Prony equation
The Prony equation (named after Gaspard de Prony) is a historically important equation in hydraulics, used to calculate the head loss due to friction within a given run of pipe. It is an empirical equation developed by Frenchman Gaspard de Prony in the 19th century: h f = L D ( a V + b V 2 ) {\displaystyle h_{f}={\frac {L}{D}}(aV+bV^{2})} where hf is the head loss due to friction, calculated from: the ratio of the length to diameter of the pipe L/D, the velocity of the flow V, and two empirical factors a and b to account for friction.