A pipeline is installed to transport a red mud slurry from an open tank in an alumina plant to a disposal pond. The line is $5 \mathrm{in}$. sch 80 commercial steel, 12,000 ft long, and is designed to transport the slurry at a rate of $300 \mathrm{gpm}$. The slurry properties can be described by the Bingham plastic model, with a yield stress of $15 \mathrm{dyn} / \mathrm{cm}^{2}$, a limiting viscosity of $20 \mathrm{cP}$, and an SG of 1.3. You may neglect any fittings in this pipeline.

(a) What delivered pump head and hydraulic horsepower would be required to pump this mud?

(b) What would be the required pump head and horsepower to pump water at the same rate through the same pipeline?

(c) If $100 \mathrm{ppm}$ of fresh Separan AP-30 polyacrylamide polymer were added to the water in case (b), what would the required pump head and horsepower be?