Fluid Flow - Reynolds Number

Solid objects like cars, boats and airplanes, things that move, experience drag because of the flow of fluid around them. When the fluid is air, the force of drag is called aerodynamic drag or air resistance. When the fluid is water, the force of drag is called hydrodynamic drag. The force of drag produced depends on the way fluid flows around the object. Whether the fluid is air, water or something else, there are two types of flow, laminar and turbulent.

Laminar flow ocurrs when the air stream around the object is smooth. Using a model car as an example, the speed of the air next to it is close to the speed of the car because air sticks to the car a little. This syrup-like property of air (or any fluid) is called viscousity. For air it is very low, but it is there. A little further from the car the air's speed drops smoothly to zero. Under these conditions, the aerodynamic drag is low.

Turbulent flow occurs when the air stream breaks up and causes little whirlwind currents next to, say, a rocket's skin. The speed of the air drops suddenly just off of its surface, a condition called wind shear. These conditions cause much higher aerodynamic drag. In water, this effect is called cavitation because air is squeezed out of the water due to the turbulant change in pressure.

Notation

Fortuneately, the air flow over many hobby models is nearly all laminar. We know this because of an indicator called the Reynolds number. Its symbol is RN.

For a Grand Prix car body, v is at most 15 feet/sec (180 in/s) and L is at most 7 inches, so RN is at most 54,308 on the official AWANA track. RN is an indicator because if it is under 100,000 then the flow will be laminar. If it is over 1,000,000 it will be turbulent. In between, in the transition range, it can be either.

Find the Reynold's number for your model vehicle using the worksheet below.

In the literature, you can find other formulations of Reynolds Number. Each may have its own limits for the transition region. This is because the units used in the parameters are on different scales. For example, the scale length may be in inches, but the velocity in feet per second. The resulting Reynolds Number will be smaller from the one calculated above by a factor of 1/12 if the other units are the same.

Many formulations use kinematic viscosity which is the dynamic viscosity used above divided by density. That's ug/p in the symbols used here. That's the inverse of p/ug which was calculaed above to make the math simpler. So we really used it too!