6.1 Derivation of Navier–Stokes Equations
The Navier–Stokes equations for the flow of an incompressible fluid (a liquid) are
where is the fluid velocity vector and are the fluid density, viscosity, and pressure, respectively and is an external force vector.
Let us first derive the last equation, called the divergence equation.
where (called in Section 3.1) is the density of a diffusing substance and is the velocity of the medium. If there is no diffusion () and no reaction (source ...