DarcyWeisbachformule

The Darcy–Weisbach equation, also called the Darcy–Weisbach formula, is a fundamental relation in fluid mechanics that quantifies frictional pressure loss in a pipe due to viscous shear and inertial effects during steady, incompressible flow. It applies to straight sections of pipe of constant diameter and allows calculation of energy losses that affect pumping and fluid transport.

For a pipe of length L and diameter D carrying a fluid with density ρ and average velocity V, the pressure drop Δp is given by Δp = f_D (L/D) (ρ V^2 / 2). The corresponding head loss is h_f = Δp/(ρ g) = f_D (L/D) (V^2/(2g)). If the flow rate Q is used, the velocity V = Q/(π D^2/4). The friction factor f_D, known as the Darcy friction factor, depends on the flow regime and surface roughness.

The friction factor f_D depends on the Reynolds number Re = ρ V D / μ and the relative roughness ε/D of the pipe. It is determined from empirical correlations or charts such as the Colebrook–White equation or the Moody diagram. In laminar flow (Re < ~2100), f_D = 64/Re. In turbulent flow, f_D decreases with increasing Re for smooth pipes, but becomes largely a function of relative roughness for rough pipes.

The equation is widely used in civil, mechanical, and chemical engineering to design and analyze piping systems, water distribution networks, HVAC systems, and process pipings. It provides a link between measurable flow conditions and energy losses, essential for pump selection and system performance.

The formula is named after Henry Darcy and Julius Weisbach, reflecting its historical development from 19th-century experiments and later refinements.