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/