Page 261 - 48Fundamentals of Compressible Fluid Mechanics

13.4. SOLUTION OF MACH ANGLE 223

subsonic
weak
solution

1.0 < M 1 < ∞
Defection angle strong θ min = sin −1 M 1 supersonic
1
weak
solution
soution

no
possible solution solution
zone

θ, Shock angle
π θ = 0
θ = π
2 θ max ∼
2
Fig. 13.9: The possible range of solution for different parameters for given upstream Mach
number

The reduced pressure difference is

(13.49)

!

c

The reduced density is ! " ! c

(13.50)
!

c

c

For large upstream Mach number and small shock angle (yet non ap-

proaching zero), , the deflection angle, c must be small as well. Equation (13.40)

can be simplified into

(13.51)

c
The results are consistent with the initial assumption shows that it was appropriate

assumption.