Math CentralQuandaries & Queries


Question from Bryan:

I need to know how much water (gal) is in a hose thats 100' long by 5" in dia.

Hi Bryan.

A fire hose filled with water is approximately equivalent to a simple tube, or "cylinder" as we mathematicians prefer to call it.

A cylinder is a shape whose volume is equal to the cross-sectional area (the circle) times the length or height. An area times a length is a volume.

So you need to find the area of the circle. Since area of a circle is π r2, where r is the radius (and the radius is half the diameter) and π is a constant of about 22/7, you can quickly find the area of the circular cross-section of the hose. (Make sure the diameter you measure is th inside diameter of the hose.) This will be in square inches, since you measured your diameter in inches.

To find the volume of the hose, first convert the length to inches as well. You want compatible units when multiplying area by length to get a volume. The length in inches is of course 1200 inches, so when you multiply that by the area of the circle, you get the volume of water in the fire hose.

But that will be in cubic inches. Most people measure the volume in liters or gallons. To do simple conversions like that, I use Google. For example, I type 20000 cubic inches in liters into Google and it reports the conversion (327.7 liters).

Stephen La Rocque.

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