Drilling mud has to be pumped down into an oil well that is $8000 \mathrm{ft}$ deep. The mud is to be pumped at a rate of $50 \mathrm{gpm}$ to the bottom of the well and back to the surface, through a pipe having an effective ID of $4 \mathrm{in}$. The pressure at the bottom of the well is $4500 \mathrm{psi}$. What pump head is required to do this? The drilling mud has properties of a Bingham plastic, with a yield stress of $100 \mathrm{dyn} / \mathrm{cm}^{2}$, a limiting (plastic) viscosity of $35 \mathrm{cP}$, and a density of $1.2 \mathrm{~g} / \mathrm{cm}^{3}$.