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Surface Stress

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The upper plate (plate 1) is moving to the right with a velocity V, the middle plate (plate 2) is free to move laterally under the action of the viscous forces applied to it. Assume steady state conditions; derive an equation for the velocity of the middle plate (plate 2). Assume the area of oil contact(Area = .9) is the same for all surfaces (i.e. upper plate (plate 1), middle (plate 2) and the bottom plate (fixed plate). See attached file.

u1 = viscosity between plates 1 and 2; t1 = distance between plates 1 and 2
u2 = viscosity between plate 2 and the fixed plate; t2 = distance between plate 2 and the fixed plate

Please give a complete solution and explain each step.

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This in-depth solution contains step-by-step calculations and explanations to derive an equation for the velocity of the middle plate.

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