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Two immiscible fluids are flowing down between two flat, infinitely long flat parallel plates as shown in

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Two immiscible fluids are flowing down between two flat, infinitely long flat parallel plates as shown in the figure below. The plate on the left is moving down with a velocity of vA, and the plate on the right is moving up with a velocity vB. The dotted line is the interface between the two fluids. The fluids maintain constant widths as they flow downward and L1and L2are not equal. The flow is incompressible, parallel, fully developed, and laminar. You may ignore surface tension, and assume that the fluids are not open to the atmosphere and that the interface between the fluids is vertical at all times. Derive equations for the velocity profiles of both fluids when the flow is at steady state.

UB Fluid Fluid L2 L1 VA

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UB Fluid Fluid L2 L1 VA

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