fluid dynamics - What does the Reynolds Number of a flow represent physically?

What does the Reynolds Number of a flow represent physically?

I am having trouble understanding the meaning and the utility of the Reynolds number for a certain flow, could someone please tell me how this type of dimensionless factor is significant and what it tells us about a problem?

Answer

From the Wikipedia article for Reynolds number:

In fluid mechanics, the Reynolds number (Re) is a dimensionless number that gives a measure of the ratio of inertial forces to viscous forces and consequently quantifies the relative importance of these two types of forces for given flow conditions.

In addition to measuring the ratio of inertial to viscous forces in a flow, the incompressible Navier-Stokes equations can be written in non-dimensional form such that the only parameter is the Reynolds number (ignoring body forces). This is very nice because it is the basis for the validity of wind tunnel testing.

Suppose we would like to measure the aerodynamics of the flow around a Boeing 747. Two (at least) options exist:

1. Build your very own full size 747, instrument it, and fly it. (extremely expensive)


2. Build a small scale model of a 747, instrument it, test inside a wind tunnel (much less expensive)

But how do we know that the flow we measure in the wind tunnel is what really happens in flight? We match the Reynolds numbers and the exact same equations model both situations--therefore the aerodynamics must be the same. (Ignoring compressibility effects.)