# Darcy Friction Factor - Brkić

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. The Brkić approximation is one way of estimating the Darcy friction factor for use in pressure drop calculations. The Brkić approximation is within 3.15% of the Colebrook-White equation.

## Darcy Friction Factor - Brkić formula

 $$\large{ \frac{1}{ \sqrt{f_d} } = -2\; log_{10} \; \left( \frac{ \frac{\epsilon}{d} }{ 3.71 } + \frac{ 2.18 \; n }{ Re } \right) }$$

### Where:

 Units English Metric $$\large{ f_d }$$ = Darcy friction factor $$\large{ dimensionless }$$ $$\large{ ln }$$ = natural logarithm $$\large{ dimensionless }$$ $$\large{ \epsilon }$$ (Greek symbol epsilon) = pipe's effective roughness height $$\large{ in }$$ $$\large{ mm }$$ $$\large{ d }$$ = pipe inside diameter $$\large{ in }$$ $$\large{ mm }$$ $$\large{ Re }$$ = Reynolds number $$\large{ dimensionless }$$ $$\large{ n }$$ = variable in Brkić (calculated below) $$\large{ dimensionless }$$

### Solve For:

 $$\large{ n = ln \; \frac{Re}{1.816\;ln \; \left( \frac{1.1 \; Re}{ ln \; \left( 1\;+\; 1.1 \; Re \right) } \right) } }$$

Tags: Friction Equations