The pressure drop in a turbulent pipe flow may be expressed in the dimensionless form of the Darcy friction factor f defined in equation 6.47 . The friction factor f is only weakly dependent upon the Reynolds number, varying approximately as . This dependence is illustrated by the lowest curve of figure 7.3 for , the minimum value for which the flow is turbulent. Because random motions close to the wall are strongly damped, turbulent pipe flow becomes laminar there, within what is called the laminar sublayer . This layer is responsible for the slight dependence of f on the fluid viscosity as embodied in the Reynolds number dependence of 7.16 .
Few pipes have very smooth walls.
Many have a surface roughness derived from their manufacture that distorts the laminar sublayer and generates additional turbulence in the flow near the wall that would not be present if the wall were completely smooth. Note that for a smooth wall , and equation 7.17 reduces to 7.16 . For very rough pipes such that , the friction factor depends only upon and not upon the Reynolds number. This occurs when the laminar sublayer is completely disrupted by the surface roughness, and the fluid viscosity plays no role in the pressure drop. The equivalent wall roughness for commercial pipes has been determined from flow tests.