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I was learning about Reynolds number in fluid mechanics and it is given as

$$Re= \frac{\rho V L}{u} $$

Physically, compares the inertia and viscous forces acting in a fluid. I get that density will affect inertia force, but how the velocity affects inertia force?

If I take two bodies having same mass, one moving with a higher speed and the other with lower, and if I subject them to same acceleration won't the inertia force be same in both the cases?

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The inertial force in Reynolds number is to do with how much mass of the fluid must be 'pushed along' when the body is going at velocity $v$ - not to do with the inertia of the body.

Reynolds number is the ratio of inertial force to viscous force, per unit area - the inertial force is $$v^2\rho$$

Inertial force is a confusing name but it's the force needed to change the momentum of all the fluid that impacts on the body when moving at velocity $v$.

The body of area $A$ comes across a volume $Av$ of fluid per second, the mass of that fluid is $Av\rho$.

If we presume it must bring it up to the same speed $v$, the change in momentum per unit area is $v^2\rho$, so that's the force per unit area - and is called 'inertial force'.

The viscous drag force, for a sphere, is from Stokes Law

$$F=6\pi r\eta v$$

so force per unit area, dividing by $\pi r^2$ and ignoring small numerical constants is $\frac{\eta v}{r}$.

Reynolds number, the ratio of inertial force to viscous drag is $$Re = \frac{v^2\rho}{\eta v/r} = \frac{\rho v r}{\eta}$$

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