- **Eulerian point-of-view:** look at particular location and see how things change there -> choosing a volume to analyze - **Lagrangian point-of-view:** see how certain fluid particles change as they move thru space -> choosing a system of particles - Easier to derive fluid laws from Lagrangian then apply to Eulerian - Can convert to/from Eulerian & Lagrangian using the **Reynold's Transport Theorem** (see full derivation on pg. 11 & 12) $ \boxed{ \underbrace{ \frac{D}{Dt} \int_{V_{sys}}\beta \rho dV }_{ \text{rate increase of }B\text{ in sys} }=\underbrace{ \frac{d}{dt} \int_{CV}\beta \rho dV }_{ \text{ rate increase of }B\text{ in CV} }+\underbrace{ \int_{CS}\beta(\rho \vec{u}_{rel}\cdot dA) }_{ \text{net rate at which }B\text{ leaves thru CS} }} $ where $\beta$ is a specific transportable quantity within the CV and system at time $t=t$ and $\vec{u}_{rel}$ is the velocity at the surface: $\vec{u}_{rel}=\vec{u}_{sys}-\vec{u}_{CS}$ ^e52112 %% %% - In a system, mass doesn't change with time -> $d\dot{m}_{sys}=0$ but may vary within the system: $ \frac{d}{dt}\int_{CV}\rho dV+\int_{CS}\rho \vec{u}_{rel}\cdot dA=0 $