterizr el relieve de la cuenca: 5−95 3750−2500 19 65.78
De acuerdo a este cálculo, se determina que el relieve sobre el cual se encuentra la cuenca del Rio Surba es fuerte.
Pendiente uniforme
Red de drenaje
Esta relaciona el desnivel que hay entre los extremos del cauce y la proyección horizontal de su longitud.
3.8−2.45 ∗100 21.2 6,37%
Es importante tener en cuenta el tipo de corrientes y el orden. Para establecer el orden de las corrientes se toman en cuenta las corrientes perennes e intermitentes y se determina por el método de Strahler. Para calcular la densidad de las corrientes se tienen en cuenta las corrientes perennes e intermitentes y se utiliza la siguiente expresión:
41.84 73,45 ²
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GRAFICAS Relación distancia-Elevación cauce principal
Elaboración: Propia En esta representación gráfica se observa que a mayor altura el cauce del rio tiene una mayor distancia. Fuente: Autor
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2. METODOLOGÍA
De acuerdo a la realización del trazado y caracterización de la cuenca del Rio Surba ubicada entre los municipios de Paipa y Duitama, correspondiente al primer taller de la asignatura se procedió a buscar datos pluviométricos de la zona, encontrando registros mensuales de estaciones localizadas dentro y fuera de la cuenca. Se determinó la precipitación media a través de los métodos como el trazado de isoyetas, media aritmética y polígonos de thiessen procedimientos que posteriormente serán explicados. Para el análisis de las intensidades máximas, se trabajó con dos (2) pluviogramas de la estación meteorológica de la UPTC, los cuales contenían registros diarios en este caso los días 01 y 02 de octubre de 2016, con una escala de intervalos de tiempo de una hora, para este análisis de intensidades se realizan las respectivas tabulaciones de datos, además de gráficos como el hietograma, la curva masa de precipitación y las curvas I-D-F. Por último se realizó el cálculo de la precipitación de diseño, utilizando datos de
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3. DESARROLLO DEL TALLER
A continuación se se explica detalladamente detalladamente cada uno de los pasos, cálculos, y demás procesos que se llevaron a cabo en la búsqueda de la precipitación media, intensidades máximas y precipitación de diseño.
3.1. PRECIPITACIÓN MEDIA DE LA CUENCA Para el cálculo de la precipitación media de la cuenca del Rio Surba, se encontraron registros pluviométricos de cuatro estaciones de las ocho que se encuentran en el área de influencia de la cuenca.
Localización de las estaciones pluviométricas
Para realizar la localización de las estaciones, se utilizaron datos de coordenadas encontrados en la página del IDEAM, los cuales se registran en la siguiente tabla.
Tabla 2. Localización de estaciones pluviométrica .
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Figura 1. Mapa de estaciones meteorológicas de categoría pluviométricas
Fuente: IDEAM
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Precipitación de Estación Surbata Bonza = 869,6 mm Distancia entre Estaciones conocidas = 10,6 cm (medido en papel)
Se calculó la isoyeta de precipitación 850,0 mm. Diferencia de precipitaciones conocidas = 869,6mm – 815,07mm= 54,53 mm Diferencia de precipitación = 850mm – 815,07mm = 34,93 mm Con estos datos se aplica una regla de tres simple, así, 54,53 mm
10,6 10,6
34,93 mm
cm
x x
34,9,933 ∗ 10 10,6,6 34 54,53 6,8 Entonces se miden a partir de la estación San Lorenzo 6,8 cm y se traza la curva isoyeta, apoyado en la dirección de las curvas de nivel topográficas.
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La precipitación media de la cuenca por el e l método del promedio aritmético es 910,4 mm.
3.1.2. 3.1 .2. MÉ TOD TO D O DE D E P OL ÍG ONOS ON OS D E THIE TH IE S S E N Para realizar los polígonos de Thiessen, se toman como base los triángulos obtenidos en la triangulación de las estaciones, posteriormente se trazan las mediatrices de respectivos triángulos, hasta que las mismas corten con el límite de la cuenca. Al realizar este método se obtuvieron siete polígonos, cada uno con su respectiva área, la cual fue obtenida mediante el uso del Planímetro, facilitado en el aula de geomática de la universidad.
Figura 2. Toma de áreas de polígonos de Thiessen
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Las áreas obtenidas fueron:
Tabla 3. Áreas de los polígonos de Thiessen. POLIGONO
ESTACIÓN
AREA (Km2)
1
San Lorenzo
6,454
2
Surbata Bonza
6,628
3
La Amarilla
0,678
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3.1.3. 3.1 .3. MÉ TOD TO D O DE D E L A S IS OY E TA S Anteriormente por medio de la interpolación se definieron las curvas isoyetas de igual precipitación. Ahora utilizando estas se toma por medio del planímetro, el área entre cada isoyetas, para aplicar la siguiente expresión.
1∗12∗2⋯∗
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Sumatoria
72,655
72570,65
Fuente: Autor
∗² 72570,65 72,655 ² , , La precipitación media de la cuenca por p or el método de isoyetas es e s de 998,84 mm.
3.2. INTENSIDADES MÁXIMAS
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Tabla 6. Datos obtenidos del pluviograma Hora
Tiempo Precipitación Tiempo Precipitación Intensidad acumulado acumulada (min) (mm) (mm/h) (min) (mm)
Los datos obtenidos para cada pluviograma se registran en las Tablas 7, 8,
Tabla 7. Datos obtenidos del pluviograma N° 1.
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Tabla 8. Datos obtenidos del pluviograma N° 2. Hora
Tiempo (min)
Tiempo acumulado (min)
Precipitación (mm)
Precipitación acumulada (mm)
Intensidad (mm/h)
445
445
0
0
0
2
447
0,4
0,4
12
98
545
0
0,4
0
10
555
2
2,4
12
7:00 14:25 14:27 16:05
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Así se realiza para cada pluviograma y los datos se registran en la siguiente tabla.
Tabla 9. Intensidades máximas para cada periodo de duración
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Grafica 2. Curva masa de precipitación-Pluviograma N°1.
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Grafica 4. Curva masa de precipitación-Pluviograma N°2
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Grafica 5. Curvas I-D-F.
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Tabla 11. Precipitaciones máximas en 24 hrs (1970-2014). AÑO
Pmáx 24 Hrs
AÑO
Pmáx 24 Hrs
AÑO
Pmáx 24 Hrs
AÑO
Pmáx 24 Hrs
AÑO
Pmáx 24 Hrs
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