Equivalent Length of a Fitting

Set Darcy–Weisbach equal to the minor-loss equation, f(L/D)(v²/2g) = K(v²/2g), and the velocity heads cancel, leaving $L_{\mathrm{eq}} = KD/f$. The point is bookkeeping: rather than tracking two different loss equations, a designer converts every valve and fitting into a phantom length of pipe, adds it to the measured run, and computes one friction loss for the whole circuit. A 90° elbow (K = 0.9) on 4 in pipe with f = 0.02 is worth 0.9 × 0.333/0.02 = 15 ft of straight pipe.

Because f cancels out of nothing here, the equivalent length depends on the pipe's friction factor, which is why the old rule "an elbow equals 30 diameters" is only true near f = 0.03. On smooth plastic with f = 0.018 the same elbow is worth 50 diameters. Fire-protection and refrigeration codes finesse this by publishing fixed equivalent-length tables for a nominated schedule and material; those tables are fine inside their intended context and misleading outside it.