If the space $W$ is constant (doesn't move with the flow), show that $$\frac{d}{dt}\int_{W}\left (\frac{1}{2}\rho |\overrightarrow{u}|^2+\rho \epsilon\right )dV=-\int_{\partial{W}}\rho \left (\frac{1}{2}|\overrightarrow{u}|^2+i\right )\overrightarrow{u} \cdot \overrightarrow{n}dA$$
where $p$ the pressure, $\rho$ the density, $\epsilon=i-\frac{p}{\rho}$ the internal energy per unit mass, $i$ the enthalpy.
How can we show that?? Do we have to use the divergence theorem??