You would like to know the thickness of a paint film as it drains at a rate of $1 \mathrm{gpm}$ down a flat surface that is $6 \mathrm{in}$. wide and is inclined at an angle of $30^{\circ}$ to the vertical. The paint is nonNewtonian and can be described as a Bingham plastic with a limiting viscosity of $100 \mathrm{cP}$, a yield stress of $60 \mathrm{dyn} / \mathrm{cm}^{2}$, and a density of $0.9 \mathrm{~g} / \mathrm{cm}^{3}$. You have data from the laboratory for the film thickness of a Bingham plastic that has a limiting viscosity of $70 \mathrm{cP}$, a yield stress of $40 \mathrm{dyn} / \mathrm{cm}^{2}$, and a density of $1 \mathrm{~g} / \mathrm{cm}^{3}$ flowing down a plane $1 \mathrm{ft}$ wide inclined at an angle of $45^{\circ}$ to the vertical, at various flow rates.

(a) At what flow rate (in gpm) will the laboratory system correspond to the conditions of the other system?

(b) If the film thickness of the laboratory fluid is $3 \mathrm{~mm}$ at these conditions, what would the film thickness be for the other system?