How to calculate flow in a pipe from pressure & pipe diameter

Updated April 17, 2017

The flow of liquids through pipes or conduits can occur in one of two basic manners, laminar or turbulent. The simplest type of system to deal with from a calculations standpoint is laminar flow. The relationships of pressure, pipe diameter and flow rates are interconnected through the following equation: FR = (Pi * (R^4) * (P -- P0))/(8 * N * L). The variables in this equation represent different physical parameters of the specific system under investigation. The FR is the flow rate given in gallons per second. R is the radius of the pipe, P0 is the pressure at one end of the pipe and P is the pressure at the other end of the pipe, L is the length of the pipe and N is the viscosity of the liquid.

Define each of the variables for your system. Record the units of the measurements and convert all measurements to standard SI units.

Determine the initial pressure of the liquid source, often measure in pounds per square inch (psi). The pressure will drop the further away from the source you move. Any pipe that ends as an open outlet will have the pressure of 0 psi or 1 atmosphere.

Find the value for the viscosity of the liquid in the pipe. This value is highly dependent on temperature. The value for water is 0.01 dynes sec/cm^2.

Plug in all the values for your system into the formula given and calculate the flow rate in your pipe.


Be sure to use measurements that have the correct units. The units for the variables are cubic centimetres per second for flow rate, centimetres for the length and radius of the pipe, atmospheres for the units of pressure and dyne seconds per square centimetre for viscosity.

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About the Author

Sean Lancaster has been a freelance writer since 2007. He has written for Writers Research Group, Alexis Writing and the Lebanon Chamber of Commerce. Lancaster holds a Doctor of Philosophy in chemistry from the University of Washington.