DarcyWeisbachmodellen

DarcyWeisbachmodellen, commonly referred to as the Darcy–Weisbach equation, is a fundamental relation in fluid mechanics used to predict frictional pressure losses in pipe flow. It provides a link between the pressure drop along a pipe and the flow conditions, pipe length and diameter, and fluid properties.

The central form of the equation is ΔP = f (L/D) (ρ v^2 / 2), where ΔP is the pressure loss, L is the pipe length, D is the pipe diameter, ρ is the fluid density, v is the average flow velocity, and f is the dimensionless friction factor. An equivalent head-loss form is Δh_f = f (L/D) (v^2 / 2g), with g as the acceleration due to gravity. The friction factor f depends on the flow regime and pipe roughness; for laminar flow, f = 64/Re, where Re is the Reynolds number. In turbulent flow, f is determined by correlations and roughness, often summarized by the Moody chart or explicit expressions such as Blasius, Swamee–Jain, or others.

Assumptions of the model include steady, fully developed, incompressible flow in a constant-diameter pipe, with energy losses other than friction treated separately as minor losses or K-factors. The equation is widely used in design and analysis of piping systems, water distribution, HVAC, and chemical-process networks to estimate pressure distributions and required pump or compressor capacities.

Limitations include its reduced accuracy for highly transient flows, significant compressibility effects, non-Newtonian fluids, or conditions where major energy losses are not well represented by the friction factor alone. History credits Darcy and Weisbach for developing and popularizing the relation in the 19th century.