Project ForgeFluid Mechanics
Bernoulli's Equation & Flow
GATE 2014
Medium
In a simple concentric shaft-bearing arrangement, the lubricant flows in the 2 mm gap between the shaft and the bearing. The flow may be assumed to be a plane Couette flow with zero pressure gradient. The diameter of the shaft is 100 mm and its tangential speed is 10 m/s. The dynamic viscosity of the lubricant is 0.1 kg/m·s. The frictional resisting force (in newton) per 100 mm length of the bearing is __________.
15.7 N(± 0.6 accepted)
Explanation
Couette-flow shear stress τ=μV/h=0.1×10/0.002=500 Pa. Shear area for 100 mm length: A=πDL=π×0.1×0.1≈0.03142 m². Force=τA=500×0.03142≈15.7 N.
Source: GATE ME 2014 (Session 1 / Set-1) (2014)
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