An open drum, $3 \mathrm{ft}$ in diameter, contains a mud that is known to be described by the Bingham plastic model, with a yield stress of $120 \mathrm{dyn} / \mathrm{cm}^{2}$, a limiting viscosity of $85 \mathrm{cP}$, and a density of $98 \mathrm{lb}_{\mathrm{m}} / \mathrm{ft}^{3}$. A $1 \mathrm{in}$. ID hose, $10 \mathrm{ft}$ long, is attached to a hole in the bottom of the drum to drain the mud out. How far below the surface of the mud should the end of the hose be lowered in order to drain the mud at a rate of $5 \mathrm{gpm}$ ?