Question

What is Reynolds number? What is its significance?

Answer 1

Reynolds number (Re) is a dimensionless quantity (Dimensionless quantity) defined as the ratio between inertial and viscous forces in a fluid flow. As all the dimensionless quantities, it is obviously independent on the units you use.

Its principal usage is the so called Dynamic Similitude (model) frequently used in fluid dynamics to design boats, submarines, aircraft, rockets and all of the devices moving at high speed in water or in air or in anther fluid.

A simple example is that of fluid displacement in a round tube. You want to determine the power of a fan pushing air into a long round pipe. If you want to design such a device either you trust a fluid dynamic modeler that uses finite element methods to solve the Navier-Stokes equations (or more advanced algorithms) or you make an experiment.

In the past, let us say until 30 years ago, no numeric models were available so what? A solution was experimentation but real-scale experiments are not worth their price, for evident reasons.

So you create a scaled down model. For the geometry of tubes this is simple, but what is the wind speed you will choose to trust the results of your experiment and scale them up to the real device?

Here the Reynolds number comes in play. Your experiment should be executed respecting not only the geometric similarity, which is obvious, but also the dynamic similarity, i.e. the scaled Reynolds number should be equal to the Reynolds number of the real flow.

In some cases you can even change the fluid and experiment with water while the final device will be in air.

The historic Reynolds experiment, whence all this procedure comes from, uses exactly this principle to determine if the flow you will have is laminar or turbulent. Reynolds experiments determined that in a round pipe, if Re < 2000 the flow is laminar, if Re > 3000 the flow is turbulent. Of course he could not experiment all the possible geometries and fluid types (density and viscosity).

He recognized the principle of dynamic similarity and made an extensive experimentation with only one fluid but, using the dimensionless quantity after his name, we can scale these results to whatever experimental setup we may imagine.

In fluid dynamics there are other dimensionless quantities used for similar purposes like the Nusselt number used in heat transfer problems or the Prandtl number but there are half a dozen of this dimensionless quantities, dealing with many different aspects of fluid flow.