Two Newtonian fluids are kept in the small gaps between three identical, large, thin parallel plates...

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Two Newtonian fluids are kept in the small gaps between three identical, large, thin parallel plates as shown. The area of each plate on one side is A. The viscosity of fluid A is twice the viscosity of fluid B. The top plate is pulled to the right at a constant velocity of 2U while the bottom plate is pulled to the left at a constant velocity of 3U. The gravitational effects can be neglected. 2U a) Determine the direction and the magnitude of velocity (in terms of U) with which the middle plate moves. Note that unlike the other two plates, the middle plate is not pulled. 3U fluid A fluid B h h b) What should the viscosity of fluid A be (in terms of the viscosity of fluid B) if the middle plate is to remain stationary? While solving parts (a) and (b), you should also (1) sketch the velocity profile in each fluid, clearly marking the key velocities, (ii) mark the directions of shear forces on the top and bottom plates, as well as on both sides of the middle plate, and (iii) determine the shear stress distribution along the vertical direction in each fluid. Two Newtonian fluids are kept in the small gaps between three identical, large, thin parallel plates as shown. The area of each plate on one side is A. The viscosity of fluid A is twice the viscosity of fluid B. The top plate is pulled to the right at a constant velocity of 2U while the bottom plate is pulled to the left at a constant velocity of 3U. The gravitational effects can be neglected. 2U a) Determine the direction and the magnitude of velocity (in terms of U) with which the middle plate moves. Note that unlike the other two plates, the middle plate is not pulled. 3U fluid A fluid B h h b) What should the viscosity of fluid A be (in terms of the viscosity of fluid B) if the middle plate is to remain stationary? While solving parts (a) and (b), you should also (1) sketch the velocity profile in each fluid, clearly marking the key velocities, (ii) mark the directions of shear forces on the top and bottom plates, as well as on both sides of the middle plate, and (iii) determine the shear stress distribution along the vertical direction in each fluid.