Problem 48P

Reconsider Prob. 5-51. Determine how long it will take to empty the swimming pool completely.

PROBLEM: The water in a 8-m-diameter, 3-m-high above ground swimming pool is to be emptied by unplugging a 3-cm- diameter, 25-m-long horizontal pipe attached to the bottom of the pool. Determine the maximum discharge rate of water through the pipe. Also, explain why the actual flow rate will be less.

Solution

Introduction

Consider the water tank of 3 meter height and 8m diameter in which a pipe is connected horizontally at the bottom of the tank having a diameter 3 cm is shown in the picture.

Step 1

From figure it's clear the pressure at the point (1) at the surface of the water in the pool is equal to the pressure at the point (2) taken at the exit end of the pipe.

The bernoulli's equation

Fluid velocity at the surface is zero

Z2 is the reference level at the pipe exit is also zero so the above equation become

Therefore the flowing velocity at the pipe end