7) A thin plate is separated from two fixed plates by very viscous liquids µ1 and µ2, respectively. The plate spacings h1 and h2 are unequal. The contact area is A between the center plate and each fluid. (a) Assuming a linear velocity distribution in each fluid, derive the force F required to pull the plate at velocity V. (b) Is there a necessary relation between the two viscosities, µ1 and µ2? (7 pts)