Chapter 1, Problem 1.48P

A thin plate is separated from two fixed plates by very viscous liquids ${\mu }_1$ and ${\mu }_2$, respectively, as in Fig. P1.48. The plate spacings h₁and h₂arc unequal, as shown. 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, ${\mu }_1$ and ${\mu }_2$ ?