The Prony equation (named after
Gaspard de Prony) is a historically important equation in
hydraulics
Hydraulics () is a technology and applied science using engineering, chemistry, and other sciences involving the mechanical properties and use of liquids. At a very basic level, hydraulics is the liquid counterpart of pneumatics, which concer ...
, used to calculate the
head loss due to
friction
Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other. Types of friction include dry, fluid, lubricated, skin, and internal -- an incomplete list. The study of t ...
within a given run of pipe. It is an
empirical equation developed by
Frenchman Gaspard de Prony in the 19th century:
:
where ''h
f'' is the head loss due to friction, calculated from: the ratio of the length to
diameter
In geometry, a diameter of a circle is any straight line segment that passes through the centre of the circle and whose endpoints lie on the circle. It can also be defined as the longest Chord (geometry), chord of the circle. Both definitions a ...
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
In fluid dynamics, the Darcy–Weisbach equation is an Empirical research, empirical equation that relates the head loss, or pressure loss, due to friction along a given length of pipe to the average velocity of the fluid flow for an incompressibl ...
, which used it as a starting point.
References
*. The Prony equation and its replacement by the Darcy–Weisbach equation are on pp. 11–12.
Eponymous equations of physics
Equations of fluid dynamics
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