# Velocity Equation

Speed Kills!
The Velocity Equation

All this week we are reviewing the MOST important water math concepts, in preparation for this Saturday’s Water Distribution Operator certification exam here in California.  Today we look at number four in our MOST Five: the Velocity Equation.

This is probably the least used equation of our MOST Five, especially for the D1 and D2 exams.  We tell folks to expect zero or one problem using this equation at those levels.  And if you do get a problem at these grades, you may be asked to find a Flow Rate, given a Velocity and the cross-sectional Area of a pipeline.  Or you may be asked to find a Velocity, given the pipe Area and the Flow Rate.  For either of these, use the Velocity Equation, Flow Rate = Velocity x Area, or Q = Av.

We are rarely given the Area directly, and instead get the Diameter of the pipeline.  But that makes for a pretty easy first step: we just calculate the cross-sectional Area of the pipe using Area = 0.785 d² (or πr²).

The best Flow Rate units to use with this formula are cubic feet per second (cfs).  These units are consistent with the normal Velocity units of feet per second and Area units of square feet.  If your Flow Rate is in gpm or MGD, make sure you convert to cfs first.

For the higher grades of Distribution exams, expect more problems using the Velocity Equation, and also expect one that requires you to find the Area instead.  However, that step may not be obvious because that won’t be the final answer requested.

The typical problem of this type will give you a Flow Rate and Velocity, and then ask for the Diameter of the pipe.  To find the Diameter, you have to find the Area first, using Q = Av.  Then you can find the diameter using Area = 0.785 d².  To get the Diameter, divide the Area by 0.785, and then hit the (very shiny, due to such rare usage!) square root key on your calculator.

But you’re still not quite through.  This calculation will give you the Diameter in feet, and you’ll almost certainly need to convert that into inches instead.

If only all the steps in this calculation were that easy!

Keep studying!  Saturday is coming fast!