Friction factor in pipe flow (fo) is defined as:
where τ0 is shear stress in the wall pipe and U∞ is fluid velocity outside boundary layer. Friction factor in pipe flow is associated with decrease in pressure as stated in the following equation for a pipe with length L and diameter D.
or
Friction factor in pipe flow is a function of Reynolds number (ReD). This function can be derived analytically for laminar flow, but depend on experimental data correlation for turbulent flow.
Friction factor for fully developed laminar flow in a smooth pipe is:
while the friction factor for fully developed turbulent flow in a smooth pipe is expressed as:
Besides using the equations above, the friction factor for turbulent flow can be found in Figure 1. In the Figure 1, surface roughness effects are classified according to the ratio e/D, where e is the equivalent roughness height. f values in the Figure 1 is four times the value of fo, (f = 4.fo). Friction factor for rough surfaces that have Reynolds number above the value listed in the Moody chart is no longer as a function of Re.
In fact, the surface of pipe is not perfectly smooth, and friction factor of turbulent flow is strongly influenced by the condition of pipe surface. Nevertheless, this does not occur in laminar flow. An explicit equation is quite useful for turbulent flow (104 > Re > 4.108) both in the smooth pipe and rough pipe had been given by Chen NH (1979), namely:
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| Figure 1: Friction factor in Pipe Flow - the Moody Diagram |
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