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 May 8th, 2012, 04:22 AM #1 Newbie   Joined: May 2012 Posts: 10 Thanks: 0 how much water is required to fill this entire system? assuming that a city has 400 miles of water pipes and that the average diameter of the pipes is 1 ft., how much water is required to fill this entire system? answer is 12,408,000 gal. (what i need is the computations to get that answer thank you! )
May 8th, 2012, 05:59 AM   #2
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Re: how much water is required to fill this entire system?

Hello, autumnsandsprings!

Quote:
 Assuming that a city has 400 miles of water pipes and that the average diameter of the pipes is 1 ft., how much water is required to fill this entire system? Answer: 12,408,000 gal.

$\text{The radius of the pipe is }\frac{1}{2}$ $\text{feet.}$
$\text{The cross-section area of the pipe is: }\,\pi\left(\frac{1}{2}\right)^2 \:=\:\frac{\pi}{4}\text{ ft}^2
\text{The length of the pipe is: }\,400\text{ miles} \,=\,2,122,000\text{ feet.}
\text{The volume of the pipe is: }\:\frac{\pi}{4}\,\times\,2,122,000 \:=\:1,658,760.921\text{ ft}^3$

$\text{One cubic foot is about 7.48\text{ gallons.}$

$\text{The capacity of the system is: }\,1,658,760.921\,\times\,7.48 \:=\:12,407,531.69 \text{ gallons}$

May 11th, 2012, 02:27 AM   #3
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Re: how much water is required to fill this entire system?

Quote:
Originally Posted by soroban
Hello, autumnsandsprings!

Quote:
 Assuming that a city has 400 miles of water pipes and that the average diameter of the pipes is 1 ft., how much water is required to fill this entire system? Answer: 12,408,000 gal.

$\text{The radius of the pipe is }\frac{1}{2}$ $\text{feet.}$
$\text{The cross-section area of the pipe is: }\,\pi\left(\frac{1}{2}\right)^2 \:=\:\frac{\pi}{4}\text{ ft}^2
\text{The length of the pipe is: }\,400\text{ miles} \,=\,2,122,000\text{ feet.}
\text{The volume of the pipe is: }\:\frac{\pi}{4}\,\times\,2,122,000 \:=\:1,658,760.921\text{ ft}^3$

$\text{One cubic foot is about 7.48\text{ gallons.}$

$\text{The capacity of the system is: }\,1,658,760.921\,\times\,7.48 \:=\:12,407,531.69 \text{ gallons}$

thank you so much!!

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