Discussion
For incompressible, laminar, fully-developed flow through a circular pipe, Darcy friction factor and Fanning friction factor are represented as \(f\) and \(C_f\), respectively. Which one of the following options is correct?
Answer: D
The relation is \(f = 4C_f\).
The Darcy factor appears in the head-loss equation \(h_f = f\frac{L}{D}\frac{V^{2}}{2g}\), while the Fanning factor is the wall shear stress scaled by dynamic pressure, \(C_f = \tau_w/(\tfrac{1}{2}\rho V^{2})\). A force balance on the pipe gives \(\tau_w = \frac{D}{4}\frac{\Delta p}{L}\), from which \(f = 4C_f\).
For laminar flow this reads \(f = 64/Re\) and \(C_f = 16/Re\). The other ratios (0.25, 0.5, 2) do not match these definitions.
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