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A pipe with inside diameter 10'' is to carry water from a reservoir to a small town in an arid land. Neglecting the friction and turbulence of the water against the inside of the pipes, what is the minimum number of 2''-inside-diameter pipes of the same length needed to carry the same volume of water to the arid town?

 Mar 1, 2021
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A pipe with inside diameter 10'' is to carry water from a reservoir to a small town in an arid land. Neglecting the friction and turbulence of the water against the inside of the pipes, what is the minimum number of 2''-inside-diameter pipes of the same length needed to carry the same volume of water to the arid town?   

 

The volume is a product of the cross-section area. 

 

A pipe with 5" radius has an area of 25π.  

A pipe with 1" radius has an area of   1π.  

 

So it looks like it'd take 25 of those 2-inch pipes to equal the volume carried by the 10-inch pipe.  Amazing.  

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 Mar 1, 2021
edited by Guest  Mar 1, 2021

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