Answer:
10.65°
Explanation:
To calculate the initial Mach Number
[tex]Sin \beta _{weak} = \frac{1}{Ma_1}[/tex]
[tex]Ma_1 = \frac{1}{sin \beta_weak}[/tex]
[tex]Ma_1 = \frac{1}{sin 30}[/tex]
[tex]Ma_1 = 2[/tex]
Now, to calculate the angle turned by the wall; we have the following expression.
[tex]tan \theta = \frac{2 cot \beta_i (Ma_1^2 sin^2 \beta_i -1 )}{Ma_1^2(k+cos2 \beta_i)+2}[/tex]
where:
[tex]\beta_i[/tex] = the angle between the initial flow direction = 40°
K is the ratio of specific heats o fair = 1.4
[tex]tan \theta = \frac{2 (cot 40) (2^2 (sin 40)^2 -1 )}{2^2(1.4+cos2 (40))+2}[/tex]
[tex]tan \theta = \frac{1.56}{8.295}[/tex]
[tex]tan \theta = 0.188[/tex]
[tex]\theta = tan ^{-1}( 0.188)[/tex]
[tex]\theta = 10.65^0[/tex]
