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 images is the fluid velocity vector and images are the fluid density, viscosity, and pressure, respectively and images is an external force vector.

Let us first derive the last equation, images called the divergence equation.

In Section 3.1 we derived the diffusion/convection/reaction equation (3.2):

images

where images (called images in Section 3.1) is the density of a diffusing substance and images is the velocity of the medium. If there is no diffusion () and no reaction (source ...

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