GATE 2023 ME – Question 19

Fluid Mechanics · Viscous flow, boundary layer and elementary turbulent flow · 1 mark · Multiple choice

Air (density = 1.2 kg/m$^3$, kinematic viscosity = $1.5 \times 10^{-5}$ m$^2$/s) flows over a flat plate with a free-stream velocity of 2 m/s. The wall shear stress at a location 15 mm from the leading edge is $\tau_w$. What is the wall shear stress at a location 30 mm from the leading edge?

$\tau_w/2$
$\sqrt{2}\,\tau_w$
$2\tau_w$
$\tau_w/\sqrt{2}$

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Correct answer: (D) $\tau_w/\sqrt{2}$

Explanation

At 30 mm, $Re_x = \frac{2 \times 0.03}{1.5 \times 10^{-5}} = 4000$, which is well below the transition value, so the boundary layer is laminar. For a laminar boundary layer $\tau_w \propto x^{-1/2}$. Doubling $x$ gives $\tau_w/\sqrt{2}$.