Compressed-Air Pipe Pressure Drop
The shop-air question the compressed-air bench never answered: how much pressure a run loses. Built from the ideal gas law and Darcy-Weisbach on this catalog's own Colebrook solver, not an empirical air constant. The trap it exists to show: standard cubic feet are a MASS measure, so 100 scfm at 100 psig is only 12.8 ACTUAL cfm - sizing off scfm directly overstates velocity nearly 8x. 100 scfm through 1-in pipe over 100 ft drops 2.18 psi; flags the 10%-of-line rule of thumb.
Formula and source
rho = P_abs x 144 / (R_air x T_R) with R_air = 53.35 ft-lbf/lb-R; Q_actual = scfm x (14.7/P_abs) x (T_R/527.67); Re = rho V D / mu; f from Colebrook-White; dP = f (L/D) rho V^2 / (2 gc) / 144.
Darcy-Weisbach with the Colebrook-White friction factor and the ideal gas law, by name; NO empirical compressed-air constant or sizing table is used.
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