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GATE 2023 AE – Question 15

Aerodynamics · Viscous flows: Hagen-Poiseuille flow, Couette flow and boundary layers · 1 mark · Multiple choice

Consider the Blasius solution for the incompressible laminar flat plate boundary layer. Among the following options, select the correct relation for the development of the momentum thickness θ with distance x from the leading edge along the length of the plate.

  1. $\theta\propto x^{2/3}$
  2. $\theta\propto x^{1/2}$
  3. $\theta\propto x^{1/7}$
  4. $\theta\propto x^{-2/3}$

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Correct answer: (B) $\theta\propto x^{1/2}$

Explanation

For the **Blasius solution** of the laminar boundary layer on a flat plate, the boundary-layer thickness and the momentum thickness grow with the square root of the distance:
$$\delta=\frac{5.0\,x}{\sqrt{Re_x}},\qquad\theta=\frac{0.664\,x}{\sqrt{Re_x}},\qquad Re_x=\frac{U_\infty x}{\nu}.$$

Since $Re_x\propto x$,
$$\theta\propto\frac{x}{\sqrt x}=x^{1/2}.$$

Answer **$\theta\propto x^{1/2}$** (B). (The $x^{4/5}$ growth belongs to a turbulent layer.)