Consider a system that resembles Couette flow but with a maj

Consider a system that resembles Couette flow, but with a major difference. In Couette flow, a fluid is trapped between two surfaces, and one of the surfaces moves with a constant velocity while the other is stagnant. Our system, on the other hand, involves two moving plates, albeit with different velocities (V1 and V2). Both plates move in the same direction. If the fluid viscosity is , the width of the plates is W and the distance between the plates is B, then obtain expressions for the following parameters in terms of V1, V2, , W, and B. a) shear stress (xy) b) volumetric flow rate of the fluid c) average velocity of the fluid Please show all the steps (beginning with the use of equations of motion) neatly in your solution.

Solution

Consider a system that resembles Couette flow, but with a major difference. In Couette flow, a fluid is trapped between two surfaces, and one of the surfaces moves with a constant velocity while the other is stagnant. Our system, on the other hand, involves two moving plates, albeit with different velocities (V1 and V2). Both plates move in the same direction. If the fluid viscosity is , the width of the plates is W and the distance between the plates is B, then obtain expressions for the following parameters in terms of V1, V2, , W, and B. a) shear stress (xy) b) volumetric flow rate of the fluid c) average velocity of the fluid Please show all the steps (beginning with the use of equations of motion) neatly in your solution.