Question

A projectile is travelling in air having pressure and temperature as

88.3 kN/m2 and – 2°C. If the Mach angle is 40°, find the velocity of the projectile. Take γ = 1.4 and

R = 287 J/kg K.

Answer 1

The semi-vertex angle α of the cone is known as Mach angle which is given by $\sin \alpha = \cfrac{C}{V}$, where C is the sonic velocity and V is the velocity of the projectile.

Since we know that $C=\sqrt{\gamma RT}$ , then we can calculate the velocity as:

$V=\cfrac{\sqrt{\gamma RT}}{\sin \alpha}=\cfrac{\sqrt{(1.4)(287\frac{J}{kgK})(271\,K)}}{\sin 40°} \\ \implies V= \cfrac{\sqrt{108887.8}}{0.642787} \dfrac{m}{s}= 513.36 \dfrac{m}{s}$

Then we conclude that the velocity of the projectile is 513.4 m/s.

Reference:

• Rajput, R. K. (2005). A textbook of engineering thermodynamics. Laxmi Publications.