Question

What is the relation between pressure and density in an adiabatic air flow?

(a) \(\frac{p_1}{p_2}\)=(\(\frac{\rho_1}{\rho_2}\))^\(\frac{1}{\gamma}\)

(b) \(\frac{p_1}{p_2}\)=(\(\frac{\rho_1}{\rho_2}\))^γ

(c) \(\frac{p_1}{p_2}\)=(\(\frac{\rho_1}{\rho_2}\))^γ+1

(d) \(\frac{p_1}{p_2}\)=(\(\frac{\rho_1}{\rho_2}\))^γ-1

This question was addressed to me during an internship interview.

My question is from Measurement of Airflow Characteristics in section Atmosphere and Air Data Measurement of Aircraft Performance

Answer 1

Correct option is (b) \(\frac{p_1}{p_2}\)=(\(\frac{\rho_1}{\rho_2}\))^γ

Easiest explanation: The relation between pressure and density in an adiabatic air flow is given by \(\frac{p_1}{p_2}\)=(\(\frac{\rho_1}{\rho_2}\))^γ where p1, p2 are pressure values and ρ1, ρ2 are density values and γ is the ratio of specific heat at constant pressure to that of specific heat at constant volume.