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In the case of the gas is isothermal
,
equation (A.31) becomes
![\begin{displaymath}
\rho_1\left(c_{is}^2+u_1^2\right)=\rho_2\left(c_{is}^2+u_2^2\right).
\end{displaymath}](img1438.png) |
(A.32) |
Eliminating
from equations (A.29) and (A.32), we obtain
![\begin{displaymath}
\left(u_1u_2-c_s^2\right)\left(u_1-u_2\right)=0,
\end{displaymath}](img1439.png) |
(A.33) |
which means
![\begin{displaymath}
u_1u_2=c_s^2.
\end{displaymath}](img1440.png) |
(A.34) |
From equation (A.29),
![\begin{displaymath}
\frac{\rho_2}{\rho_1}=\frac{u_1}{u_2}=\frac{u_1^2}{c_s^2}.
\end{displaymath}](img1441.png) |
(A.35) |
This indicates the postshock velocity
the ratio of the postshock density to the preshock
density becomes large.
Kohji Tomisaka
2007-07-08