Equation of Mass Continuity

The equation of mass conservation is,

By use of a vector identity, Eqn. 16 may be expressed as,

This simply states that, at any point, the density increases if there is material flow into the region (∂/∂t > 0 for ∇.ρv < 0) and decreases with material flow away from the region (i.e., positive divergence).