The
Prony equation is a historically important equation in
hydraulicsHydraulics 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
frictionFriction is the force resisting the relative lateral motion of solid surfaces, fluid layers, or material elements in contact. It is usually subdivided into several varieties:...
within a given run of pipe. It is an empirical equation developed by
FrenchmanFrance , officially the French Republic , is a country located in Western Europe, with several overseas islands and territories located on other continents. Metropolitan France extends from the Mediterranean Sea to the English Channel and the North Sea, and from the Rhine to the Atlantic Ocean...
Gaspard de PronyGaspard Clair François Marie Riche de Prony was a French mathematician and engineer, who worked on hydraulics. He was born at Chamelet, Beaujolais, France.He was Engineer-in-Chief of the École Nationale des Ponts et Chaussées....
in the 19th century:
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The
Prony equation is a historically important equation in
hydraulicsHydraulics 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
frictionFriction is the force resisting the relative lateral motion of solid surfaces, fluid layers, or material elements in contact. It is usually subdivided into several varieties:...
within a given run of pipe. It is an empirical equation developed by
FrenchmanFrance , officially the French Republic , is a country located in Western Europe, with several overseas islands and territories located on other continents. Metropolitan France extends from the Mediterranean Sea to the English Channel and the North Sea, and from the Rhine to the Atlantic Ocean...
Gaspard de PronyGaspard Clair François Marie Riche de Prony was a French mathematician and engineer, who worked on hydraulics. He was born at Chamelet, Beaujolais, France.He was Engineer-in-Chief of the École Nationale des Ponts et Chaussées....
in the 19th century:
where
hf is the head loss due to friction, calculated from: the ratio of the length to
diameterIn 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.