6Incompressible Fluid Flow
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.
In Section 3.1 we derived the diffusion/convection/reaction equation (3.2):
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 ...
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