Question

Which of the following is the full-law calibration equation?

(a) pp-p=p0\(\Bigg[\Big\{1+\frac{\gamma-1}{2}\left(\frac{V_c}{a_0}\right)^2\Big\}^{\frac{\gamma}{\gamma-1}}-1\Bigg]\)

(b) pp-p=p0\(\Bigg[\Big\{1+\frac{\gamma+1}{2}\left(\frac{V_c}{a_0}\right)^2\Big\}^{\frac{\gamma}{\gamma-1}}-1\Bigg]\)

(c) p-p0=p0\(\Bigg[\Big\{1+\frac{\gamma-1}{2}\left(\frac{V_c}{a_0}\right)^2\Big\}^{\frac{\gamma}{\gamma-1}}-1\Bigg]\)

(d) pp-p=p0\(\Bigg[\Big\{1+\frac{\gamma-1}{2}\left(\frac{V_c}{a_0}\right)^2\Big\}^{\frac{\gamma}{\gamma+1}}-1\Bigg]\)

This question was posed to me at a job interview.

Asked question is from Measurement of Airspeed in section Atmosphere and Air Data Measurement of Aircraft Performance

Answer 1

Right option is (a) pp-p=p0\(\Bigg[\Big\{1+\frac{\gamma-1}{2}\left(\frac{V_c}{a_0}\right)^2\Big\}^{\frac{\gamma}{\gamma-1}}-1\Bigg]\)

To explain I would say: The full-law calibration equation is  pp-p=p0\(\Bigg[\Big\{1+\frac{\gamma-1}{2}\left(\frac{V_c}{a_0}\right)^2\Big\}^{\frac{\gamma}{\gamma-1}}-1\Bigg]\) where pp, p, p0 are pressures, Vc is calibrated air speed and a0 is speed of sound and γ is the ratio of specific heat at constant pressure to that of specific heat at constant volume.