How to Fill a 7.2m Pool in 2 Hours

[cscott]

A 5/8-inch diameter hose is used to fill a round pool 7.2 m in diameter. How long will it take to fill it to a depth of 1.5 m if water leaves the hose at 0.28 m/s?

$$V_{pool} = \pi(3.6)^2 \cdot 1.5 = 61.1 \mbox{m}$$

$$5/8 in = 0.127m, r_{hose} = 0.063.5$$

$$V/s = \pi(0.063.5)^2 \cdot 0.28 = 8.9 \cdot 10^{-3}$$

$$\frac{61.1}{8.9 \cdot 10^{-3}} = 6865.2 s = 2 h$$

Look ok?

 

[tony873004]

no.
0.127m = 5 inches, not 5/8 of an inch.

 

[cscott]

no.
0.127m = 5 inches, not 5/8 of an inch.

that would make sense. I guess my converter doesn't like fractions.

Besides that, is the method ok?

 

[cscott]

Hmm... I get 13 days if I fix the conversion (d = 0.0159m.) This seems like a bit much.

 

[nrqed]

Hmm... I get 13 days if I fix the conversion (r = 0.0159m.) This seems like a bit much.

The method sounds right to me.
This is a huge pool to be filled with a tiny hose! several day si snot surprising to me.

 

[daveb]

The hose is 5/8 inch diameter, not radius. But yes, the method works withthe correct numbers.

 

[cscott]

Alright, thanks!