Yenifer Blanco
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APLICACIONES
Ejercicio 1. (Teorem (Teoremaa de Torrice Torricelli lli). ). En la figura adjunto se muestra una tubería descargando agua con un gasto de 1.5 litros por segundo, en un tanque, A, que tiene un diámetro de 120 cm, el cual a su vez descarga a través de una llave de paso con un diámetro de ½ pulgada a otro tanque, B, de 60 cm de diámetro y 90 cm de alt altura (h3). El tanque A se encuentra sobre un pedestal a
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Calcular: a. La altura a la cual el nivel del agua en el tanque A se estabiliza. b. La velocidad a la cual llega el agua al tanque B. c. El tiempo en que tarda en llenarse el tanque B.
1
1 h
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Solución a) Aunque la ecuación para la velocidad de descarga de un
tanque (Teorema de Torricelli) la obtuvimos ya, lo haremos nuevamente para recordar el procedimiento. Aplicando la ecuación de Bernoulli entre los puntos 1 (carga) y 2 (descarga), se tiene:
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Es un hecho que el área de sección transversal del tanque, A 1,es mucho mayor que el área de descarga en el punto 2, A 2, y de acuerdo con la ecuación de continuidad la velocidad de desplazamiento del nivel de líquido en el tan tanque, v 1, será mucho menor que la velocidad de descarga del flu fluido, v 2, resultando que despreciable la primera, por lo que la ecuación de Bernoulli se reduce a:
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Con Δh = h1 – h2. Aplicando la l a condición condición de equilibrio equilibri o que sucede cuando
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Finalmente :
Solución
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Despejando v 3:
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•
Ejercicio 2. Por un tubo de Vénturi Vénturi,, que tiene tiene un diámetro diámet ro
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a. ¿Cuántos metros met ros cúbicos de agua por segundo circulan por el tubo?
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A 1, v 1 y A 2, v 2 representan las áreas y velocidades en la parte ancha y angosta de la tubería, respectivamente. resp ectivamente. Para conocer conocer el gasto es necesario necesa rio encontrar el valor de una de las dos velocidades en e n la ecuación ecuación anterior, anterior, por lo l o que es necesario utilizar utiliz ar una segunda ecuación que las contenga, para lo cual utilizamos la ecuación de Bernoulli: Bernoulli :
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