When the fluid pressure $p$ is not uniform (for example, as depicted on the right side of the wall in figure~\ref{fig_pressure_distribution_plate_two}), the situation is more complex: the force must be obtained by integration. The surface is split in infinitesimal portions $\diff S$, and the corresponding forces are summed up as:

When the fluid pressure $p$ is not uniform (for example, as depicted on the right side of the wall in figure~\ref{fig_pressure_distribution_plate_two}), the situation is more complex: the force must be obtained by integration. The surface is split in infinitesimal portions of area $\diff S$, and the corresponding forces are summed up as:

\begin{IEEEeqnarray}{rCcCl}

F_\text{pressure}& = &\int_S \diff F & = &\int_S p \diff S \label{eq_pressure_force_scalar}

F_\text{pressure}& = &\int_S \diff F_\text{pressure}& = &\int_S p \diff S \label{eq_pressure_force_scalar}

\end{IEEEeqnarray}

\begin{equationterms}

\item for a flat surface.

\item where the $S$-integral denotes an integration over the entire surface.