Water flows through a conveyance system consisting of two pipes, A and B, in series. Total head loss through the two pipes is 28 feet. Pipe A is 12 inches in diameter and 1200 feet long. Pipe B is 8 inches in diameter and 600 feet long. It is proposed to add a third Pipe C, to extend the system an additional 900 feet. Determine the diameter of Pipe C to maintain the present flow rate if the total head loss through the three pipes cannot exceed 40 feet. Assume that f = 0.021, 0.020, and 0.022 for Pipes A, B, and C, respectively.