Why in the water formula q equals 7.48 x a x v WHERE v equals fps BUT q equals gpm?

Answer 1

We've never seen this formula before, but from what you've told us with your question,

we think we have it figured out, and we also think you made a tiny mistake.

It looks like this is a formula to calculate the amount of water that flows through

some kind of opening ... like maybe a big fire-hose ... if you know the area of the

opening and the speed of the flow.

'a' is the area of the opening, and 'v' is the speed of the flow .

The reason for the units that you're asking about is simple: If you're trying to find out

how much water you'll use up, the most convenient unit to use is: gallons for every

minute it keeps flowing. And if you have something stuck in the pipe or the hose that

measures the speed of the flow, it's going to be something like a little propeller that

spins as the water flows past it; the faster the water flows, the faster it spins, and

it measures the speed of the water, in something like miles-per-hour or feet-per-second.

Those are the most convenient units to use for volume of flow and speed of flow.

Now, you might not completely understand the next paragraph. It's just here to fill in

a gap for some other readers. But we do want to make sure that you do read the

last paragraph.

7.48 is the number of gallons in 1 cubic foot. So if [ 'a' x 'v' ] is the number of cubic feet

per minute, then the formula gives gallons per minute. So 'a' must be the cross-section

area in square-feet, and 'v' must be the flow-rate in feet per minute.

Finally, we think there's a tiny mistake in the question ... in order to make everything

work out right, we think 'v' must be 'feet per minute', not 'feet per second'.