The Wind Tunnel (Page 2)

From now on we'll just use "Re" when we mean the Reynolds number. The mathematical definition of Re is:

In aerodynamics, Greek letters of the alphabet are used as abbreviations for fluid properties like viscosity, density, specific heat ratio (which is used to calculate the speed of sound), etc.

The first letter that looks like a script letter "p" is the Greek letter "rho" and is the symbol for density. The Greek letter "mu" in the denominator is the symbol for dynamic viscosity ( there is another type of viscosity called kinematic viscosity that uses a different symbol) The letter "U" is the symbol for freestream velocity. We're going to use the velocity of a Pete Sampras serve for this. "L" is the characteristic length of the object. For a tennis ball L would be equal to the diameter of the ball; on a wing L would be a "chord" length (the length of a line drawn from the leading to trailing edge of the wing).

Now let's fill in the numbers. The density and viscosity of air on a standard day (60 F) at sea level is 1.225 kg/m³ and 1.8 X10^-5 kg/m-s, respectively. The length (diameter) of a tennis ball is 0.06569 meters (2.586 inches). A Pete Sampras serve is 120 MPH or 53.64 meters/sec.

We're going to use all the metric values above; so Re = (1.225)(.06569)(53.64)/(.000018). Multiplying all this out Re = 239801 which is about 2.4 X 10⁵.

So if we wanted to use the 11" diameter Wilson ball in the wind tunnel, its aerodynamics would be identical to a standard size tennis ball if its Re was 2.4 X 10⁵. How do we make Re the same? We vary the velocity. Think about it. The density and viscosity of the air didn't change but the length did. The diameter of the 11" ball was longer than the standard tennis ball. That means we have to reduce the velocity to make the Re the same for the two balls. Fortunately, that's how wind tunnels work - we're able to change the speed of the tunnel.

Think of an airplane during the design cycle. We don't build a large multi-million dollar aircraft to see if it has enough lift - we build a small model, place it in a wind tunnel, measure the lift on the model and then use these scaling laws to determine what the lift will be on the large airplane. You don't have to build multiple models, or find fluids with different viscosities or densities, you just match the Re through the velocity.