Value of the Reynolds Number in constant velocity flows

Question

Consider a fluid flowing such that all the particles have same velocity, what will be the Reynolds Number for such a flow?

We know that Reynolds number,

$$Re=\frac{inertia \,forces}{viscous \,forces}$$

in a fluid.

In a flow in which the particles have same velocities there will be no viscous forces acting on the fluid particles. Also, (and I'm not sure of this) since the particles have same velocities there will be no inertia forces too, because there is no acceleration. Then, from the definition of Reynolds Number, $Re = \frac{0}{0}$, which is not defined.

So what actually is the Reynolds number of a flow with constant velocity?

Answer 1

Let's start with a quick review of the term - "viscosity".

The viscosity of a fluid is a measure of its resistance to deformation at a given rate, it quantifies/characterizes the internal frictional force between adjacent layers of fluid that are in relative motion. In general, viscosity depends on a fluid's state, such as its temperature, pressure, and rate of deformation (which is negligible for Newtonian Fluids). Zero viscosity (no resistance to shear stress) is observed only at very low temperatures in superfluids; or a monatomic ideal gas, in which the internal energy of molecules is negligible. (Ref)

The sketch and formulation below may help you to gain a better understanding of the force terms, on which Renolds Number is derived/based upon.

https://www.grc.nasa.gov/www/BGH/reynolds.html

From all of the above, we can draw the conclusion that Renolds Number will always be a real number, or "zero" if $V = 0$.