## Reynolds number

Reynolds number [for Osborne Reynolds], dimensionless quantity associated with the smoothness of flow of a fluid. It is an important quantity used in aerodynamics and hydraulics. At low velocities fluid flow is smooth, or laminar, and the fluid can be pictured as a series of parallel layers, or lamina, moving at different velocities. The fluid friction between these layers gives rise to viscosity. As the fluid flows more rapidly, it reaches a velocity, known as the critical velocity, at which the motion changes from laminar to turbulent (see turbulence), with the formation of eddy currents and vortices that disturb the flow. The Reynolds number for the flow of a fluid of density ρ and viscosity η through a pipe of inside diameter d is given by Rdv/η, where v is the velocity. The Reynolds number for laminar flow in cylindrical pipes is about 1,000.

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## Reynolds number

Reynolds number A dimensionless number expressing the balance of viscous and interstitial forces on a small element of moving fluid. The transition from laminar to turbulent flow depends on the Reynolds number (R) which is equal to ρvd/η, where ρ is the fluid density, v the fluid velocity, d the diameter of the pore space through which flow occurs, and η the viscosity. For laminar flow, the Reynolds number is less than 500, while turbulent flow occurs when R is greater than 1000. Darcy's Law for groundwater flow is valid for values of R less than about 1–10.