The Reynolds number is the most important dimensionless number in fluid dynamics providing a criterion for dynamic similarity. It is named after Osbourne Reynolds (1842-1912). Typically it is given as follows:
- vs - mean fluid velocity,
- L - characteristic length (equal to diameter 2r if a cross-section is circular),
- η - (absolute) dynamic fluid viscosity,
- ν - kinematic fluid viscosity: ν = η / ρ,
- ρ - fluid density.
Two flows with equal Reynolds numbers and the same geometry are similar. For the flow in a model and the real flow holds in appropriate points:
The similarity of flows
Quantities marked with * concern the flow around the model and the others the real flow. This is useful for experiments with reduced model in the water channel or in the wind tunnel, where we get data for the real flows. Note that in compressible flow the Mach number must also be equal for the two flows to be similar.
See also: