The quantity: ρ V l / μ
is called the Reynolds number.
ρ is the fluid density, V is the speed,
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
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
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.