A sludge is to be transported by pipeline. It has been determined that the sludge may be described by the power law model, with a flow index of 0.6 , an apparent viscosity of $50 \mathrm{cP}$ at a shear rate of $1 \mathrm{~s}^{-1}$, and a density of $95 \mathrm{lb}_{\mathrm{m}} / \mathrm{ft}^{3}$. What hydraulic horsepower would be required to pump the sludge at a rate of $600 \mathrm{gpm}$ through a $6 \mathrm{in}$. ID pipe that is 5 miles long?