The Differential Form of Continuity

Inside this lesson

Convert the integral continuity equation to differential form using the divergence theorem
State ∂ρ/∂t + ∇·(ρV) = 0 and interpret each term (local density change and divergence of mass flux)
Reduce the equation to ∇·V = 0 for incompressible flow and explain what divergence-free means
Write the Cartesian form and check whether a given velocity field is incompressible

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Educational content covering topics typical of a first- and second-year mechanical engineering curriculum. Not a substitute for accredited coursework, and not suitable for real fluid-system design without review by a licensed professional engineer.