GATE 2020 AE – Question 50

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

A laminar flat-plate boundary layer has $\delta/x=5.2/\sqrt{Re_x}$ and velocity varies linearly with wall distance inside it. Free-stream velocity is 3 m/s and kinematic viscosity $1.5\times10^{-5}$ m²/s. Find displacement thickness at x = 0.5 m, in mm to 2 decimals.

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Correct answer: 4.00 to 4.20

Explanation

$Re_x=Ux/\nu=3(0.5)/(1.5\times10^{-5})=100000$. Therefore δ = 5.2(0.5)/√100000 = 0.0082219 m. For u/U = y/δ, $\delta^*=\int_0^\delta(1-y/\delta)dy=\delta/2$. Thus displacement thickness is 4.11 mm.

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