A massive, precisely machined, $2$ m diameter granite sphere rests on a $1\mathrm{.}2$ m diameter cylindrical pedestal as shown below. When the pump is turned on and the water pressure within the pedestal reaches $50$ kPa $($gauge$),$ the sphere rises off the pedestal, creating a $0\mathrm{.}1$ mm gap through which the water flows. The sphere can then be rotated about any axis with minimal friction. $($a$)$ Estimate the pump flowrate, $Q_0,$ required to accomplish this. Assume the flow in the gap between the sphere and the pedestal is essentially viscous flow between fixed, parallel plates. $($b$)$ Describe what would happen if the pump flowrate were increased to $2Q_0.$