Prony equation

{{Short description|Hydraulics equation for frictional head loss}}

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:

: $h_f = \frac{L}{D} (aV + bV^2)$

where h_f 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.

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

References

{{citation|contribution=Henry Darcy (1803–1858): Immortalised by his scientific legacy|first=Craig|last=Simmons|pages=3–24|title=Aquifer Systems Management: Darcy's Legacy in a World of Impending Water Shortage: Selected Papers from the International Association of Hydrogeologists (IAH) Dijon Symposium, Dijon, France, 30 May–1 June 2006|editor-first=Laurence|editor-last=Chery|publisher=Taylor & Francis / Balkema|location=Leiden, The Netherlands|year=2007|isbn=9780415443555}}. The Prony equation and its replacement by the Darcy–Weisbach equation are on pp. 11–12.

Category:Eponymous equations of physics

Category:Equations of fluid dynamics