Friction Factor

Written by Jerry Ratzlaff on . Posted in Classical Mechanics

Friction Factor

Also known as the Moody Friction Factor or Darcy Weibach friction factor it is a dimensionless number used in internal flow calculations with the Darcy-Weisbach equation. Depending on the Reynolds Number, the friction factor, abbreviated as f, may be calculated one of several ways.

  • Abbreviated as \(f\)

laminar flow

In laminar flow, the friction factor is independent of the surface roughness, \(\epsilon\). This is because the fluid flow profile contains a boundary layer where the flow at the surface through the height of the roughness is zero.

For Re<2100, the friction factor may be calculated by:


transitional flow

For \(2100<Re<3x10^3\) (transitional flow regime), the friction factor may be estimated from the Moody Diagram.

turbulent flow

Methods for finding the friction factor f are to use a diagram, such as the Moody Diagram, the Colebrook-White Equation, or the Swamee-Jain Equation.

Using the diagram or Colebrook-White equation requires iteration. Where the Swamee-Jain equation allows f to be found directly for full flow in a circular pipe.

colebrook-white equation

The '''Colebrook-White equation''' is used to iteratively solve for the Darcy Weisbach Friction Factor ''f''.

'''For Free Surface Flow:'''

\(\frac{1}{\sqrt{f}} = -2 \log (\frac{e}{12R} + \frac{2.51}{Re\sqrt{f}})\)

'''For Full Flow (Closed Conduit):'''

\(\frac{1}{\sqrt{f}} = -2 \log (\frac{e}{14.8R} + \frac{2.51}{Re\sqrt{f}})\)

Where ''f'' is a function of:

\(e\) = roughness height (m, ft)

\(R\) = hydraulic radius (m, ft)

\(Re\) = Reynolds Number (unitless)

Because the iterative search for the correct ''\(f\)'' value can be quite time-consuming, the Swamee-Jain equation can be used to solve directly for ''\(f\)''.

swamee-jain equation

The Swamee-Jain Equation is accurate to 1.0% of the Colebrook-White Equation for \(10^{-6} < \frac{\epsilon}{D} < 10^{-2}\) and \( 5,000 < Re < 10^8\).

\(f = \frac{0.25}{[log (\frac{\epsilon}{3.7D} + \frac{5.74}{Re^{0.9}})]^2}\)


\(ε\) = roughness height ( ft)

\(D\) = pipe diameter ( ft)

\(Re\) = Reynolds Number (unitless).

Friction Factor calculator


Tags: Equations for Friction