Plumbing Math, Sizing Calculations, and Fixture Units
Core Arithmetic
Sizing questions reward disciplined unit handling. Convert everything to consistent units before calculating. Remember that a cubic foot holds 7.48 gallons, a gallon of water weighs 8.33 pounds, and one psi equals 2.31 feet of head. Slope is rise over run: a 1/4-inch-per-foot slope is a 2 percent grade. Pipe volume uses the internal diameter, not nominal size.
Fixture Units and Demand
Drainage sizing uses fixture units (FU or DFU), a relative measure of waste load, not gallons. Water supply sizing uses both fixture units and gallons per minute, with demand curves converting total FU to probable flow. Traps are sized by fixture unit load and by the fixture drain outlet. Vent sizing uses FU and developed length of the vent, and the trap arm length is limited by the fixture drain size (commonly the trap arm may not exceed the developed length equal to the trap arm diameter times a code factor, and must slope uniformly).
Traps in Exam Questions
The most common errors: using nominal pipe size to compute volume, forgetting to add the vertical rise to developed length, mixing fixture units for drainage with water supply values, and ignoring that a building drain and building sewer are sized the same but named differently. Watch for questions giving flow in gallons per minute and asking for pipe size - you must consult a sizing table rather than guess.
Worked Example
A 2-inch pipe at 1/4 inch per foot over 40 feet drops 10 inches. For volume: a 100-foot run of 2-inch Schedule 40 pipe (internal diameter about 2.067 inches) holds roughly 1.7 gallons per 10 feet - about 17 gallons - so verify by formula: area × length ÷ 231 for gallons when dimensions are in inches.