Fluid mechanics has been notoriously difficult to understand. This is primarily because the fundamental equations that describe fluid flow, the Navier-Stokes equations, can be nearly impossible to solve. In the year 2000, the Clay Mathematics Institute offered $1 million to the first person who could prove the existence of well-behaved solutions to the Navier-Stokes equations in three dimensions. Over 20 years later, this prize is still up for grabs.

Engineers have developed several strategies for getting around the difficulty of directly solving the Navier-Stokes equations. One such strategy is making carefully-chosen approximations that simplify the equations down to a form that is more solvable. Additionally, there are methods to investigate fluid flows qualitatively, without hard numbers. One such qualitative method is oil film flow visualization, which is a method of observing flow patterns on the surface of a body.

Oil film visualization experiments take place in wind tunnels, and there are two primary steps to the process. First, when the wind tunnel is stopped, a pigment-oil mixture is applied to the test surface (for example, an airplane wing). Then, the wind tunnel is turned on, and the oil is swept away, leaving behind marks that uncover the flow patterns. One factor that makes oil film visualization particularly attractive is that it can be done using relatively cheap and readily available materials. For example, the oil itself can be kerosene or standard aviation fuel, and the pigment that colors the oil could be powdered classroom chalk. Oil film visualization is particularly useful in noticing places where air flow separates, or diverges away, from the surface of a model plane. These points of separation are important to study because they are closely associated with increases in drag and a loss of lift.

Furthermore, it is worth noting that engineers typically implement oil film methods when studying high-speed flows, where a quantity called the Reynold’s number is large. Now, I find this to be a perfect opportunity to discuss Reynold’s number, which comes up time and again in aerospace engineering. Renyold’s number, or Re for short, is a fundamental, dimensionless quantity in fluid mechanics that captures how important friction is. When a fluid flow has a large Reynold’s number, such as 1 million, then pressure forces are 1 million times more important than friction forces. When a flow has a small Reynold’s number, such as 50, then friction forces are only 50 times less important than pressure forces.

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