Acrylic latex paint can be described as a Bingham plastic with a yield stress of $200 \mathrm{dyn} / \mathrm{cm}^{2}$, a limiting viscosity of $50 \mathrm{cP}$, and a density of $0.95 \mathrm{~g} / \mathrm{cm}^{3}$.

(a) What is the maximum thickness at which a film of this paint could be spread on a vertical wall without running?

(b) If the power law model were used to describe this paint, such that the apparent viscosity predicted by both the power law and Bingham plastic models is the same at shear rates of 1 and $100 \mathrm{~s}^{-1}$, what would the flow rate of the film be if it has the thickness predicted in (a)?