GATE XE 2021 Paper 1 — page 57

Questions 169–171 of 175. Imported answers require review unless explicitly marked reviewed.

In an incompressible fluid, the horizontal divergence is −0.01 s⁻¹. Then, the vertical velocity at 50 m above a flat surface is ____ m s⁻¹. Round off to one decimal place.

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In an atmosphere, temperature (T) decreases linearly with height above the ground (z), i.e., T(z) = T₀ − γ z, where γ is a constant. Surface pressure is 900 hPa. If the atmosphere is at rest, then the value of z at which the pressure decreases to half of that at the surface is ____ m (round off to the nearest integer).

Take acceleration due to gravity g = 10 m s⁻², gas constant R = 300 J kg⁻¹ K⁻¹, T₀ = 300 K and γ = 1/30 K m⁻¹, and the atmosphere behaves as an ideal gas.

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In a local Cartesian system, a zonal jet has a form u(y) = u₀ (1 − y²/L²), for −L ≤ y ≤ L. Here, y is the meridional distance measured from the axis of the jet and is positive northward. The vertical component of vorticity of this flow at y=L/2 is ____ s⁻¹. Round off to 3 decimal place.

Take u₀ = 50 m s⁻¹ and L = 5 km.

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2021 · Paper 1

Question 16

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Question 18