REYNOLDS NUMBER (R)

Reynolds number is a non-dimensional parameter that is used when viscous force is dominant.  Reynold’s number represents the ratio between inertia force F_I and viscosity force F_V. 

Reynolds number is used for the following types of flow:

§  Completely submerged flow e.g. ship

§  Completely enclosed e.g. flow through pipes and plates

§  Viscous flow e.g settling of particles in fluids

§  Flow in flow meter in pipes, venturi meter, or orifice meter

The Reynolds number can be expressed as:

  

     

Below is the equation for dynamic similarity where viscous forces are predominant.

Example 1
An underwater missile, diameter 2m and length 10m is tested in a water tunnel to determine the forces acting on the real prototype. A 1/20^th scale model is to be used. If the maximum allowable speed of the prototype missile is 10 m/s, what should be the speed of the water in the tunnel to achieve dynamic similarity?

For dynamic similarity the Reynolds number of the model and prototype must be equal:

So the model velocity should be

As both the model and prototype are in water then, m_m = m_p and r_m = r_p so


Note that this is a very high velocity. This is one reason why model tests are not always done at exactly equal Reynolds numbers. Some relaxation of the equivalence requirement is often acceptable when the Reynolds number is high. Using a wind tunnel may have been possible in this example. If this were the case then the appropriate values of the r and m ratios need to be used in the above equation.