Material volume
= Material volume
{title2=$V(t)$}
A <material volume> is a region containing the same fluid particles at every time: its boundary moves with the fluid <velocity field>. Its <mass> is fixed by <mass conservation>, while its <volume> can change in compressible motion. Applying the <Reynolds transport theorem> to its <volume> gives $d|V(t)|/dt=\int_{V(t)}\nabla\cdot\mathbf u\,dV$. A <material volume element> is the infinitesimal version.