# Darcy Friction Factor - Free Surface Flow

Written by Jerry Ratzlaff on . Posted in Fluid Dynamics

Darcy friction factor formulas, a dimensionless number, are equations that allow you to calculate the friction losses in pipe flow and open channel flow. Free surface flow describes flow that experiences zero shear forces.  An example of this is open channel flow, such as a canal used for shipping or irrigation.  The Darcy friction factor is used in the Darcy-Weisbach equation to determine pressure drop.

## Darcy Friction Factor - Free Surface Flow formula

 $$\large{ \frac{1}{ \sqrt{f_d} } = -2\; log_{10} \; \left( \frac{ \epsilon }{ 12 \; r_h } + \frac{ 2.51 }{ Re \; \sqrt{f_d} } \right) }$$

### Where:

 Units English Metric $$\large{ f_d }$$ = Darcy friction factor $$\large{ dimensionless }$$ $$\large{ r_h }$$ = hydraulic radius $$\large{ ft }$$ $$\large{ m }$$ $$\large{ \epsilon }$$  (Greek symbol epsilon) = pipe's effective roughness height $$\large{ ft }$$ $$\large{ m }$$ $$\large{ Re }$$ = Reynolds number $$\large{ dimensionless }$$

Tags: Friction Equations