Math CentralQuandaries & Queries


Question from mhd, a student:

dear sir,
how i can find volume of the pipe elbow of 4inches?

Hi there.

The elbow of the pipe is something like a piece of a donut. The shape of a donut is called a "torus". I think you are describing a part of a torus whose pipe diameter is 4 inches (so the radius "r" of the pipe is 2 inches).

It is interesting that the volume of a full torus is equal to the cross-sectional area ( π r2 ) times the circumference of the centerline of the torus. For your partial torus, this is the length of the curve in the absolute middle of the pipe. You will need to measure this length (let's call it L).

So multiply the length in inches of the curve through the center of the elbow by 12.6 (that's π 22 ) and you'll have the number of cubic inches of volume of the elbow.

Hope this helps,
Stephen La Rocque.

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