Page 317 - Aerodynamics for Engineering Students

Compressible flow 299

Taking y = 1.4 for air, these equations become:

(6.41a)

and
P2
6-+ 1
P2 - P1 (6.42~1)
P2
P1 6+-
PI
Eqns (6.42) and (6.42a) show that, as the value of p2/p1 tends to (y + l)/(*/ - 1)
(or 6 for air), p2/p1 tends to infinity, which indicates that the maximum possible
density increase through a shock wave is about six times the undisturbed density.

6.4.3 Static pressure jump across a normal shock
From the equation of motion (6.37) using Eqn (6.36):

P1 P1 PI
or
E- 1 =./M:[1-3
P1

but from continuity u2/u1 = p1/p2, and from the RankineHugoniot relations p2/p1 is
a function of (p2/p1). Thus, by substitution:

Isolating the ratio p2/p1 and rearranging gives

(6.43)

Note that for air

P2 - 7M: - 1 (6.43a)
-_
P1 6
Expressed in terms of the downstream or exit Mach number M2, the pressure ratio
can be derived in a similar manner (by the inversion of suffices):

(6.44)