Question

What will be the pressure-height ratio of air at an altitude of 9144m? (L0=-0.0065 K/m, T0=288.15K, P0=101325 N/m^2)

(a) 0.297

(b) 0.596

(c) 0.359

(d) 0.458

I had been asked this question in unit test.

This intriguing question comes from Standard Atmospheric Model topic in division Atmosphere and Air Data Measurement of Aircraft Performance

Answer 1

The correct choice is (a) 0.297

The explanation: The answer is 0.297.

Given L0=-0.0065 K/m, T0=288.15K, P0=101325 N/m^2, H=9144m, we know g0=9.81m/s^2, R=287 J/kg-K

From \(\frac{p}{p_0}\)=[1 + \(\frac{L_0}{T_0}\)H]^\(\frac{-g_0}{RL_0}\)

\(\frac{P}{P_0}\)=[1 + \(\frac{-0.0065}{288.15}\)9144]^\(\frac{-9.81}{287*-0.0065}\)

 \(\frac{P}{P_0}\)=0.297.