GATE ME 2021 Set 1 — Question 32
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Fluid Mechanics → Viscous & Pipe Flow → Parallel Plate & Hagen-Poiseuille
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Question
Consider fully developed, steady state incompressible laminar flow of a viscous fluid between two large parallel horizontal plates. The bottom plate is fixed and the top plate moves with a constant velocity of m/s. Separation between the plates is mm. There is no pressure gradient in the direction of flow. The density of fluid is kg/m, and the kinematic viscosity is m/s. The average shear stress in the fluid is ________ Pa (round off to the nearest integer).
Correct answer
79 to 81
Solution
For a steady laminar flow between parallel plates with no pressure gradient (Couette flow), the velocity profile is linear: , where is the velocity of the top plate and is the separation. The shear stress is given by .
1.Calculate the velocity gradient: .
2.Calculate the dynamic viscosity: .
3.Calculate the shear stress: .
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