...How does one calculate the Reynolds number for a wing in water?

From : Don Stackhouse

Reynolds number ("Re") is the density of the fluid, times the speed, times some characteristic dimension (typically chord in the case of an airfoil, typically diameter in the case of a pipe), divided by the absolute viscosity of the fluid. If you do it right, the answer should be dimensionless (i.e.: the dimensions of the things in the numerator should together be the same as the dimensions of things in the denominator, so that the dimensions all cancel each other out, resulting in a "dimensionless number").

Since "kinematic viscosity" is the viscosity divided by the density, Re is also equal to the speed times the dimension divided by the kinematic viscosity.

The kinematic viscosity of water is much less than air, because of its far greater density. Re's in water at about 65 degrees F will be about 14.5 times greater than the Re of that same surface at the same speed in sea level std. day air. The Re of a wing at sea level in std. conditions air is:

Re (air) = 778 x speed (mph) x chord (inches)

The Re in 65 deg.F water for that same airfoil is:

Re (H2O) = 11,400 x speed (mph) x chord (inches)

However, that's not the whole story. The kinematic viscosity of water is very sensitive to temperature. At just above freezing, it's about 1.57 times greater than at 65 F, so the equation becomes:

Re (H2O@33F) = 7230 x speed (mph) x chord (inches)

At a water temperature of 85 F, the kinematic viscosity is down to about 81% of its value at 65 F, so the equation becomes:

Re (H2O@85F) = 14,000 x speed (mph) x chord (inches)

For example, an wing with a chord of 1" traveling at 10mph would have an Re of what?

At :	33F	65F	85F
Re=	72.3K	114K	140K

In general, the Re's of airfoils operating in water will be much higher than the same airfoils operating in air. However, since the required "wing areas" in this much denser fluid tend to be smaller, the Re's you tend to run into are likely to be similar to what we encounter with model sailplanes. In addition, the profound effects of temperature will probably give you a much wider range of Re's to deal with, unless you plan to only operate in a constant-temperature heated swimming pool. The cumulative effect of all these factors could make for a very knotty design problem!

Don Stackhouse
DJ Aerotech