A coal slurry is to be transported by pipeline. It has been determined that the slurry may be described by the power law model, with a flow index of 0.4 , an apparent viscosity of $50 \mathrm{cP}$ at a shear rate of $100 \mathrm{~s}^{-1}$, and a density of $90 \mathrm{lb}_{\mathrm{m}} / \mathrm{ft}^{3}$. What horsepower would be required to pump the slurry at a rate of $900 \mathrm{gpm}$ through an $8 \mathrm{in}$. sch 40 pipe that is 50 miles long?