GATE CE 2017 Set 1 — Question 12
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Water Resources Engineering → Laminar & Turbulent Flow → Flow Between Parallel Plates
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Question
For a steady incompressible laminar flow between two infinite parallel stationary plates, the shear stress variation is
Correct answer
(B) linear with zero value at the center
Solution
In a steady incompressible laminar flow between two parallel stationary plates (Plane Poiseuille flow), the velocity profile is parabolic. The shear stress is related to the velocity gradient by Newton's law of viscosity: .
For this specific flow, the shear stress distribution is linear across the gap. It varies from zero at the center line (where the velocity is at its maximum and the gradient is zero) to a maximum value at the stationary plates (where the velocity is zero due to the no-slip condition).
For this specific flow, the shear stress distribution is linear across the gap. It varies from zero at the center line (where the velocity is at its maximum and the gradient is zero) to a maximum value at the stationary plates (where the velocity is zero due to the no-slip condition).
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