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1.2.3 Fluxes through surface

Fluxes through surface element \bgroup\color{DEFcolor}$d\!A$\egroup with normal vector \bgroup\color{DEFcolor}$\hat{\ensuremath{\mathchoice{\mbox{\boldmath$\displaysty...
...x{\boldmath$\scriptstyle n$}}
{\mbox{\boldmath$\scriptscriptstyle n$}}}}$\egroup:

Mass transport \bgroup\color{DEFcolor}$\rightarrow$\egroup change of mass per time:

\begin{displaymath}
\rho   \ensuremath{\mathchoice{\mbox{\boldmath$\displaysty...
...tstyle n$}}
{\mbox{\boldmath$\scriptscriptstyle n$}}}} \; d\!A
\end{displaymath} (8)
Momentum transport and acceleration by pressure force along surface normal \bgroup\color{DEFcolor}$\rightarrow$\egroup change of momentum per time
\begin{displaymath}
\left[ \rho   \ensuremath{\mathchoice{\mbox{\boldmath$\dis...
...$}}
{\mbox{\boldmath$\scriptscriptstyle n$}}}} \right] \; d\!A
\end{displaymath} (9)
Energy transport and work done by pressure \bgroup\color{DEFcolor}$\rightarrow$\egroup change of total energy per time
\begin{displaymath}
\left[ \rho e_{\rm ik}+ P\right] \ensuremath{\mathchoice{\m...
...tstyle n$}}
{\mbox{\boldmath$\scriptscriptstyle n$}}}} \; d\!A
\end{displaymath} (10)
Shear forces (friction) are ignored.

There are no torsional forces (only relevant in solids).