Passing through a shock front moving with a speed , the physical variables , , and
Since the basic equations of hydrodynamics is unchanged after chosing a system moving ,
the continuity equation
gives an equation for a steady state as
Considering a region containing the shock front at
which extends from
and integrating the above equation, we get
Thus, we obtain the jump condition conserning the mass coservation as
where the quatities with suffix 1 are for preshock and those with suffix 2 are for postshock.
Equation of motion for steady state
where we used equation(A.29).