Continuity Equation

Theorem
AliasesConservation of Mass
ConditionsContinuum Hypothesis

Statement

The Continuity Equation expresses the principle of conservation of mass for a fluid. In differential form, it states that the time rate of change of density plus the divergence of the mass flux is zero.

Mathematical Form

∂ρ∂t+∇⋅(ρv)=0\frac{\partial\rho}{\partial t} + \nabla\cdot(\rho\mathbf{v}) = 0

Incompressible Flow

For a fluid with constant density (ρ=const\rho = \text{const}): ∇⋅v=0\nabla\cdot\mathbf{v} = 0

Relationships

  • Basis: Fluid Dynamics
  • Derivation: Reynolds Transport Theorem