Continuity and Navier Stokes Equations

The following are sets of both continuity and dynamic equations for incompressible Newtonian fluids, in vector notation and Cartesian, Cylindrical and Spherical coordinate systems. Vectorial properties are shown in bold type.

Vector Notation

Continuity

in general, or

for an incompressible fluid

Navier Stokes

in general, or

for an incompressible fluid

For the individual coordinate systems the equations are only quoted for incompressible flow.

Continuity

Navier Stokes

Continuity

or

Navier Stokes

Spherical polar Coordinates

Continuity

or

Navier Stokes

The terms in and represent centrifugal forces acting in the r direction due to velocity in the or directions and the terms in and represent Coriolis forces.

David Balmer