Units are used to help quantify and define physical measurements. Some units are very easy to convert while others are a bit more complicated. In the case of GPM (gallons per minute), you sometimes need to convert this into flow velocity as this quantity may be needed for certain calculations, design considerations, or just to know how fast the water is flowing.
GPM and velocity
If you don’t know what GPM is, it’s an abbreviation for gallons per minute which is the volumetric flow rate or the rate of volume change (in gallons) over time (in minutes). The units of this volumetric quantity, liquid gallons, are used with the United States Customary System of Units. GPM is commonly used to represent the flow of water through pipes, the capacity of pumps, and also has uses in the design of water and wastewater treatment plants.
Sometimes you may want a velocity over a volumetric flow rate. The velocity is just the distances covered over a given interval of time. In this case, feet per second are likely the best units for velocity of water through a structure. To get from GPM to velocity requires just a simple formula but perhaps its best to explain how this formula came about and what is involved in the conversion from volumetric flow rate to velocity.
Cross-sectional area
Before you start converting units you need to know the cross-sectional area. The cross-sectional area is the measurement of the area that the water is traveling perpendicular to or through. For example, a pipes cross-sectional area is the circular area of the pipe that the water flows through. Basically, if you were to cut the pipe into slices you would produce many cross-sections of the object and measuring the area of that slice would give you the cross-sectional area. Knowing the shape of the cross-section, you can find its area using the proper dimensions and standard area equations for different shapes. It is best to get the area in units of square feet. If you get an area in square inches, then just divide by 144 which is the unit conversion factor from square inches to square feet.
Creating the equation
With the cross-sectional area known, you can convert the gallons per minute to cubic feet per second. This is relatively easy as some conversion charts have the conversion from GPM to cubic feet per second which is just multiplying by 0.02228.
With the new volumetric flow rate, you can divide it by the cross-sectional area of the object the water is traveling through to get the velocity that the water is moving at. The resulting equation is shown below:
Velocity = ( GPM * 0.0228 )/ (Cross-sectional area)
Example Problem:
The flow rate of water through a 6 inch pipe is 800 GPM, what is the flow velocity of the water?
So you have your numbers from the equation and you know what the area of a circle is
A = PI x R^2 (R is the radius and equals half the diameter)
A = 3.14 x (6/2)^2 = 28.26 square inches
Convert to feet
A = 28.26 / 144 = 0.196 square feet as the cross sectional area of the pipe
Now go to your equation for Velocity
Velocity = 800 * 0.0228 / (0.196)
Velocity = 9.09 feet per second
