GATE ME 2016 Set 2 — Question 50
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Fluid Mechanics → Fluid Properties & Statics → Fluid Properties
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Question
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/m.Viscosity of the fluid kg/m-s and density kg/m.
Correct answer
26.3 to 26.5
Solution
The flow is a simple Couette flow between two parallel plates. The velocity profile is linear: , where m/s is the velocity of the top plate and mm m is the gap. The shear stress is constant throughout the gap and is given by Newton's law of viscosity:Substituting the given values:The force per unit area required to maintain the bottom plate stationary is equal to the magnitude of the shear stress exerted by the fluid on it, which is N/m.
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