When calculating relative pipe roughness, Є=k/d, what is k?

• A. Pipe diameter
• B. Length of protrusions on the pipe wall
• C. Roughness height
• D. Internal circumference

Answer: (B)

Relative pipe roughness is a dimensionless measure of how rough the interior surface is, obtained by comparing the height of the roughness features to the pipe diameter. In the expression Є = k/d, the symbol k represents the roughness height—the vertical size of the surface irregularities or protrusions on the pipe’s inside wall. This height is what causes additional friction for the flowing fluid, and dividing it by the internal diameter yields a unitless quantity that characterizes roughness for flow calculations. The diameter is what you normalize by; the length or height of the protrusions is the roughness height, not the diameter or the circumference of the pipe.