DarcyWeisbachModell

The Darcy–Weisbach model, commonly referred to as the Darcy–Weisbach equation, is a fundamental tool in fluid mechanics for predicting frictional pressure losses in pipe flow. It relates the pressure drop Δp along a pipe to the pipe’s length L, diameter D, the fluid’s density ρ, and the average velocity v, via the equation Δp = f (L/D) (ρ v^2 / 2). The dimensionless factor f, the Darcy friction factor, captures the effect of flow regime and pipe roughness and is the key unknown in the model.

In practice, f depends on the Reynolds number Re = ρ v D / μ (or v D / ν) and the relative roughness ε/D of the pipe. For laminar flow (Re < 2000), f = 64/Re. For turbulent flow, f varies with Re and ε/D and is commonly obtained from the Moody diagram or solved from the Colebrook–White equation: 1/√f = −2 log10( (ε/(3.7D)) + (2.51/(Re√f)) ). Several explicit approximations exist (for example Swamee–Jain or Haaland) to avoid implicit solving.

The Darcy–Weisbach model is widely used in hydraulic engineering, including water distribution networks, oil and gas pipelines, and HVAC piping, due to its applicability to Newtonian, incompressible fluids and its physical basis in energy losses. For compressible gases or transient conditions, the model may be augmented or used with correction factors. The model bears a historical association with Henry Darcy and Julius Weisbach.