Page 316 - Aerodynamics for Engineering Students
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298 Aerodynamics for Engineering Students
Momentum, in the absence of external and dissipative forces
P1 + Plu: = Pz + P24 (6.37)
Energy
(6.38)
6.4.2 Pressure-density relations across the shock
Eqn (6.38) may be rewritten (from e.g. Eqn (6.27)) as
which on rearrangement gives
(6.39)
From the continuity equation (6.36):
and from the momentum equation (6.37):
1
u2--1 =Tb1 -Pz)
m
Substituting for both of these in the rearranged energy equation (6.39)
(6.40)
and this, rearranged by isolating the pressure and density ratios respectively, gives the
RankineHugoniot relations:
7+1 PZ 1
(6.41)
(6.42)
