Reynolds number

A dimensionless figure (symbol: Re) named after the physicist Osborne Reynolds. It is used in fluid mechanics and can be understood as the ratio between inertial and viscous forces. It has been shown that the turbulence characteristics of geometrically similar bodies are identical when the Reynolds number remains constant. This characteristic allows for instance realistic model tests in the wind and water channel.

The Reynolds number is defined by Re = ρ ⋅ v ⋅ d / η = v ⋅ d / ν

Where ρ is the density of the liquid, v the flow velocity of the liquid with respect to the body and d the characteristic length of the body. The characteristic length, also known as reference length, is defined or must be defined for each problem. For flow bodies, the length of the body in the direction of the flow is usually chosen. The kinematic viscosity v of the liquid is differentiated from the dynamic viscosity η = ν ⋅ ρ by the factor ρ.

If the Reynolds number exceeds a (problem-dependent) critical value Re crit, a so far laminar flow becomes prone to even the smallest disturbances. In accordance, for Re > Re crit, a change from laminar to turbulent flow must be calculated.