Chapter 4, Problem 98P

The narrow gap between two closely spaced circular plates initially is filled with incompressible liquid. At t = 0 the upper plate, initially h₀ above the lower plate, begins to move downward toward the lower plate with constant speed, V₀, causing the liquid to be squeezed from the narrow gap. Neglecting viscous effects and assuming uniform flow in the radial direction, develop an expression for the velocity field between the parallel plates. Hint: Apply conservation of mass to a control volume with the outer surface located at radius r. Note that even though the speed of the upper plate is constant, the flow is unsteady. For V₀ = 0.01 m/s and h₀ = 2 mm, find the velocity at the exit radius R = 100 mm at t = 0 and t = 0.1 s. Plot the exit velocity as a function of time, and explain the trend.