Topic: Fluid Mechanics
An air flow with Mach number 2.0 passes through a normal shock wave. If the ratio of specific heats of air is 1.4, find the shock strength.
- A. 2.5
- B. 3.5
- C. 1.5
- D. 4.5
Answer: B. 3.5
Explanation: Shock strength is defined as $\frac{\Delta P}{P_1} = \frac{P_2 - P_1}{P_1} = \frac{P_2}{P_1} - 1$.
For a normal shock wave, the pressure ratio is $\frac{P_2}{P_1} = 1 + \frac{2\gamma}{\gamma+1}(M_1^2 - 1)$.
$\frac{P_2}{P_1} = 1 + \frac{2(1.4)}{1.4+1}(2^2 - 1) = 1 + \frac{2.8}{2.4}(3) = 1 + 3.5 = 4.5$.
Shock strength = $4.5 - 1 = 3.5$.