Two similar rigid, plane rectangular plates are joined along the edge of length b by a smooth, oil-tight hinge. The plates make a small angle α = α(t) with one another. The space between the plates is filled with a Newtonian oil, which is squeezed out as the plates are pushed together by a force F perpendicular to each plate, applied at the outer edge. Assume α << 1, and a << b so Vx is negligible. Assume creeping flow in your analysis and neglect gravity. 

a) Use order of magnitude analysis and any relevant information to simplify the equations of motion.
 b) Show that P ≠ f(z). Derive an explicit expression for Vy (in terms of known parameters and/or pressure gradient term(s)).  

c) Calculate ∂P/∂y at the outer free edge, i.e. y = a, in terms of α ≡ dα/dt and known parameters.