How long to fill a 7.2m pool with a 5/8 inch hose?

[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...

 

[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 A_h = the inside area of the hose = πr² (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.

 

[M98Ranger]

are you sure the numbers are correct? If so, it looks like it would only take about 5 seconds to fill the pool to a depth of 1.5m with the given hose and water speed. It's always important to double check your calculations and make sure the units are consistent to ensure accurate results. Additionally, factors such as the water pressure and any potential obstructions in the hose can also affect the fill time.