Friction Factor
Friction factor, abbreviated as f, also called Moody friction factor or Darcy-Weibach friction factor, a dimensionless number, is 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.
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:
| \(\large{ f = \frac{64}{Re} }\) |
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''.
Free Surface Flow
| \(\large{ \frac{1}{\sqrt{f}} = -2\; \log \;(\frac{\epsilon}{12\;r_h} + \frac{2.51}{Re\sqrt{f}}) }\) |
Full Flow (Closed Conduit)
| \(\large{ \frac{1}{\sqrt{f}} = -2\; \log \;(\frac{\epsilon}{14.8\;r_h} + \frac{2.51}{Re\sqrt{f}}) }\) |
Where:
\(\large{ \epsilon }\) (Greek symbol epsilon) = absolute roughness
\(\large{ f }\) = friction factor
\(\large{ r_h }\) = hydraulic radius
\(\large{ Re }\) = Reynolds number
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 \(\large{ 10^{-6} < \frac{\epsilon}{d} < 10^{-2} }\) and \(\large{ 5,000 < Re < 10^8 }\).
| \(\large{ f = \frac{0.25}{[log \; (\frac{\epsilon}{3.7\;d} + \frac{5.74}{Re^{0.9}})]^2} }\) |
Where:
\(\large{ \epsilon }\) (Greek symbol epsilon) = absolute roughness
\(\large{ d }\) = inside diameter of pipe
\(\large{ Re }\) = Reynolds number
Friction Factor calculator