The Lagrangian and non-conservation form of the continuity equation can be obtained by applying mass conservation to a moving fluid element, which states that the mass of a moving fluid element does not change in time. Mathematically, this can be written as:

\[ \frac{d}{d t} \iiint_{\mathcal{V}(t)} ho d \mathcal{V}=0 \]

Using the ideas from Section 2.4, where we applied a time derivative to the momentum of a moving fluid element, derive the Lagrangian form of the mass continuity equation as well as the non-conservation form of the continuity equation.