# 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.

**Cartesian Coordinates**

**Continuity**

**Navier Stokes**

**Cylindrical polar Coordinates**

**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
Last modified: Wed Aug 12 12:57:21 BST