GATE 2016 ME (ME2) – Question 50
Consider fluid flow between two infinite horizontal plates which are parallel (the gap between them being 50 mm). The top plate is sliding parallel to the stationary bottom plate at a speed of 3 m/s. The flow between the plates is solely due to the motion of the top plate. The force per unit area (magnitude) required to maintain the bottom plate stationary is _________ N/m2. Viscosity of the fluid µ = 0.44 kg/m-s and density ρ = 888 kg/m3.
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Correct answer: 26.3 to 26.5
Explanation
With no pressure gradient, the velocity profile varies linearly from0 to3m/s across0.050m. Shear stress is μdu/dy=0.44·3/0.050=**26.4N/m²**. The external restraining force per unit area on the bottom plate must oppose this shear with equal magnitude.