# Relative Roughness

Written by Jerry Ratzlaff on . Posted in Dimensionless Numbers

Relative roughness, abbreviated as k, a 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

$$\large{ k = \frac {\epsilon} {d} }$$
Symbol English Metric
$$\large{ k }$$ = relative roughness   $$\large{ dimensionless }$$
$$\large{ \epsilon }$$  (Greek symbol epsilon) = absolute roughness $$\large{ in }$$ $$\large{ mm }$$
$$\large{ d }$$ = pipe inside diameter $$\large{ in }$$ $$\large{ mm }$$