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To PI or not to PI

Leslie Chaim
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Joined: May 22, 2002
Posts: 336
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"?



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Sonny Pondrom
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Joined: Jun 05, 2001
Posts: 128
Does a 10" line have an inside diameter of 10 inches?
Arjun Shastry
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Joined: Mar 13, 2003
Posts: 1874

fred rosenberger
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Joined: Oct 02, 2003
Posts: 11499

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 ]

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Arjun Shastry
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Joined: Mar 13, 2003
Posts: 1874
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.
SJ Adnams
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Joined: Sep 28, 2001
Posts: 925
I think Poiseuille's Law applies here.

which means that the flow is proportional to r^4

which means 100million 1" tubes!!
SJ Adnams
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Joined: Sep 28, 2001
Posts: 925
strike that - 10,000 is the answer
I agree. Here's the link:
subject: To PI or not to PI