In fluid dynamics, the continuity equation is a mathematical statement that, in any steady state process, the rate at which mass enters a system is equal to the rate at which mass leaves the system. ^[1] In fluid dynamics, the continuity equation is analogous to Kirchhoff's Current Law in electric circuits.

The differential form of the continuity equation is:

where ρ is fluid density, t is time, and u is fluid velocity. If density (ρ) is a constant, as in the case of incompressible flow, the mass continuity equation simplifies to a volume continuity equation:

which means that the divergence of velocity field is zero everywhere. Physically, this is equivalent to saying that the local volume dilation rate is zero.