= Material volume element
{title2=$D(\delta V)/Dt=(\nabla\cdot\mathbf u)\delta V$}
A <material volume element> contains the same fluid particles as it moves and deforms. If its edges transform with the local <velocity gradient>, its volume changes at a rate equal to the trace of that gradient, giving $D(\delta V)/Dt=(\nabla\cdot\mathbf u)\delta V$. <Mass conservation> states $D(\rho\delta V)/Dt=0$, not that its volume is always fixed. These two identities give the material form of the <continuity equation>, $D\rho/Dt=-\rho\nabla\cdot\mathbf u$.
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