Stationary Shock
For a stationary shock, and for the 1D Euler equations we have
In view of equation (12) we can simplify equation (14) to
which is a statement of Bernoulli's principle, under conditions where gravitational effects can be neglected.
Substituting and from equations (12) and (13) into equation (15) yields the following relationship:
where represents specific enthalpy of the fluid. Eliminating internal energy in equation (15) by use of the equation-of-state, equation ( 4), yields
From physical considerations it is clear that both the upstream and downstream pressures must be positive, and this imposes an upper limit on the density ratio in equations (17) and (18) such that . As the strength of the shock increases, there is a corresponding increase in downstream gas temperature, but the density ratio approaches a finite limit: 4 for an ideal monatomic gas and 6 for an ideal diatomic gas . Note: air is comprised predominately of diatomic molecules and therefore at standard conditions .
Read more about this topic: Rankine–Hugoniot Conditions
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