1. [5 pts] A large movable plate is located between two large fixed plates as shown in the figure. It is moving with a constant velocity of Un. The total

gap between the plates is L. The fluid above the plate has a viscosity of u and the fluid below the plate has a viscosity of k.u where k is a constant number. Both fluids are Newtonian fluids and they have linear velocity distribution. Derive an expression for the distance h (depicted in the figure).in order to obtain minimum force to move the plate at constant velocity. (Assume constant pressure everywhere and no thickness for the middle plate.)