Reynold’s Number

It is an important dimensionless quantity in fluid mechanics, denoted by Re. Although, the concept was introduced by Sir George Stokes in 1851, it was named only in 1908 by Arnold Sommerfeld after Osborne Reynolds.

It ideally gives a ratio of inertial forces to viscous forces within a fluid which is introduced due to relative internal movement between different fluid velocities. This relative movement between the different layers of the fluid causes something called fluid friction, something similar to rubbing your two hands together. This type of friction decides when a flow becomes turbulent because a fluid with higher viscosity will be able to take more relative movement between the layers.

This number tells us whether a given fluid is in laminar flow or turbulent flow and most importantly predict the transformation from laminar to turbulent flow. It is used to study the flow of air over an aircraft wing. Knowing when the flow will become turbulent is extremely important for designers and ultimately in light of safety, for aircrafts.

This is seen to be most effective when the Reynolds number is high i.e when the object being propelled is relatively large and is passing through a medium of low viscosity.

At large Reynolds numbers, the inertial forces, which are directly proportional to the fluid density and square of the it’s velocity, are large relative to the viscous forces, and thus the viscous forces cannot prevent the random and rapid fluctuations of the fluid.

However, at small or moderate Reynolds numbers, the viscous forces are large enough to suppress these fluctuations and to keep the fluid “in line.”

The Reynolds number at which the flow becomes turbulent is called the critical Reynolds number, Recr.

Reynolds numbers are used in airfoil design to manage “scale effect” when computing characteristics. Fluid dynamicists define the chord Reynolds number R as: R = Vc/v, where V is the flight speed, c is the chord length, and ν is the kinematic viscosity of the fluid in which the airfoil operates.