Tools › Building Systems › Plumbing › Plumbing Pipe Sizing › Example
Small building with 10 flush-valve closets: Hunter's demand curve, the BMS 79 pressure budget, a 4-in stack with its vent and the building drain
| Tool | Plumbing Pipe Sizing |
| Source | Hunter, R. B. (1940). Methods of Estimating Loads in Plumbing Systems. NBS BMS 65 (Tables 1, 2, 7 and 9); Hunter, R. B. (1941). Water-Distributing Systems for Buildings. NBS BMS 79 (section V, Table 8); Wyly, R. S., and Eaton, H. N. (1961). Capacities of Stacks in Sanitary Drainage Systems for Buildings. NBS Monograph 31 (eqs 46, 52, 53, 55, 59, Tables 12–14, A-8). |
| Level | Professional |
Problem
A small public building has 10 flush-valve water closets (weight 10, p = 0.03, q = 27 gpm), 10 lavatories (weight 2), 4 service sinks (weight 3) and 2 showers (weight 4, p = 1/15, q = 8 gpm). The main holds 60 psi, the highest fixture is 25 ft up, a 2-in disk meter is installed, flush valves need 15 psi, the developed length is 150 ft plus 75 ft of fittings, the pipe is type L copper (C = 150) at 60 °F with 8 ft/s allowed. Find the design demand, the smallest copper main, and check a 4-in cast-iron stack carrying 80 DFU over 3 branch intervals with a 60-ft vent, and a 4-in building drain at 2 percent carrying the 140 DFU.
Inputs to Enter
- Fixtures: 10 WC flush valve (10 FU, p 0.03, q 27 gpm, 10 DFU), 10 lavatories (2 FU, 2 DFU), 4 service sinks (3 FU, 3 DFU), 2 showers (4 FU, p 0.0667, q 8 gpm, 4 DFU); flush valves predominate; computed curve; 1 % exceedance; no continuous demand
- Supply: 60 psi main, 25 ft lift, 2-in disk meter, 15 psi fixture minimum, 150 ft developed + 75 ft fittings, copper type L, Hazen-Williams C 150, 60 °F, 8 ft/s
- Stack: 80 DFU, 4 in, 3 branch intervals, r_s = 7/24, vent 60 ft; drain: 4 in, 2 %, n 0.013, 2 ft/s
Answers
- 140 fixture units → n_eq = 14 flush valves; exact design factor m = 2 (54 gpm); Hunter's interpolated curve m = 2.8 → 75.6 gpm (his drawn curve reads 76.2); normal approximation 51.4 gpm; exact joint distribution of the closets and showers 54 gpm
- Pressure budget: static 10.83 psi, meter 25 (75.6/160)² = 5.58 psi, available 60 − 10.83 − 5.58 − 15 = 28.59 psi over 225 ft = 12.71 psi per 100 ft
- 2-in copper L (ID 1.985 in): V = 7.84 ft/s, Hazen-Williams 4.51 psi/100 ft (Colebrook 4.47), loss 10.14 psi, residual 33.4 psi at the fixture; 1-1/2 in fails at 13.6 ft/s
- Stack: 80 DFU → 59.4 gpm (curve 1); capacity at 7/24 full 27.8 (7/24)^(5/3) 4^(8/3) = 143.8 gpm = 532 FU; fill 0.172; V_t = 3.0 (59.4/4)^0.4 = 8.83 ft/s, L_t = 4.05 ft; height rule S_3 = 240 × 5/4 = 300 FU, 100 per interval
- Vent: Q_a = 59.4 (1 − 0.172)/0.172 = 287 gpm, f = 0.0330; 2-in vent 30.6 ft, 2-1/2 in 74.4 ft (selected for 60 ft), 3 in 220 ft
- Drain: 140 DFU → 75.6 gpm; 4 in half full at 2 % carries 60.4 gpm at 3.08 ft/s, minimum slope for 2 ft/s 0.0084; the design flow runs at 0.573 D and 3.26 ft/s, so a 5-in drain is the smallest half full
Notes
The tool's default inputs are this case; press Submit. The fixture values are Hunter's (BMS 65 Table 1, Table 7; BMS 79 Table 6) and the building is the tool's own, checked by numpy/scipy (References/Plumbing-Sizing/checks/pl_check.py) in test_plumbing_pipe_sizing.php (528 checks), which also reproduces Hunter's Table 2, Table 3 and Table 9, his worked examples (1,325 FU → 247 gpm), the BMS 79 example and Monograph 31's Tables 12 to 14.