Water Velocity Calculator

Enter the flow rate and diameter of the pipe to calculate the velocity of the water traveling through.

Results:

  ft/s
  mi/h
  m/s
  km/h


How to Calculate Water Velocity

Water velocity is a measure of the speed of water flowing through a closed pipe system.[1] Water velocity can be found using a simple formula:

v = QA

Thus, the velocity v is equal to the flow rate Q divided by the cross-sectional area A.

diagram showing the velocity is equal to flow rate divided by cross-sectional area

When using this formula all units should be in the same form. If the flow rate is measured in cubic meters per second, then the area should be in square meters, and if the flow rate is measured in cubic feet per second then the area should be in square feet.

The cross-sectional area of a pipe can be found using the formula:

A = πr²

The area A is equal to π times the radius r squared.

For example, let’s find the water velocity given a flow rate of 35 cubic feet per second and a 1″ diameter pipe.

Start by finding the cross-sectional area of the pipe.

Diameter in feet = 1″ ÷ 12 = 0.0833333333′
Radius = 0.0833333333′ ÷ 2 = 0.0416666667′
Area = π × 0.0416666667²
A = π × 0.001736111111111
A = 0.005454152777778 sq ft

Next, calculate the velocity.

v = 350.005454152777778
v = 6417.1 ft³/s

Alternative Formula

The formula above works great when flow rate is measured in the cubic form of a standard length unit. But when flow rate is measured in gallons per minute or liters per minute things get a little tricker.

In this case, start by converting the flow rate to cubic feet per second or cubic meters per second.

Alternatively, if the flow rate is measured in gallons per minute, the following formula can be used to calculate water velocity.

v = 0.408 × Q

Thus, the velocity v in feet per second is equal to 0.408 times the flow rate Q in gallons per minute divided by the pipe diameter D in inches squared.[2]

For example, let’s find the water velocity given a flow rate of 15 gallons per minute and a 0.75″ diameter pipe.

Start by finding the cross-sectional area of the pipe.

v = 0.408 × 150.75²
v = 0.408 × 150.5625
v = 6.120.5625
v = 10.88

So, the velocity of water inside a 0.75″ pipe with a flow rate of 15 gpm is equal to 10.88 ft/s.

References

  1. Hunter, The Handbook of Technical Irrigation Information, https://www.hunterindustries.com/sites/default/files/tech_handbook_of_technical_irrigation_information.pdf
  2. Ace Pumps, Useful Calculations and Conversions, https://www.acepumps.com/en/index.php?/site/applications/C34/Calc