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In the case of the gas is isothermal
,
equation (A.31) becomes

(A.32) 
Eliminating from equations (A.29) and (A.32), we obtain

(A.33) 
which means

(A.34) 
From equation (A.29),

(A.35) 
This indicates the postshock velocity the ratio of the postshock density to the preshock
density becomes large.
Kohji Tomisaka
20070708