# Value of the Reynolds Number in constant velocity flows

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?

• That is probably why Reynolds numbers are calculated using a characteristic length. Commented Mar 10, 2022 at 14:17

## 1 Answer

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.

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

• r13, I'm not able to understand how this addresses my query. I'm not interested in determining the Reynolds number for a stationary fluid (V=0), but rather for a fluid which is moving at a constant velocity. Commented Mar 12, 2022 at 11:11
• Re = fluid densityVL/viscosity - note "V" is the average flow velocity, not the change in velocity.
– r13
Commented Mar 12, 2022 at 16:33