Homework Help: Answer check Volume, velocity

1. Nov 20, 2003

kashmirekat

A 5/8 inch diameter (inside) garden hose is used to fill a round swimming pool 7.2m in diameter. How long will it take to fill the pool to a depth of 1.5m if water issues from the hose at a speed of 0.28m/s?

5/8in = 0.0159m
A = pi(3.6m)^2 = 40.7 m^2
V = (40.7m^2)(1.5m) = 61.07 m^3
v = 0.28m/s
t = ?

t = V/(vA) = (61.07m^3)/(0.28m/s)(40.7m^2) = 5.36s

That seems like a pretty short time to fill the pool...

2. Nov 20, 2003

jamesrc

I think you just mixed up your areas. Your volume to be filled, V, is correct, but the time to fill should be $t = \frac{V}{vA_h}$, where Ah = the inside area of the hose = &pi;r2 (r = 5/16 in.)

Your calculated time would be correct if you were using a hose with the same cross sectional area as the pool.

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