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### Volume of Water Passing through a Pipe

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Date: 08/12/97 at 16:35:15
From: veronica
Subject: Volume

My husband asked me if I remembered the math formula for "volume".
I searched with Infoseek and found you. Can you help?

Thank you,

Veronica from Tennessee
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Date: 08/12/97 at 17:48:33
From: Doctor Mike
Subject: Re: Volume

Hi Veronica,

This is sort of a tough one because there are so MANY answers.

The volume of a rectangular box is Width times Length times Height.
Make sure you use the same units consistently. For instance, if the
box is 1 foot by 2 feet by 3 inches, then you have to do some
conversion. If you use feet, the answer will be 1*2*(1/4) cubic feet.
If you use inches, the answer will be 12*24*3 cubic inches.

The volume of a "tin can" cylinder is  pi*R*R*H where R is the radius
of the circle at the end, H is the height, and pi is that famous
number 3.1415926535898............

So, maybe I accidentally picked the ones you were interested in,
but if not, write back and say what shape you want to find the
volume of.

-Doctor Mike,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```

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Date: 08/12/97 at 18:14:56
From: veronica
Subject: Re: Volume

Thanks Dr. Math,

I bet you are still laughing at this Tennessee farm girl. I mis-spoke
the question.  Perhaps I can re-state:

The situation:

I have a 12" cylinder pipe under a bridge in my meadow that flood
water sometimes passes through.

My husband wants to know how many gallons of water per minute this
pipe can handle.

Somehow I thought there was a formula for this.

I know length of the pipe....resistence.....water pressure all factor
into this. I just don't know how to answer him.

Veronica
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Date: 08/12/97 at 19:23:01
From: Doctor Mike
Subject: Re: Volume

>I bet you are still laughing at this Tennessee farm girl.

Never !

Let's start with the easy part.  Assuming the 12" is the inside
diameter of the pipe, the radius is 6, and the radius squared is
36. The area of the circular pipe opening is then 36*pi square
inches. Pi is about 3.1415926535898 - or just use the "pi key"
One square foot is 144 square inches, so the cross-sectional area
of this pipe is less than one square foot.

Multiply that cross-sectional area by the length of the pipe to
get the volume in cubic inches of the pipe. This just tells how
much the pipe will hold. This says nothing about through-put.
In fact, the diameter is the important thing, not the length.

>I know length of the pipe....resistence.....water pressure all factor
>into this.

You bet, there are a lot of variables.  The most important is how
fast the water is moving. If it is a real gully-washer you might
be able to assume that the pipe stays completely full. Reasonable?

If you assume that the water flows through this circular opening
at the rate of, say, 3 feet per second, then the volume of water
flowing through the opening is the same as the volume of water
that would fit into a 3-foot-long cylinder with radius 6. That
volume would be pi*6*6*36 = 4071.5 cu. in. or 2.356 cu. ft. This
would give it a flow capacity of 2.356 cu. ft. per second, or
about 141 cu. ft. per minute. Keep in mind that I have made a
lot of assumptions for my sample calculations. Also I used the
fact that there are 12*12*12 = 1728 cubic in. per cubic foot.

If you want to get wet you could go out there during some storm
and try to roughly measure the speed of the water. Put a leaf
into the water and count "one thousand and one, one thousand and
two" etc., to roughly measure how long it takes to flow a certain
measured distance.  Then observe whether our assumption of a
100 percent full pipe is correct.  If it looks as if it never gets
much above 2/3 full then you would decrease the through-put
correspondingly.

>I just don't know how to answer him.

Say, "it depends", and you need some empirical data that it
would be real nice of him to help you gather. Let us know if
you need to ask anything more as you get closer to the answer.
The effects of resistance or swirling water within the pipe are
much beyond this straightforward type of analysis.  Good luck.

-Doctor Mike,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
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Associated Topics:
High School Geometry
High School Higher-Dimensional Geometry
High School Practical Geometry

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