Math problem - Gallons/Minute

[lisacan]

I know this is probably a dumb question but I'm blond (lol, kidding) and have been out of school for a couple of years (actually, more than a couple! lol)

Here's the math problem:

I have 15 inch wide bucket that has 7 inches of water already in it. In 8 minutes, the water rises to 10 inches, how do I figure out how many gallons/minute the water is rising?

Thanks!!!

Lisa

 

[Leejosepho]

1 gallon = 231 cubic inches.

A 15" round bucket would hold about 175 cubic inches per inch of height.

A 3" rise in a 15" round bucket would be about 525 cubic inches, or 2-1/4 gallons.

2-1/4 gallons over 8 minutes would be a little over 1 quart per minute.

If you are using a typical 5-gallon pail, however, the above numbers do not fit. But, when a 5-gallon pail is filled to a little below the top, dividing 5 by the number of minutes it took to get there will tell you how much you are getting per minute.

 

[Sponsor]

 

[lisacan]

Thank you!

 

[Verdeboy]

In case you need the formula for this:

A bucket is considered a cylinder.

The volume of a cylinder equals the (area of the base) x height = ¶r2h

That should read pi x (radius squared) x height

pi=3.14

r= radius = 1/2 the diameter of the bucket = 7.5 in.

H=height = 7 in.

Initially you have V1 = 3.14 x (7.5 x 7.5) x 7 = 1,236 cubic inches of water

After 8 minutes you have V2 = 3.14 x (7.5 x 7.5) x 10 = 1,766 cubic inches of water

Now subtract V2 - V1 to get the change in volume: 1,766 - 1,236 = 530 cubic inches. So the volume increased by 530 cubic inches in 8 minutes.

We need to know the change in volume for 1 minute: 530 divided by 8 = 66

So your increase is 66 cubic inches per minute.

Now we have to convert cubic inches to gallons.

As LeeJosepho wrote: 1 gallon = 231 cubic inches

If you solve this algebraically 231 cubic inches = 0.29 gal.

So the answer is 0.29 gal/min