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GATE 2016 ME (ME2) – Question 24

Fluid Mechanics · Fluid properties, fluid statics, forces on submerged bodies, stability of floating bodies · 1 mark · Multiple choice

Assuming constant temperature condition and air to be an ideal gas, the variation in atmospheric pressure with height calculated from fluid statics is

  1. linear
  2. exponential
  3. quadratic
  4. cubic

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Show answer and explanation

Correct answer: (B) exponential

Explanation

Hydrostatic equilibrium gives dp/dz=−ρg. For isothermal ideal gas, ρ=p/(RT), so dp/p=−g dz/(RT). Integration yields p=p0exp(−gz/(RT)), an **exponential variation, B**. A constant-density assumption would instead give a linear relation.