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. @eigensteve on Twitter eigensteve.com databookuw.com This video was produced at the University of Washington %%% CHAPTERS %%% https://www.seevid.ir/fa/w/Fk3X6o39KEI Introduction & Overview https://www.seevid.ir/fa/w/Fk3X6o39KEI Mass Continuity Recap https://www.seevid.ir/fa/w/Fk3X6o39KEI Control Volumes and Death Stars https://www.seevid.ir/fa/w/Fk3X6o39KEI Smoothness Conditions and Shockwaves https://www.seevid.ir/fa/w/Fk3X6o39KEI Incompressible Flows https://www.seevid.ir/fa/w/Fk3X6o39KEI Math https://www.seevid.ir/fa/w/Fk3X6o39KEI Incompressible Fluid Flows https://www.seevid.ir/fa/w/Fk3X6o39KEI Divergence Free Condition