The Continuity Equation: A PDE for Mass Conservation, from Gauss's Divergence Theorem

This video dives into Gauss's Divergence theorem to derive the partial differential equation (PDE) for mass conservation, known as the continuity equation. This is one of the most fundamental equations in fluid mechanics. Specifically, for incompressible flows, the mass continuity equation reduces to a condition that the velocity field must be divergence free everywhere.

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This video was produced at the University of Washington

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0:00 Introduction & Overview
1:38 Mass Continuity Recap
3:21 Control Volumes and Death Stars
6:30 Smoothness Conditions and Shockwaves
8:56 Incompressible Flows
10:55 Math
14:16 Incompressible Fluid Flows
16:15 Divergence Free Condition