Reynolds number

The Reynolds number is a dimensionless parameter in fluid mechanics. It expresses the relative importance of inertial effects, associated with a fluid's motion, and viscous effects, associated with internal friction. A common form is Re = ρUL/μ, where ρ is fluid density, U a characteristic speed, L a characteristic length and μ the dynamic viscosity. Since kinematic viscosity is ν = μ/ρ, the equivalent expression is Re = UL/ν. The values of U and L must be chosen to suit the physical problem, such as average speed and pipe diameter for flow through a pipe.

In many familiar settings, a lower Reynolds number indicates that viscosity strongly influences the flow, while at a higher Reynolds number inertial effects are more prominent. This comparison helps characterize patterns such as orderly laminar motion and irregular turbulent motion. The Reynolds number does not, by itself, set a universal threshold between these regimes: critical values depend on flow geometry, boundary conditions, surface roughness and disturbances. For flow in a circular pipe, a transition value around 2,000–2,300 is often used as a guide, but actual transition can occur over a range and may be delayed or accelerated by the conditions of the experiment.

The Reynolds number is useful in model testing because flows with matching dimensionless parameters can have comparable relative force effects, when the relevant geometry and other conditions are also appropriately matched. Engineers and researchers use it when studying external aerodynamics, pipes, ducts, channels, machinery and other fluid systems. In aerodynamics, Reynolds-number effects influence boundary layers, separation and drag. In internal flows, the number helps organize analysis of pressure losses and flow regimes. It is one of several similarity parameters; compressibility, gravity, surface tension or other effects may require additional dimensionless numbers.

The quantity is named for the British engineer and physicist Osborne Reynolds. In an 1883 paper, he described experiments on whether water motion in a channel was direct or sinuous, investigating the conditions associated with the transition in flow and the law of resistance. His work helped establish the importance of relating flow behavior to characteristic scales and fluid properties.