Plumbing Mathematics, Sizing, and Isometric Analysis
Units the exam mixes together
Keep drainage fixture units (DFU) separate from water supply fixture units (WSFU) - one sizes drains, the other sizes supply piping, and their tables are not interchangeable. Sizing also depends on developed length: the measured pipe run plus an equivalent length for each fitting. Add the fittings before entering the table.
Conversions worth memorizing
- 1 psi of pressure = 2.31 ft of elevation (0.433 psi per foot of rise).
- 1 gal = 231 in³; 1 ft³ = 7.48 gal.
- Area of a circle = 0.7854 × d².
- Slope: 1/4 in/ft = 2 percent; 1/8 in/ft = 1 percent.
- 45° offset: travel = offset × 1.414 (the rise and run each equal the offset).
- 22.5° offset: travel = offset × 2.613. 60° offset: travel = offset × 1.155.
Reading an isometric
Start at the building drain and work upstream. Identify the building sewer, stacks, fixture branches, and vents; check that every fixture has a trap, every trap has a vented arm, and every horizontal drain slopes toward the stack. Isometric questions usually hide a flat or back-sloped section, a missing vent, or a trap arm that is too long for its diameter.
Worked example: A 2-inch drain runs 40 ft at 1/4 in/ft. Total fall = 40 × 0.25 = 10 in. Change it to a 45° offset of 18 in: travel = 18 × 1.414 = 25.5 in. And a fixture 20 ft above the meter loses 20 × 0.433 ≈ 8.7 psi of static pressure.