A high-rise condominium building has condominium units stacked symmetrically from floor to floor. The following number and type of plumbing fixtures serve each condominium: one bathtub, two water closets, two lavatories, one kitchen sink, and one dishwasher. Assume that the horizontal fixture branches serving these fixtures flow into a single waste stack and single vent stack. Each stack serves seven condominium units. Assume the vent stack extends through the roof and is 78 ft long. Determine the minimum pipe diameter required for:
a. The horizontal fixture branch
b. The waste stack at base of stack
c. The vent stack at top of stack