Significance of kinematic and dynamic viscosity

[Waqar Amin]

It is stated that kinematic viscosity is the ratio of dynamic viscosity to density. can anyone elaborate it further that what are the uses of both types of viscosities and why we differentiate them.does dynamic viscosity reates with static fluid?

 

[boneh3ad]

It is really just a term of convenience. Oftentimes, the equations of fluid mechanics are manipulated such that you end up with $\mu/\rho$ terms, so it is simply much easier to carry around a $\nu$ instead of a fraction. This is commonly seen with the Reynolds number, which has a $\mu/\rho$ term in it.

 

[Waqar Amin]

then how kinematic viscosity is termed as momentum diffusivity, i m very confused with these terms.

 

[boneh3ad]

Well, as with any sort of viscosity, it is really a measure of how momentum is diffused through a fluid. If you are familiar with the heat equation, you should notice some analogs between it and the Navier-Stokes equations.

The heat equation:
$$\frac{\partial \phi}{\partial t} = c^2\nabla^2 \phi$$

The incompressible Navier-Stokes equation:
$$\frac{\partial \mathbf{v}}{\partial t} + \mathbf{v}\cdot\nabla\mathbf{v}=-\frac{1}{\rho}\nabla p + \nu\nabla^2\mathbf{v} + \mathbf{f}$$

The heat equation is a simplified version of the diffusion equation that describes the diffusion of basically any quantity through a material. In heat transfer, $c^2=\alpha=\frac{k}{\rho c_p}$ is the thermal diffusivity.

In the Navier-Stokes equations, notice that the $\nu\nabla^2\mathbf{v}$ term takes the same form, only the N-S equations are a momentum balance, so the kinematic viscosity, $\nu$, is essentially a diffusivity constant that describes how momentum diffuses through the medium. In other words, it describes one particle's ability to affect the momentum of the adjacent particles.

 

[Waqar Amin]

i have understand. thanxx for your help boneh3ad. :)