Question

What is the mach number of the aircraft which is moving in air at an indicated total temperature is 780K and the temperature, recovery factor at that point are 300K and 2?

(a) 1

(b) 2

(c) 0.1

(d) 0.2

I got this question in an interview for internship.

The origin of the question is Measurement of Air Temperature in portion Atmosphere and Air Data Measurement of Aircraft Performance

Answer 1

Right answer is (b) 2

For explanation I would say: The answer is 2. Given r=2, T=300K, Ti=780K and we know γ of air is 1.4. From the formula Ti=T[1+r\(\frac{\gamma-1}{2}\)M^2].

On substituting the values in the formula, we get 780=300[1+2\(\frac{1.4-1}{2}\)M^2].

On solving we get M=2.