Cross-sectional area of a fire hose

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Quandaries & Queries

Question from Tom, a student:

My question is this I know the equations for the final answer but the book skips how to get to one section of the equation. Q=(a)(v)
A= The cross-sectional area of the conduit in square feet (ft2). So if you have a 5 inch hose how do they get A=0.136 ft2 ? And I know the velocity already v= velocity in ft per second.

Hi Tom.

A fire hose has a round cross section, so that's a circular area.

The area of a circle is π r². The diameter of your hose is 5 inches, so the radius is half of that: 2.5 inches.

That makes the cross-sectional area A = π (2.5 inches)² = 19.63 inches².

Since 1 foot = 12 inches, we see that 1² foot² = 12² inches².
So there are 144 square inches in a square foot.

This means to convert from 19.63 inches² to feet², we divide by 144:

19.63 ÷ 144 = 0.136

Cheers,
Stephen La Rocque.

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