A solvent-extraction operation is carried out continuously in a plate column with gravity flow. The unit is operated 24 h/day. A feed rate of 1500 ft3/day must be handled 300 days per year. The allowable velocity per square foot of cross-sectional tower area is 40 ft3 of combined solvent and charge per hour. The annual fixed costs for the installation can be predicted from the following equation:
where Fsf = cubic feet of solvent per cubic foot of feed. Operating and other variable costs depend on the amount of solvent that must be recovered, and these costs are $0.04 for each cubic foot of solvent passing through the tower. What tower diameter should be used for optimum conditions of minimum total cost per year?