Page 256 - 48Fundamentals of Compressible Fluid Mechanics

218 CHAPTER 13. OBLIQUE-SHOCK

Note that Maximum Deflection Mach Number’s equation can be extend to more
complicated equation of state (aside the perfect gas model).
This typical example for these who like mathematics.

Example 13.1:
Derive perturbation of Maximum Deflection Mach Number’s equation for the case
. Hint,
Start with equation (13.31) and neglect all the terms that are relatively small.

of a very small upstream Mach number number of the form of
SOLUTION

under construction

13.4.2.2 The case of of c

. Thus, first the transition line
has to be determined. This can be achieved by the standard

The second range in which
. The analysis shows regardless to
is when c
in–which
. This can be partially

mathematical procedure by equating
for specific value of as

the value of upstream Mach number
following .
when c

demonstrated by evaluating the terms, ,, , and,
,

(13.36)

, E

With values presented in equations (13.36) for " and becomes
, E

.

)

"

" < < E < E <

(13.37)
9

"

) E
and 9

(13.38)

< E <

"
.