The Prony equation is a historically important equation in hydraulics

Hydraulics

Hydraulics is a topic in applied science and engineering dealing with the mechanical properties of liquids. Fluid mechanics provides the theoretical foundation for hydraulics, which focuses on the engineering uses of fluid properties. In fluid power, hydraulics is used for the generation, control,...

, used to calculate the head loss due to friction

Friction

Friction is the force resisting the relative motion of solid surfaces, fluid layers, and/or material elements sliding against each other. There are several types of friction:...

 within a given run of pipe. It is an empirical equation developed by Frenchman

France

The French Republic , The French Republic , The French Republic , (commonly known as France , is a unitary semi-presidential republic in Western Europe with several overseas territories and islands located on other continents and in the Indian, Pacific, and Atlantic oceans. Metropolitan France...

 Gaspard de Prony

Gaspard de Prony

Gaspard Clair François Marie Riche de Prony was a French mathematician and engineer, who worked on hydraulics. He was born at Chamelet, Beaujolais, France and died in Asnières-sur-Seine, France.-Education and early works:...

 in the 19th century:


where h_f is the head loss due to friction, calculated from: the ratio of the length to diameter

Diameter

In geometry, a diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints are on the circle. The diameters are the longest chords of the circle...

 of the pipe L/D, the velocity of the flow V, and two empirical factors a and b to account for friction.

This equation has been supplanted in modern hydraulics by the Darcy–Weisbach equation, which used it as a starting point.