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Hidráulica Básica Presión absoluta = Presión atmosférica +Presión manom étrica
Pe=1 atm
i Diferencia de resiones
Pi > Pe En el gráfico se observa que la presión interna empuja el manómetro de vidrio dando una diferencia de niveles . Pe = Presión externa Pi = Presión interna CASO 2 : Es cuando la presión dada es igual a la presión atmosférica (a presión manométrica nula); deberá emplearse la siguiente ecuación ecuación : Presión absoluta = Presión atmosférica Pe
Pi No hay diferencia de presión
Pi =Pe
En el gráfico se observa que el manómetro de vidrio no muestra ninguna variación de niveles. CASO 3 :
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Tecsup Virtu@l
Hidráulica Básica Pe Pi
Pi < Pe
Bomba de vacío
En la figura se muestra que el manómetro de vidrio muestra una situación de succión ocasionado por el vacío que existe en el tanque.
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Hidráulica Básica
2.4. TUBERÍA Sí queremos mover un líquido de un depósito A al depósito B se tiene que usar una tubería. La tubería es la conducción apropiada para trasladar un fluido de un lugar a otro. A
B
El líquido se traslada de A hasta B, por que existe una diferencial de niveles entre ambos tanques.
La circulación cesa cuando se igualan los niveles. Para lograr un mayor flujo se tendría que usar una bomba. 2.5. TRASLADO DE UN FLUIDO FLUIDO POR GR AVEDAD Si disponemos de un depósito A, que está a un nivel mayor de depósito B, es posible por gravedad trasegar el fluido de A hacia B. Para lograr un mayor caudal se tiene que usar una bomba. A
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Hidráulica Básica
2.6. ¿ PORQUÉ USAR UNA BOMBA? Sí se quiere aumentar la velocidad de descarga, o elevar un líquido, hay necesidad de usar una bomba, por ejemplo sí deseamos elevar elevar un líquido del depósito A hasta hasta B.
B
A
Podemos decir que para transportar un fluido puede usar la carga de la gravedad (de un depósito de un mayor nivel a menor nivel) o por medio de una bomba. En una bomba hay que identificar la entrada de líquido o zona de succión y la salida de líquido o zona de descarga o impulsión. Descarga Succión
2.7. ¿ QUÉ SON LOS MAN ÓMETROS? Son dispositivos que se colocan en la admisión y descarga de una bomba para medir las presiones de succión y descarga respectivamente.
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Hidráulica Básica
2.8. ¿QUÉ TIP TIP O DE MAN ÓMETRO ES MÁ S COMÚN USAR , Y COMO FUNCION A? El manómetro más común es el de tubo Bourdon. Este es un tubo de pared delgada y curvado en forma de C, un extremo es fijo y el otro libre, este está conectado a un mecanismo de piñon-biela. Al aplicar presión interna al tubo, este se endereza proporcionalmente a dicha presión, el extremo libre mueve el mecanismo y hace girar un indicador ante una escala graduada.
3 . CARGAS ESTATICAS 3.1. PRESIÓN DE GRAVEDAD La presión de gravedad puede ocasionar una resistencia en la bomba. “R” es la resistencia que se puede ocasionar debido a la presión de la gravedad.
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Hidráulica Básica
Cuando el agua se eleva de A hacia B, la resistencia ocasionada por la presión de la gravedad debe ser superada.
3.2. CARGA ESTÁTICA ESTÁTICA DE DESCARGA Es la distancia a la cual un líquido se eleva desde la descarga de la bomba hasta el otro nivel, se denomina carga estática de descarga.
Carga estática de descarga
3.3. CARGA ESTÁTICA DE SUCCIÓN La carga estática de succión es la distancia que desciende un líquido desde un nivel
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Hidráulica Básica
3.4. ELEVACIÓN ESTÁTICA ESTÁTICA DE SUCCI ÓN La elevación estática de succión, succión, es la distancia distancia del nivel del suministro del líquido al eje central de la bomba, estando el nivel de suministro debajo de la bomba.
Elevación estática de succión
3.5. CARGA ESTÁTICA TOTAL La distancia vertical, medido entre el punto de descarga y el de succión se llama carga estática total.
Carga estática total
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Hidráulica Básica
4 . CIRCULACIÓN DE LÍQUIDOS EN TUBERÍAS 4.1. PERFIL DE VELOCIDAD Los líquidos al circular en tuberías, las cuales son generalmente de sección transversal circular, desarrollan diferentes velocidades desde la pared del tubo al centro de la tubería. Se dice que muestran un perfil de velocidades, en donde se observa como la velocidad desde cero (pared de tubería) hasta una velocidad máxima (en el eje de la tubería).Sin embargo para todos los cálculos se utiliza la velocidad media V, la cual se estima como una velocidad promedio del fluido en la tubería.
V máx
V min
4.2. TIPOS DE FLUIDOS Los líquidos al circular por las tuberías lo pueden realizar a altas velocidades y su perfil de velocidad es plano, se dice que el régimen de flujo es turbulento.
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Tecsup Virtu@l 4.3.1.
Hidráulica Básica EJERCICIO EJERCICIO DE APLICACIÓN Se tiene un sistema de tubería de 4 pulgadas por donde circula un aceite de densidad 58,9 lbs/pie3, y una viscosidad de 1,5 centipoises, si la velocidad media es 20 pies/s. Determine su número de Reynolds SOLUCIÓN Las diversas variables que intervienen en el número de Reynolds tienen que estar en las mismas unidades para que salga adimensional, por ello se tiene que apelar en algunos casos a los factores de conversión de unidades. Hay que tener en cuenta que las unidades de las variables, v, d , µ,, ρ deben estar en un mismo sistema de unidades. Los valores de las variables son: Diámetro = 4 pulgadas pulgadas = 4/12 pies = 0,3333 pies Velocidad = 20 pies/s Viscosidad = 1,5 1,5 cp cp = 1,5 cp. 0,000672 0,000672 lb/pie.s = 1,008. 1,008. 10-3 lb/pie.s Densidad = 58,9 lb/pie
3
1 cp
Aplicando la ecuación ( 1 ) : Número de Reynolds =
0,3333 pie. 20 p/s . 58,9lb/pie 3 1,008. 10-3 lb/pie.s
= 3,89 . 105
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Hidráulica Básica SOLUCIÓN Con la información: Caudal = 200 gpm Densidad =70,5 lb/pie3 Diámetro interno = 4,026 pulgadas Viscosidad = 1,2 cp Remplazando en la ecuación ( 2 ) :
N RE = 50,6 4.4.2.
200 • 70,5 4,026 • 1,2
= 1,47 • 10
5
TIPOS DE FLUJO Por la forma de cómo se desplazan las líneas de flujo en las conducciones, se dice que los regímenes de flujo pueden ser: laminar o turbulento.
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Hidráulica Básica
4.6. RUGOSIDA D RELATIVA RELATIVA ( /D) Es una relación entre el espesor de la rugosidad ( µ ) y el diámetro de la tubería, D. 4.7. TABLA DE RUGOSIDAD RELATIVA Es una tabla elaborada en función del material que es construido la tubería y el diámetro de la misma. Normalmente son expresiones lineales construido en papel logarítmico. Para un determinado diámetro nominal de la tubería y para un tipo de material que está manufacturado la tubería, se evalúa la rugosidad relativa µ /D .
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Tecsup Virtu@l 4.7.1.
Hidráulica Básica EJERCICIO EJERCICIO DE APLICACIÓN Asumiendo que la tubería tubería de transporte de un líquido es de acero comercial de 4 pulgadas de diámetro nominal, determine ¿ cuál es su rugosidad relativa? Solución Teniendo en cuenta que utilizando la información del tipo de material de la tubería y el diámetro nominal, por intersección en el gráfico, se calcula que la rugosidad relativa es de 0,00043.
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Hidráulica Básica
5 . PÉRDIDA DE CARGA 5.1. ECUACIÓN DE BERNOULLI Es una ecuación utilizada en la determinación de las pérdidas de carga en un sistema de bombeo, cuyo objetivo es obtener la potencia de la bomba. Se aplica el principio de conservación de la energía. En la figura se elige un punto (1) en la superficie del tanque de abastecimiento y un punto (2) en la superficie del tanque que llega al tanque elevado.
(2)
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Donde estos valores son: h2 = carga estática estática total; altura vertical vertical medida desde la superficie del tanque 1 al tanque 2. Hb es la carga de la bomba. La pérdida de carga debido a la fricción, Pf, se produce en el sistema de tuberías por la presencia de una serie de accesorios: válvulas, expansiones, codos y tubería recta, todos ellos ocasionan pérdida de energía y estos pueden expresarse en unidades de longitud. Cuando en el sistema de bombeo no hay una diferencia de carga estática (h2), quiere decir los dos tanques están al mismo nivel, la ecuación se reduce a:
Hb = Pf La expresión significa que la carga de la bomba será igual a la pérdida de carga debido a la fricción; es decir la bomba debe vencer las pérdidas por fricción. 5.2. DIAGRAMA DE MOODY Es un método gráfico para evaluar el factor de fricción “f”. Dicho factor interviene en la ecuación de pérdida de carga debido a la fricción. En el diagrama se utiliza como parámetros el número de Reynolds y la rugosidad
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Tecsup Virtu@l 5.2.1.
Hidráulica Básica EJERCICIO EJERCICIO DE APLICACIÓN: Si se tiene un líquido cuyo número de Reynolds es de 250000, 250000, que circula por una tubería de una rugosidad relativa de 0,001 ¿cuál es el factor de fricción? SOLUCIÓN : Teniendo en cuenta los dos parámetros: rugosidad relativa (ε /D) y el número de Reynolds, vamos al diagrama de Moody y determinamos que el factor f = 0,021
ε
f = f = 0,021
/D = 0,001
Rugosidad
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Hidráulica Básica
5.3. ECUACIÓN DE PÉRDIDA DE CARGA La pérdida de carga en un sistema de flujo de fluidos se debe tanto a las pérdidas en tuberías rectas por efecto de la rugosidad, como también por efecto de los distintos accesorios que pueden ser: válvulas ,teés, codos, expansiones, contracciones, medidores de flujo, etc.
La pérdida de presión en una tubería horizonta l Manómetros indicadores de presión Pi
Q
Pf
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Tecsup Virtu@l 5.3.1.
Hidráulica Básica EJERCICIO EJERCICIO DE APLICACIÓN Se tiene un sistema de tubería a través del cual circula agua a la temperatura de 80°F, la longitud equivalente total es de 83 pies, la densidad es de 62,4 lb/pie3, el fluido circula con un flujo volumétrico de 300 gpm, y el diámetro de la tubería es de 3,068 pulgadas. El factor de fricción es de 0,015. Determine la pérdida de presión del sistema. Solución. Aplicando la fórmula tenemos: ∆p
∆
= 0,000216 f L
ρ
Q2 d5
P = 0,000216. 0,015. 83. 62,4. 300 2 / (3,068)5 P = 1510,25/ 271,82 271,82 = 5,55 lb/ pulg 2
5.4. LONGITUD EQUIVALENTE EN ACCESORI ACCESORI OS, REDUCCIONES Y EXP ANSI ONES
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Hidráulica Básica RESISTENCIA DE CODOS, CODOS, TEES TEES Y CURVAS. (MEDI DO EN LONGITUD EQUIVALENTE, PI ES) Diámetro nominal pulgs. ½
1 2
Codo
o
Curva
90
R=1D 4.5 5 25
R=1.5D 3 35
o
90
R=5D 2.5 3
R=10D 4 5
Te Fluj lujo curv curvoo Fluj lujo rec recto
8 11
3 35
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Hidráulica Básica Resistencias de tuberías en entrada y salida horizontal (Longitud equivalente, pies) Coeficiente de resistencia Diámetro nominal de tuberías en pulg.
K=1.0
K=0.78
K=0.5
K=0.23
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Hidráulica Básica
Diámetro nominal( pulgadas) d1 ¼ 1 11 /2 2
d2 ½ ½ ¾ ¾ 1 1
d2
D1
d2
D1
0.6 1.2 0.6 1.6 1.2 22
d1
d2
d1
d2
0.5 0.7 0.6 1.0 0.9 13
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Hidráulica Básica
5.5. TUBERÍAS Las tuberías son las conducciones metálicas de sección transversal circular, a través de los cuales circulan los fluidos; es decir, los líquidos o gases. Aunque las tuberías son de diversos materiales, lo común son las tuberías de acero comercial. Estas conducciones normalmente se acoplan por roscado, machihembrado, empleo de bridas o a soldadura. Los tubos de acero se fabrican por doblado longitudinal de platinas de acero con junta de tope o solapada, soldada a presión en la máquina. Las tuberías se clasifican de acuerdo al número del catálogo (Schudele) en los tipos siguientes: 10, 20, 30, 40, 60, 80, 100, 120, 140, 160 cifras que representan el valor
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Hidráulica Básica TABLA DE VALORES PARA TUBERÍ A DE CATALOGO 40
Tamaño Diámetro Espeso diámetro externo r nominal (pulg) (pulg) pulgadas ½ ¼ ¾
0.405 0.540 0 675
Diámetro interno
Diámetro interno (pulg)
Sección transversal
d D d2 d3 d4 d5 a A 2 pulg pies pulg pie2 0.068 0.269 0.0224 0.0724 0.0195 0.005242 0.00141 0.057 0.00040 0.088 0.364 0.0303 0.1325 0.0482 0.01756 0.00639 0.104 0.00072 0 091 0 493 0 0411 0 2430 0 1198 0 05905 0 02912 0 191 0 00133
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Tecsup Virtu@l 5.6. EJERCICIOS EJERCICIOS DE APLICACIÓN
Hidráulica Básica
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Tecsup Virtu@l PROBLEMA 2:
Hidráulica Básica
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Tecsup Virtu@l SOLUCIÓN :
Hidráulica Básica
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Tecsup Virtu@l 6 PRUEBA DE AUTOCOMPROBACIÓN AUTOCOMPROBACIÓN
Hidráulica Básica
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Tecsup Virtu@l 7 RESPUESTAS A LA PRU EBA DE AUTOCOMPROB ACIÓN
Hidráulica Básica
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