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GATE 2020 CH – Question 43

Fluid Mechanics and Mechanical Operations · Flow through pipes, friction factors, flow meters and pumps · 2 marks · Multiple choice

An incompressible Newtonian fluid flows steadily and fully developed, laminar, through horizontal circular pipes I and II at the same volumetric rate. Pipe II has twice pipe I’s diameter. Find wall-shear-stress ratio τᵢ/τᵢᵢ.

  1. 0.5
  2. 2
  3. 4
  4. 8

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Correct answer: (D) 8

Explanation

For laminar circular-pipe flow, $\tau_w=8\mu\overline V/D$. At fixed volume flow Q, $\overline V=4Q/(\pi D^2)$, giving $\tau_w=32\mu Q/(\pi D^3)$. Thus wall shear scales as D⁻³ and $\tau_I/\tau_{II}=(D_{II}/D_I)^3=2^3=8$, D.

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