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GATE 2020 CH – Question 46

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

Fully developed laminar Bingham-plastic flow is in a tube of radius 0.01 m under a 10 kPa drop over length 1.0 m. The profile is flat for r < r꜀ and sheared outside as shown, with r꜀ = 0.001 m. The finite-centre-stress balance is $d(r\tau_{rx})/dr=r(-\Delta P/L)$. Find yield-stress magnitude in Pa.

Diagram for GATE 2020 CH question 46
  1. 1
  2. 5
  3. 8
  4. 12

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Correct answer: (B) 5

Explanation

Integrating the force balance and excluding a singular centre term gives $|\tau_{rx}(r)|=\Delta P\,r/(2L)$. The plug boundary r꜀ occurs where shear stress reaches the yield stress. Hence $\tau_y=10000(0.001)/[2(1)]=5$ Pa, B. The tube radius sets wall stress; the smaller plug radius sets the requested yield stress.

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