Page 320 - Aerodynamics for Engineering Students

302 Aemdynamics for Engineering Students

For air

M:+5
M2 - (6.49a)
2-7Mf-1
Inspection of these last equations shows that M2 has upper and lower limiting
values:

For M1 403 M2 + E = (l/& = 0.378 for air)

ForM1+ 1 M2+ 1

Thus the exit Mach number from a normal shock wave is always subsonic and for air
has values between 1 and 0.378.

6.4.8 Velocity change across the normal shock

The velocity ratio is the inverse of the density ratio, since by continuity u2/u1 = p1/p2.
Therefore, directly from Eqns (6.45) and (6.45a):

(6.50)

or for air

(6.50a)

Of added interest is the following development. From the energy equations, with cpT
replaced by [r/(-y - l)lp/p, pl/p~ and p2/p2 are isolated:

-
!!! - (cPTo - $) ahead of the shock
P1 Y
and

E = (cPTo - 2) downstream of the shock
P2 7
The momentum equation (6.37) is rearranged with plul = p2u2 from the equation of
continuity (6.36) to

P2
u1--2=--- P1
p2u2 PlUl
and substituting from the preceding line