The continuity equation is a mathematical expression of the law of conservation of mass, and its general form is (see the basic equation of fluid mechanics):

or

For stable motion and incompressible fluids, the continuity equation can be simplified as:

Where v=0 and v= 1 correspond to incompressible fluid and steady-state motion respectively. For plane and axisymmetric motion, there is a flow function ψ, which is derived from the continuity equation. Therefore,

(Plane motion)

(Axisymmetric motion)

Where u, v, vx and vr are components of velocity vectors in rectangular coordinates (x, y, z) and cylindrical coordinates (r, φ, z) respectively.