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### Feet Per Second

```Date: 02/22/2003 at 15:10:12
From: Steve
Subject: Formula

To determine the velocity in a pipe in ft. per second:

Velocity  =  gpm   x    0.3208
___________________

A

Where:      A is area of pipe in sq. inches, gpm is gallons
per minute (US)

In regards to this formula, how does the numerical figure 0.3028 apply
(where does this figure originate)?
```

```
Date: 02/23/2003 at 09:19:12
From: Doctor Jeremiah
Subject: Re: Formula

Hi Steve,

One gallon is 231 cubic inches, so:

in^3 = gal x 231 in^3/gal

in^3/min = gal/min x 231 in^3/gal

A in^2 x in/min = gal/min x 231 in^3/gal

Which gives us an equation of:

in/min = gal/min x 231 in^3/gal
----------------------
A in^2

But we aren't looking for inches per minute.
We are looking for feet per second.

in/min = ft/sec x in/ft x sec/min
in/min = ft/sec x 12 in/ft x 60 sec/min
ft/sec = in/min / (12 in/ft x 60 sec/min)

So, if we divide both sides of the equation by 12x60 we will end up
with feet per second:

in/min = gal/min x 231 in^3/gal
----------------------
A in^2

in/min           gal/min       231 in^3/gal
--------------------- = ------- x ---------------------
12 in/ft x 60 sec/min    A in^2   12 in/ft x 60 sec/min

gal/min       231 in^3/gal
ft/sec = ------- x ---------------------
A in^2   12 in/ft x 60 sec/min

But 231/(12x60) = 0.32083 so the formula can be written as:

gal/min
ft/sec = ------- x 0.32083
A in^2

Which is the same as the formula you wrote.

- Doctor Jeremiah, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
Elementary Measurement
Middle School Measurement

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