 Fluid element

A fluid element is a small material parcel followed as it moves with a velocity field. It contains the same particles throughout its motion when no molecular exchange is included in the idealization. The continuum approximation requires it to be large enough to average microscopic structure while small enough to assign approximately local fields.

Its centre follows a Lagrangian trajectory, and its shape can stretch and rotate. For its volume $\delta V$, $D(\delta V)/Dt=(\nabla \cdot \mathbf{v})\delta V$. Mass conservation keeps $\rho \delta V$ constant, so expansion decreases the parcel's mass density. An incompressible flow preserves the parcel's volume, but can still distort it strongly through shear strain. A fixed box in space is a different object: material can enter and leave that box, requiring boundary fluxes in its balance laws.