a$)$ A normal shock wave forms on the intake of an aircraft flying

at Mach $2\mathrm{.}0$ at $5$ km altitude, where the ambient static

temperature and pressure is $255$ K and $54$ kPa respectively.

Calculate the rise in static pressure and temperature when

the air flows through the normal shock wave formed at the

intake.

$[4$ marks$]$

b$)$ Suppose now that the air forms an oblique shock wave at

the wing leading edge of an aircraft so it is compressed

through a wing half angle of $12.$ Determine the rise in static

pressure and temperature in this case. How are your

findings relevant to the design of supersonic aerofoils?

$[8$ marks$]$

c$)$ The analysis is now extended to the flow past a symmetric

diamond aerofoil at a zero angle of attack, shown in figure

Q$2,$ with the same inlet conditions, semi$-$angles at the

leading and trailing edges of $12$ and a chord length of $1$ m $.$

Calculate the total drag per unit length in the spanwise

direction on the aerofoil.

Figure Q$2$: Flow past a symmetrical diamond$-$shaped aerofoil $($not to scale$).$