# Tag Info

Take an area element $\mathrm{d}S$ perpendicular to the $x$-axis. How much energy is transported through this in unit time? Well, the flow rate is $v_x\mathrm{d}S$, and the energy density is $\frac{1}{2}\rho v^2 + \rho \varepsilon$, where $\varepsilon$ is internal energy. So multiplying these we have the energy transportation rate through $\mathrm{d}S$, ...