#LyX 2.1 created this file. For more info see http://www.lyx.org/
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\begin_body

\begin_layout Standard
\begin_inset Formula $K=\frac{\partial F}{\partial x}=S_{l}\frac{\partial p}{\partial x}=S_{l}\frac{\partial p}{\partial\rho}\frac{\partial\rho}{\partial x}=S_{l}c_{0}^{2}$
\end_inset


\end_layout

\begin_layout Standard
\begin_inset Formula $\rho=\rho_{0}\frac{V_{0}}{V}$
\end_inset

, 
\begin_inset Formula $V=V_{0}+S_{l}x$
\end_inset


\end_layout

\begin_layout Standard
\begin_inset Formula $\frac{\partial\rho}{\partial x}=-S_{l}\frac{\rho_{0}}{V_{0}}$
\end_inset


\end_layout

\begin_layout Standard
Such that
\end_layout

\begin_layout Standard
\begin_inset Formula $K=-S_{l}^{2}\frac{\rho_{0}c_{0}^{2}}{V_{0}}=-S_{l}^{2}\frac{p_{0}}{\gamma V_{0}}$
\end_inset


\end_layout

\end_body
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