Darcy-Weisbach equation

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Where is it supposed that the formula should not be from Darcy but from de Voisin? - Didelidoo ( discussion ) 09:38, Jun. 1, 2015 (CEST)

The Darcy-Weisbach equation is an important empirical formula in the hydraulics of pipe flows . It can be used to calculate the pressure and energy losses due to pipe friction over the given length of a pipe .

The Darcy-Weisbach equation is said to have been developed by Henry Darcy together with Julius Weisbach in Freiberg as a variant of the Prony equation by Gaspard de Prony . The formula was apparently only mistakenly ascribed to Darcy; instead it comes from Jean François d'Aubuisson de Voisin  (1834) and Weisbach (1845).

It is:

${\displaystyle h_{f}=\lambda \cdot {\frac {L}{D}}\cdot {\frac {v^{2}}{2g}},}$

in which:

• h _f loss height (pressure loss)
• ${\displaystyle \lambda }$ Pipe friction coefficient , depending on the material properties of the pipe and the flow velocity
• L / D ratio of length to diameter of the pipe
• v mean flow velocity
• g acceleration due to gravity

To calculate the influencing factors on the volume flow , which play a role especially in the design of pipelines (given min.volume flow, sought inlet / outlet pressure), the equation can be transformed with the help of Bernoulli's equation :

${\displaystyle \Leftrightarrow p_{1}-p_{2}=\lambda \cdot {\frac {L}{D}}\cdot {\frac {\rho }{2}}\cdot \left({\frac {\dot {V}}{A}}\right)^{2},}$

in which:

• p ₁ inlet pressure
• p ₂ outlet pressure
• ${\displaystyle \rho }$ Density of the fluid
• ${\displaystyle {\dot {V}}}$ Volume flow
• ${\displaystyle A={\frac {\pi \cdot D^{2}}{4}}}$ Cross-sectional area of the pipe.

Initially, there was no data on the dependence of the pipe friction coefficient on the flow velocity, which is why the empirical Prony equation was used instead of the Darcy-Weisbach equation. Later there were a variety of other empirical equations, especially the Hazen-Williams equation , which were usually much easier to use in calculations. It was only with the advent of calculators and computers that the simplicity of calculation no longer played such an important role. Therefore, the generally valid Darcy-Weisbach equation is preferred today.

See also

• Darcy Law

Individual evidence

1. ^ GO Brown: The History of the Darcy-Weisbach Equation for Pipe Flow Resistance . In: Environmental and Water Resources History . American Society of Civil Engineers, 2003, pp. 34-43 , doi : 10.1061 / 40650 (2003) 4 (English).
2. ^ Herbert Sigloch: Technical fluid mechanics . 8th, updated Edition Springer, Berlin 2011, ISBN 978-3-642-22844-5 , pp. 139 .