Darcy-Weisbach equation



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The Darcy-Weisbach equation is an important and widely used equation in hydraulics. It enables calculation of the head loss due to friction within a given length of pipe.

The equation was initially a variant on the Prony equation; this variant was developed by Henry Darcy of France, and further refined into the form used today by Julius Weisbach of Saxony in 1845:

h_f = f \cdot \frac{L}{D} \cdot \frac{V^2}{2g}

where the head loss due to friction hf is a function of:

  • a Darcy friction factor, f
  • the ratio of the length to diameter of the pipe, L/D
  • the velocity of the flow, V
  • the standard constant for acceleration due to gravity g.

The equation can also be written in terms of pressure loss:

\Delta p = \lambda \cdot \frac{L}{D} \cdot \frac{\rho V^2}{2}

where the pressure loss due to friction Δp is a function of:

  • the coefficient of turbulent flow, λ
  • the ratio of the length to diameter of the pipe, L/D
  • the density of the fluid, ρ
  • the velocity of the flow, V

The pressure loss equation can be derived from the head loss equation by multiplying each side by ρ and g. This will demonstrate that λ and f are equivalent.

The friction factor f varies according to the parameters of the pipe and the velocity of the flow, and is known to high accuracy within certain flow regimes. For laminar flows, λ is simply equal to 64/Re, the Hazen-Williams equation, most of which were significantly easier to use in calculations. However, since the advent of the calculator, ease of calculation is no longer a major issue, and so the Darcy-Weisbach equation's generality has made it the preferred one.

Methods for finding the friction factor f are to use a diagram, such as the Moody chart, the Swamee-Jain equation allows f to be found directly for full flow in a circular pipe.

 
This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Darcy-Weisbach_equation". A list of authors is available in Wikipedia.