The functional dependence of friction factor on the Reynolds number and relative roughness is rather complex. It is found from exhaustive set of experiments and is usually presented in the form of curve-fitting formula/data. The most common graphical representation of friction factor dependence on surface roughness and Reynolds number is shown in "Moody Chart" (Fig. 4). This chart is valid universally for all steady, fully developed, incompressible flows.

The following inferences may be made from Moody chart (Fig. 4).

• For laminar flows ( ), and is independent of surface roughness
• At very high Reynolds number , the flow becomes completely turbulent (wholly turbulent flow) and is independent of Reynolds number. In this case, the laminar sub-layer is so thin that the surface roughness completely dominates the character of flow near the wall. The pressure drop responsible for turbulent shear stress is inertia dominated rather than viscous dominated as found in case of laminar viscous sub-layer. Hence, the friction factor is given by,
• The friction factor at moderate Reynolds number is indeed dependent on both Reynolds number and relative roughness.
• Even for smooth pipes , the friction factor is not zero i.e. there is always head loss, no matter how smooth the pipe surface is. There is always some microscopic surface roughness that produces no-slip behavior on the molecular level. Such pipes are called "hydraulically smooth".