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Pressure-density relations across the shock
Eqn (6.38) may be rewritten (from e. g. Eqn (6.27)) as
7 Pi
2 7 – 1 pi
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which on rearrangement gives
From the continuity equation (6.36):
. , 1 1
М2 + Ml = /И I—— 1—
P2 Pi
and from the momentum equation (6.37):
m2 – мі =4-(рі -/>2)
m
Substituting for both of these in the rearranged energy equation (6.39)
JLr(a_e)=i(f,,_„)(l+±)
7 -1 VPi Р2/ Pl /°2/
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and this, rearranged by isolating the pressure and density ratios respectively, gives the Rankine-Hugoniot relations:
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l-H* Ml |