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Daniel D'Orazio edited untitled.tex
over 9 years ago
Commit id: e9399358f3d40c8440adce3952f24dbcda47d1fe
deletions | additions
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index 467f757..754c2ec 100644
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\begin{equation}
c^{\rm{ad}}_{s} = \sqrt{\frac{dP}{d\rho}} = \sqrt{\gamma \frac{P}{\rho}} = \sqrt{\gamma RT}
\end{equation}
The isothermal equation of state $P=(c^{\rm{iso}}_{s})^2 \rho$ gives us that $c^{\rm{iso}}_{s} =
\sqrt{RT$
and \sqrt{RT}$. So we can write
\begin{equation}
\int{\frac{dP}{\rho}} = \frac{(c^{\rm{ad}}_{s})^2 }{\gamma -1}
= \frac{\gamma (c^{\rm{iso}}_{s})^2 }{\gamma -1} \quad \rm{Adiabatic} \ \rm{Flow}
\end{equation}