# Relative Roughness

Written by Jerry Ratzlaff on . Posted in Dimensionless Numbers

Relative roughness ( $$k$$ ) (dimensionless number) of a pipe is a ratio of the surface roughness to the diameter of the pipe.

Since the relative roughness is a dimensionless number, both the absolute roughness and diameter must carry the same units.  The relative roughness is used with the Moody Diagram when solving for the friction factor of a system.

### Relative Roughness FORMULA

$$\large{ k = \frac {\epsilon} {D} }$$

Where:

$$\large{ k }$$ = relative roughness

$$\large{ \epsilon }$$  (Greek symbol epsilon) = absolute roughness

$$\large{ D }$$ = diameter of the pipe