Reynolds Transport Theorem: The Unsung Hero

Been reviewing fundamentals for a new project and rediscovered how elegant the Reynolds Transport Theorem really is:

$$\frac{D}{Dt}\int_{CV} \rho \phi , dV = \int_{CV} \frac{\partial (\rho \phi)}{\partial t} , dV + \int_{CS} \rho \phi (\vec{V} \cdot \hat{n}) , dA$$

It's literally the bridge between Lagrangian (following particles) and Eulerian (fixed control volume) descriptions of flow.

Every conservation equation in fluid mechanics stems from this beauty. Yet most courses rush through it to get to Navier-Stokes. We should appreciate the fundamentals more! ⚡