# Reynolds Number

The quantity: ρ V l / μ is called the Reynolds number.

ρ is the fluid density, V is the speed, μ is the fluid viscosity, and l is some characteristic length. This length is, like the areas in the definition of dimensionless force coefficients, agreed on as a standard by whoever is using it. So, we have chord Reynolds numbers which are based on wing chord lengths or Reynolds numbers based on the diameter of a sphere, or any other characteristic length that can be devised.

The Reynolds number is one of the most important and strange dimensionless numbers. It varies over many orders of magnitude and expresses the importance of viscosity: high Reynolds numbers can be achieved by decreasing the viscosity or making the length or speed very large.

The Reynolds number, in a sense, represents a ratio of pressure to shear forces:
ρ V l / μ = ρ V2 / μ (V/l)
ρ V2 is related to the pressure while μ V/l is related to μ dU/dy, the shear stress.

The range of Reynolds number -- from McMasters.

Viscosity, and hence Reynolds number, strongly affects the performance of wings and airfoils, making it an important parameter to match in wind tunnel tests. It is often not possible to match these dimensionless parameters precisely.

The plot below shows the effect of Reynolds number on maximum lift to drag ratio for two dimensional airfoil sections. Note the plight of insects.

The plot here shows the effect of Reynolds number on the maximum section lift coefficient of a few typical airfoil sections. Note that these are not necessarily the best sections for high lift, though.

Recent studies have shown that substantial changes in CLmax are seen even at quite high Reynolds numbers, making it difficult to extrapolate data on small wind tunnel models.