The ETSI pipeline was designed to carry coal slurry from Wyoming to Texas at a rate of $30 \times 10^{6}$ tons/year. The slurry behaves like a Bingham plastic, with a yield stress of $100 \mathrm{dyn} / \mathrm{cm}^{2}$, a limiting viscosity of $40 \mathrm{cP}$, and a density of $1.4 \mathrm{~g} / \mathrm{cm}^{3}$. Using the cost of ANSI 1500\# pipe and $\$ 0.07 / \mathrm{kWh}$ for electricity, determine the most economical diameter for the pipeline if its economic lifetime is 25 year and the pumps are $50 %$ efficient.