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GATE 2024 AE – Question 42

Aerodynamics · Viscous flows: Hagen-Poiseuille flow, Couette flow and boundary layers · 2 marks · Multiple choice

Consider a flat plate, with a sharp leading edge, placed in a uniform flow of speed $U$. The direction of the free-stream flow is aligned with the plate. Assume that the flow is steady, incompressible and laminar. The thickness of the boundary layer at a fixed stream-wise location $L$ from the leading edge of the plate is $\delta$. Which one of the following correctly describes the variation of $\delta$ with $U$?

  1. $\delta \propto U$
  2. $\delta \propto U^{3/2}$
  3. $\delta \propto U^{1/2}$
  4. $\delta \propto U^{-1/2}$

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Correct answer: (D) $\delta \propto U^{-1/2}$

Explanation

The Blasius thickness is $\delta = \frac{5L}{\sqrt{Re_L}} = 5\sqrt{\frac{\nu L}{U}}$, so at a fixed $L$, $\delta \propto U^{-1/2}$.