The GATE Grind

GATE 2024 AE – Question 38

Flight Mechanics & Space Dynamics · Atmosphere: Properties of the standard atmosphere · 2 marks · Multiple choice

As per the International Standard Atmosphere model, which one of the following options about density variation with increase in altitude in the isothermal layer is correct?

  1. remains constant
  2. increases linearly
  3. decreases linearly
  4. decreases exponentially

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Correct answer: (D) decreases exponentially

Explanation

In an isothermal layer the hydrostatic equation $dp = -\rho g\,dh$ with $p = \rho RT$ and constant $T$ gives $\rho = \rho_1 e^{-g(h - h_1)/RT}$, so density falls exponentially with height.