Page 279 - 48Fundamentals of Compressible Fluid Mechanics

13.4. SOLUTION OF MACH ANGLE 241

The conditions in zone 4 and zone 3 have to have two things that are equal,
and they are the pressure and the velocity direction. It has to be noticed that the
velocity magnitudes in zone 3 and 4 do not have to be equal. This non continuous
velocity profile can occurs in our model because it is assumed that fluid is non–
viscous.
If the two sides were equal because symmetry the slip angle was zero. It is
to say, for the analysis, that only one deflection angle exist. For the two different
deflection angles, the slip angle has two extreme cases. The first case is where
match lower deflection angle and second to match the higher deflection angle. In
this case, it is assumed that the slip angle moves half of the angle to satisfy both of
the deflection angles (first approximation). Under this assumption the continuous
in zone 3 are solved by looking at deflection angle of which
results in
9
9
c 7 8

4
4
4

9
+-"1 -+
with the additional information -9 +- " ) +1+-+1 9 7 8 - "-+
)

c 7 5 5 7 8

4
4
9
) +-+1+-
90+-91+
+1"- 1+
+
9
)
-
"-+
and Mach
3.8006

And in zone 4 the conditions are due to deflection angle of 9

7
7 8

c 7 8

4
4
4

" 9
+ 90"
+
with the additional information -9 " + + + 9 7 8 -+ )0"

c 7 5 7 8

4
4
7 8

+ 9
" -9
+-9)1)
+ -
)0"
+
-+
From these tables the pressure ratio at zone 3 and 4 can be calculated
+
5

7

"=),"
"
+

To reduce the pressure ratio the deflection angle has to be reduced (remember
+1"-+ + -
that at weak weak shock almost no pressure change). Thus, the pressure at zone
)#
. .
3 has to be reduced. To reduce the pressure the angle of slip plane has to increase

to a larger number.
from 9