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GATE 2017 ME (ME2) – Question 27

Fluid Mechanics · Bernoulli's equation and fluid acceleration · 1 mark · Multiple choice

In laminar zero-incidence flow over a flat plate, wall shear is $\tau_w$. Positions $x_1,x_2$ are measured downstream from the leading edge. If $x_1>x_2$, then ______.

  1. $\tau_w(x_1)=\tau_w(x_2)=0$
  2. $\tau_w(x_1)=\tau_w(x_2)\ne0$
  3. $\tau_w(x_1)>\tau_w(x_2)$
  4. $\tau_w(x_1)<\tau_w(x_2)$

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Show answer and explanation

Correct answer: (C) $\tau_w(x_1)>\tau_w(x_2)$

Explanation

For the laminar zero-pressure-gradient boundary layer, local skin friction is proportional to Re(x)⁻¹/². With fixed free-stream speed and properties, wall shear is proportional to x⁻¹/². Since x2>x1, shear at x1 is greater: **C**. The growing boundary layer reduces the near-wall velocity gradient.