Continuity Equation

A local balance relation expressing how the time rate of change of a field's density equals the negative divergence of its flux plus any local sources or sinks.

The Continuity Equation is the local mathematical statement of mass conservation for a continuum fluid: ∂ρ/∂t + ∇·(ρ v) = 0, where ρ is density and v the velocity field. Under the incompressible, constant‑density assumption it reduces to ∇·v = 0; for steady one‑dimensional flow it implies ρ A V = constant (mass flow rate conserved).