Water is to be transferred at a rate of $500 \mathrm{gpm}$ from a cooling lake through a $6 \mathrm{in}$. diameter sch 40 pipeline to an open tank in a plant that is 30 miles from the lake.

(a) If the transfer pump is $70 %$ efficient, what horsepower motor is required to drive the pump?

(b) An injection station is installed at the lake that injects a high polymer into the pipeline to give a solution of $50 \mathrm{ppm}$ concentration with the following properties: a low shear-limiting viscosity of $80 \mathrm{cP}$, a flow index of 0.5 , and a transition point from low shear Newtonian to shear thinning behavior at a shear rate of $10 \mathrm{~s}^{-1}$. What horsepower is now required to drive the same pump to achieve the same flow rate?