Darcy-Weisbach Equation
The Darcy-Weisbach equation calculates the pressure drop caused by friction in a pipe: ΔP = f · (L/D) · (ρv²/2). It applies to any Newtonian fluid in any flow regime, which is why it is the standard method for pipe network analysis — unlike empirical alternatives such as Hazen-Williams, which are limited to water at typical temperatures.
Definition
The Darcy-Weisbach equation relates pressure drop to the friction factor (f), pipe length (L), internal diameter (D), fluid density (ρ), and mean velocity (v). The friction factor depends on the Reynolds number and the relative roughness of the pipe wall (ε/D). For laminar flow, the friction factor comes from the Hagen–Poiseuille relationship, which gives f = 64/Re. For turbulent flow, f is obtained from the Colebrook-White equation or the Moody chart.
Engineering context
The Darcy-Weisbach equation is preferred because its friction factor responds to both the Reynolds number — which carries fluid properties, temperature, and viscosity — and the relative roughness ε/D, which carries pipe condition. This is exactly what empirical alternatives miss: Hazen-Williams has no viscosity or temperature term, so it is valid only for water at ambient conditions, while Shell-MIT carries a viscosity term but no roughness term, leaving it blind to pipe condition and aging. Because Darcy-Weisbach captures both effects, it remains valid for viscous liquids, hot water, chemicals, and compressible gas (applied incrementally). Every pressure drop result in a FluidFlow model is built on this method, with the friction factor solved from the Hagen–Poiseuille relationship in laminar flow and iteratively from Colebrook-White in turbulent flow, so pipe sizing, pump selection, and energy studies share one consistent basis. Pressure drop scales with velocity squared, which makes velocity the core economic trade-off in pipe sizing: halving the velocity cuts friction pressure drop by roughly 75% from the velocity effect alone, with a further reduction from the larger pipe diameter on top.
Related definitions
Reynolds number · Friction factor · Absolute roughness · System curve · Pump curve
See it in FluidFlow
See the Darcy-Weisbach equation applied across a full pipe network. FluidFlow solves the friction factor as part of the network solution — from the Hagen–Poiseuille relationship in laminar flow and Colebrook-White in turbulent flow.
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Related content
Reviewed by the FluidFlow Engineering Team · Last reviewed: June 2026 · Applies to FluidFlow v3.54 (steady-state analysis)
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