Topic: Fluid Mechanics
Air is accelerated isentropically from 100 m/s to 300 m/s in a nozzle. If the temperature at the inlet is 127°C, the inlet Mach number is (take R = 287 J/(kg K) and specific heat ratio = 1.4)
- A. 0.249
- B. 0.442
- C. 0.747
- D. 0.333
Answer: A. 0.249
Explanation: The actual inlet velocity is $V_1 = 100$ m/s. The inlet temperature in Kelvin is $T = 127 + 273 = 400$ K. The velocity of sound (acoustic velocity) for an ideal gas is $C = \sqrt{\gamma R T} = \sqrt{1.4 \times 287 \times 400} \approx 400.898$ m/s. The Mach number at the inlet is the ratio of actual velocity to the velocity of sound, $M = V_1 / C = 100 / 400.898 \approx 0.249$.