Dynamic or Kinematic Viscosity

A quick description on how to use which measure of resistance to strain rate from where they appear in NS momentum balance terns.

The dynamic description is given by the navier stokes equation, which is analogus to a newtonian momentum balance on a fluid element. The material derivative

$$\overbrace{ \left( \frac{\partial}{\partial t}+\bf{v}\cdot\nabla \right) }^{\frac{D}{Dt}} \left(\rho \mathbf{v}\right) = -\nabla p+\mu\nabla^2\mathbf{v} +\rho \mathbf{g}$$