The Alaskan pipeline runs 798 miles from Prudhoe Bay to Valdez. Both cities are at sea level. The design specifications for the pipeline require a capacity of 2.4 million barrels per day (1 barrel = 42 gallons). The crude oil is maintained at 140°F in the pipeline. At this temperature, the oil has a density of 53.7 lbm/ft3 and a viscosity of 0.00257 lbm/ft-s. The pipe is made of commercial steel. Along the pipeline are pumping stations capable of boosting the oil pressure. Each pumping station can provide a pressure increase of 1100 psi.

a. Construct a plot that shows the pipe diameter as a function of the number of pumping stations, N, for 1 ≤ N ≤ 30

b. The Alaskan Pipeline is 48-inch nominal diameter and has 12 pumping stations.
How does this compare to the plot that was generated in part (a) of this problem?

c. Use the plot generated in part (a) to discuss some of the issues that helped engineers arrive at the decision to construct a 48-inch pipeline with 12 pumping stations.