Darcy-Weisbach equation

The Darcy-Weisbach equation is an important and widely used equation in hydraulics. It enables calculation of the head loss due to friction within a given run of pipe.

The equation was initially a variant on the Prony equation; this variant was developed by Henry Darcy of France, and further refined into the form used today by Julies Weisbach of Saxony in 1845:

where h_f is the head loss due to friction, calculated from: a friction factor f, the ratio of the length to diameter of the pipe L/D, the velocity of the flow V, and the standard constant for acceleration due to gravity g.

The friction factor f varies according to the parameters of the pipe and the velocity of the flow, and is known to high accuracy within certain flow regimes. However, data on its variation with velocity was initially lacking, so this equation was outperformed at first by the empirical Prony equation in many cases. In later years it was eschewed in many special-case situations in favor of a variety of empirical equations, notably the Hazen-Williams equation, most of which were significantly easier to use in calculations. However, since the advent of the calculator, ease of calculation is no longer a major issue, and so the Darcy-Weisbach equation's generality has made it the preferred one.