A coal-water slurry containing $65 %$ (by weight) coal is pumped from a storage tank at a rate of $15 \mathrm{gpm}$ through a $50 \mathrm{~m}$ long $1 / 2 \mathrm{in}$. sch 40 pipeline to a boiler where it is burned. The storage tank is at $1 \mathrm{~atm}$ pressure and $80^{\circ} \mathrm{F}$, and the slurry must be fed to the burner at $20 \mathrm{psig}$. The specific gravity of coal is 2.5 , and it has a heat capacity of $0.5 \mathrm{Btu} /\left(\mathrm{lb}_{\mathrm{m}}{ }^{\circ} \mathrm{F}\right)$.

(a) What power must the pump deliver to the slurry if it is assumed to be Newtonian with a viscosity of $200 \mathrm{cP}$ ?

(b) In reality, the slurry is non-Newtonian and can best be described as a Bingham plastic, with a yield stress of $800 \mathrm{dyn} / \mathrm{cm}^{2}$ and a limiting viscosity of $200 \mathrm{cP}$. Accounting for these properties, what would the required pumping power be?

(c) If the pipeline is well insulated, what will the temperature of the slurry be when it enters the boiler, for both case (a) and case (b)?