Hopefully you haven’t entirely checked out yet. Still here? Awesome.
So we’ve established that we can think of and describe air as a fluid, like water.
And if there are individual air molecules that behave according to regular physics, that means they experience friction due to the molecules around them.
Imagine a large pipe half-filled with flowing water. Each vertical “layer” of fluid will experience friction from the layers above and beneath it due to the interactions of the water molecules. The very bottom layer will also experience friction from moving next to the pipe itself.
The term viscosity is what describes these frictional forces between the adjacent layers of fluid.
- A liquid with low viscosity, like acetone, has very little friction between those layers. The liquid appears to move very quickly and easily.
- A liquid with high viscosity, like honey, has a lot of friction between those layers. It needs much more force to overcome that friction and so it moves more slowly.
Viscosity is an inherent property of any fluid—it only varies slightly based on temperature and other factors, but is otherwise relatively constant.
One quirk of us aero engineers is that we really like nondimensionalized (unitless) numbers and coefficients. They make it easier to do apples-to-apples comparisons of situations with very different conditions.
One of these nondimensionalized numbers that we love is the Reynolds number. What this number does is describe a fluid flow by providing the ratio of its inertial forces to the forces due to viscosity.
In other words, this number compares the tendency of a fluid to stay at rest or in motion to the force required to change the speed of the fluid.
Say you have a flow of water blasting out of a hose: it’ll have a certain amount of inertia due to its density and speed, and will also have a specific viscosity value because of the fluid type. Depending on its speed, it’ll probably spray pretty far once out of the hose.
But if you replace the water with something like olive oil, the increased viscosity of the fluid will change the behavior. Given that same speed inside the hose, the oil won’t travel nearly as far after exiting the hose.
In this example, we could say that the water flowing through the hose had a higher Reynolds number than the oil flow, because the ratio of its inertia to its viscosity was higher.
Once we move to talking about flows of air, we can flip this—because our viscosity stays pretty much constant, our Reynolds number is a useful measure of the difference in inertia between flows. To put it very simply, the Reynolds number helps us characterize the energy of a fluid flow.
Okay, cool…but what does this have to do with bees?