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The proportionality coefficient is the dimensionless "Darcy friction factor" or "flow coefficient". This dimensionless coefficient will be a combination of geometric factors such as π, the Reynolds number and (outside the laminar regime) the relative roughness of the pipe (the ratio of the roughness height to the hydraulic diameter).
The Colebrook–White equation is a formula that relates the Darcy friction factor f to the Reynolds number Re and the pipe relative roughness ε / Dh for turbulent flow in smooth and rough pipes. It can be solved numerically or with explicit reformulations using the Lambert W function.
Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other. Learn about the different types of friction, such as dry, fluid, lubricated, skin and internal, and how they affect mechanical energy, wear, and performance.
Learn how to calculate the force gain of a flexible line wound around a cylinder using the capstan equation. Find examples, applications, derivation and generalizations of the formula.
The Darcy-Weisbach equation was difficult to use because the friction factor was difficult to estimate. [7] In 1906, Hazen and Williams provided an empirical formula that was easy to use. The general form of the equation relates the mean velocity of water in a pipe with the geometric properties of the pipe and slope of the energy line.
The Manning formula or Manning's equation is an empirical formula estimating the average velocity of a liquid in an open channel flow. It depends on the hydraulic radius, the stream slope, and the Gauckler–Manning coefficient, which varies with surface roughness and sinuosity.
Belt friction is the friction force between a belt and a surface, such as a pulley or a bollard. Learn how to calculate the belt tension, the friction coefficient and the limit values of the tangential forces using the belt friction equation and the generalization for a rope on an orthotropic surface.
The Moody chart or Moody diagram is a graph that relates the Darcy–Weisbach friction factor, Reynolds number and surface roughness for fully developed flow in a circular pipe. It can be used to predict pressure drop or flow rate down such a pipe and is based on experimental data and theoretical analysis.
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