GATE 2021 ME (ME1) – Question 32
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 $U=4$ m/s. Separation between the plates is 5 mm. There is no pressure gradient in the direction of flow. The density of fluid is 800 kg/m³, and the kinematic viscosity is $1.25\times10^{-4}$ m²/s. The average shear stress in the fluid is _____ Pa (round off to the nearest integer).
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Correct answer: 80
Explanation
Dynamic viscosity is $\mu=\rho\nu=0.1$ Pa·s. With no pressure gradient this is plane Couette flow, with linear velocity gradient U/h=4/0.005=800 s⁻¹.
Shear is uniform: $\tau=\mu U/h=\mathbf{80}$ Pa. Its average is therefore also 80 Pa.