60 Consider the flow shown in the figure. Liquidl in the first layer has a viscosity...

  

Transcribed Image Text:

60 Consider the flow shown in the figure. Liquidl in the first layer has a viscosity l and is flowing under a constant pressure drop in the x- direction, dP/dx=K. Liquid is in contact with a second liquid of viscosity 2. The following assumptions are used: All flows are steady, Newtonian and incompressible. Plate of area A Liquid2 (12) h2 Liquidl (11) h1 Fixed plate The flow velocity in both layers is only in the x-direction and depends only on y. The second layer (liquid2) is thin such that the velocity field can be assumed linear. The velocity in the first layer is not necessarily linear The lower plate is fixed, while a force F is acting on the upper plate to maintain it moving at a constant velocity. Both plates have an area A. Determine the expression of the flow velocity at the interface between the two liquids. Express your answer in terms of the parameters of the problem, i.e. ul, 2, h1, h2, F, A and K. [Ans. u h, F - K 60 Consider the flow shown in the figure. Liquidl in the first layer has a viscosity l and is flowing under a constant pressure drop in the x- direction, dP/dx=K. Liquid is in contact with a second liquid of viscosity 2. The following assumptions are used: All flows are steady, Newtonian and incompressible. Plate of area A Liquid2 (12) h2 Liquidl (11) h1 Fixed plate The flow velocity in both layers is only in the x-direction and depends only on y. The second layer (liquid2) is thin such that the velocity field can be assumed linear. The velocity in the first layer is not necessarily linear The lower plate is fixed, while a force F is acting on the upper plate to maintain it moving at a constant velocity. Both plates have an area A. Determine the expression of the flow velocity at the interface between the two liquids. Express your answer in terms of the parameters of the problem, i.e. ul, 2, h1, h2, F, A and K. [Ans. u h, F - K