Friction Loss Calculator

Created by Luis Hoyos
Last updated: Aug 31, 2022

Calculating the friction loss in a pipe is essential to design a pipe system properly, as this friction affects the required electrical power and the pump's efficiency.

With this calculator, you can calculate the friction loss in a pipe that carries water. If you're dealing with another fluid, use our Darcy Weisbach equation calculator to calculate the pipe pressure loss.

Apart from calculating the head loss (in meters of water), if you click on the advanced mode of this tool, you'll obtain the pressure loss (in pressure units).

In the rest of this article, we present the equations used to calculate friction loss.

What is friction loss?

Like solids, fluids present resistance to movement (friction). This friction arises from two sources:

  • The friction between the adjacent fluid layers. It is occasioned by the fluid viscosity.
  • The friction between the pipe wall and the fluid in contact with it. It is occasioned by the surface roughness of the pipe wall.

The higher this friction, the higher the pumping power requirements will be.

The formula for friction loss calculation in a pipe

This calculator uses the Hazen-Williams equation to calculate the head loss in a pipe that carries water:

HL=10.67 L Q1.852C1.852D4.87H_{\text{L}} = \frac{10.67 \ L \ Q^{1.852}}{C^{1.852}D^{4.87}}

, where:

  • HLH_L — Head loss, calculated in meters (m) of water;
  • LL — Pipe length, in m;
  • QQ — Volumetric Flow rate, in cubic meters per second (m³/s);
  • CC — Pipe roughness coefficient, a dimensionless number that will depend on the pipe material (click on the advanced mode to know it); and
  • DD — Pipe inner diameter, in m;

This empirical equation allows calculating the head loss in a pipe, using its diameter, length, material, and flow rate. It has the advantage of being simpler than the more general Darcy-Weisbach equation, as it doesn't require calculating the Darcy friction factor. At the same time, it has the disadvantage of being limited to water and no other fluids.

To convert the head loss in meters to pressure loss in pascals, multiply the head loss (in m) by the specific weight of the fluid:

PL=HLγ=HLρgP_{\text{L}} = H_{\text{L}} \gamma = H_{\text{L}} \rho g

, where:

  • PLP_{\text{L}} — Pressure loss, in Pascals (Pa);
  • γ\gamma — Specific weight, in newtons per cubic meter (N/m³);
  • ρ\rho — Fluid density, in kilograms per cubic meter (kg/m³); and
  • gg — Gravity acceleration, which equals approximately 9.807 meters per square second (m/s²)

For water, at 20°C, the specific weight equals 9780 N/m³ and the density 998.23 kg/m³.

Hazen-Williams equation in U.S. customary units (Imperial)

If you need to calculate the pressure loss in a pipe and are using the U.S. customary units, the friction loss formula is similar:

PL=4.52 L Q1.852C1.852D4.87P_{\text{L}} = \frac{4.52 \ L \ Q^{1.852}}{C^{1.852}D^{4.87}}

, where:

  • PLP_{\text{L}} — Pressure loss, calculated in pounds per square inch gauge (psig);
  • LL — Pipe length, in feet (ft);
  • QQ — Volumetric flow rate, in gallons per minute (GPM);
  • CC — Pipe roughness coefficient, a dimensionless number that will depend on the material; and
  • DD — Pipe inner diameter, in inches (in);

To convert the pressure loss in psig to head loss in feet, it is a bit trickier, as units are not homogenous:

  1. Convert the pressure loss from psig to lb/ft². To do it, multiply the pressure in psig by 144.
  2. Obtain the specific gravity in lb/ft³. For water at 70 °F, it equals 62.30 lbf/ft³.
  3. Divide the pressure loss in lb/ft² by the specific gravity in lb/ft³.

For example, if the friction loss in the pipe were 2 psi, we would convert it to feet of water the following way:

HL=2×14462.30 ft=4.6 ft.H_{\text{L}} = \frac{2 \times 144}{62.30} \text{ ft} = 4.6 \text{ ft}.
Luis Hoyos
Hazen-Williams equation
Pipe Diameter
Pipe Length
Volumetric Flow rate
Friction Head Loss
of Water
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