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To PI or not to PI

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You had a 10" water line that broke down. Unfortunately, there's only 1" pipe available for replacement.

How many 1" pipes is needed (and why/how) to replace the one 10"?

Cheers,

Leslie

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Does a 10" line have an inside diameter of 10 inches?

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100

lowercase baba
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100. assuming that the flow isn't restricted by surface area of the pipe...

a 10" (i'm assuming this is the inside diameter) pipe has an area of PI * r^2. if our diam. is 10, our radius is 5. so the 10" pipe has a cross-section area of 25PI.

Each 1" pipe has a radius of 1/2", or an area of (1/4)PI. so, we need 100 pipes.

However, the first pipe has a surface area equal to 10PI (times the length, which we can ignore). the 100 pipes have a surface area of 100PI.

I am not a fluids engineer, but i would imagine that more surface area would result in more friction, slowing down the flow, but i have no idea how to calculate that.
[ July 02, 2004: Message edited by: fred rosenberger ]

Arjun Shastry
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Yes, I think so.Factor that determines is I think Reynold's numebr.Ratio of inertial force to viscous force.Bigger pipe will have more intertia.

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I think Poiseuille's Law applies here.

which means that the flow is proportional to r^4

which means 100million 1" tubes!!