Consider a Mach 4 flow over a compression corner with a deflection angle of \(32^{\circ}\). Calculate the oblique shock wave angle for the weak shock case using (a) Fig. 4.8 and (b) the \(\beta-\theta-M\) equation, Eq. (4.19). Compare the results from the two sets of calculations.

Figure 4.8:

\[\begin{equation*}
\tan \beta=\frac{M^{2}-1+2 \lambda \cos \left[\left(4 \pi \delta+\cos ^{-1} \chi\right) / 3\right]}{3\left(1+\frac{\gamma-1}{2} M^{2}\right) \tan \theta} \tag{4.19}
\end{equation*}\]

Transcribed Image Text:

90 80 Strong shock 70- 60 Weak shock Shock wave angle , degrees 30 20 10 50' 40 M = 2 M = 3 M = 5 0 - M < 1- 10 15 20 25 M M (0. max for M = 5 30 35 40 45 Deflection angle . degrees