Code Stories · why the rule exists
Drainage Fixture Units (DFU): Hunter's Probability Method
The rule in Massachusetts today
Water closet, tank type = 4 DFU; water closet, valve operated = 6 DFU; lavatory = 1; horizontal fixture branch 2 in. = 6 DFU max; 3 in. = 34 DFU, not more than four water closets (facts.json, verified against 248 CMR 10.15).
- Water closet, tank type = 4 DFU (248 CMR 10.15 Table 1)
- Water closet, valve operated = 6 DFU (248 CMR 10.15 Table 1)
- Lavatory = 1 DFU (248 CMR 10.15 Table 1)
- Bathtub or tub & shower unit = 2 DFU (248 CMR 10.15 Table 1)
- Shower stall, residential = 2 DFU (248 CMR 10.15 Table 1)
- Kitchen sink, residential (with or without disposer) = 2 DFU (248 CMR 10.15 Table 1)
- Laundry connection, residential = 3 DFU (248 CMR 10.15 Table 1)
- Horizontal fixture branch 1-1/2 in. = 3 DFU max (248 CMR 10.15 Table 2)
- Horizontal fixture branch 2 in. = 6 DFU max (248 CMR 10.15 Table 2)
- Horizontal fixture branch 3 in. = 34 DFU max, not more than four water closets (248 CMR 10.15 Table 2)
- 3 in. horizontal branch: not more than four water closets (248 CMR 10.15 Table 2 footnote)
- Horizontal fixture branch 4 in. = 160 DFU max (248 CMR 10.15 Table 2)
- Stack 3 in. = 48 DFU max, no more than four water closets (248 CMR 10.15(7) Table 3)
- Continuous/semi-continuous flow: 2 fixture units per gpm (248 CMR 10.15(2)(b))
Why it exists
No building runs every fixture at once, and sizing pipes as if it did wastes money. Sizing for the average load would fail at peak times. Roy B. Hunter at the National Bureau of Standards treated fixture use as a probability problem: given how long each fixture flows and how often it is used, how many are likely to be flowing at the same moment? He weighted fixtures on an 'arbitrary scale' (fixture units) and designed for a load that would be exceeded only a small fraction of the time. His worked example gave 'wholly satisfactory service 99 percent of the time.' Because the method is statistical, doubling the number of fixtures does not double the design load. That is why fixture-unit totals do not convert linearly to flow.
How it came to be
- 1924 — Hunter's own reference [1] is the Commerce Department's earlier plumbing requirements, the base his work built on. archive.org
- 1936 — Hunter cites MIT's Thomas R. Camp on water-closet hydraulics, published by the Massachusetts State Association of Master Plumbers. archive.org
- 1940 — BMS 65 defines the fixture unit. archive.org
- 1940 — Hunter's design criterion. archive.org
- 1940 — Hunter is explicit that the method estimates a probability, not a maximum. archive.org
- 1940 — For drainage, Hunter gives the water closet the same weight whether it has a flush valve or a tank. archive.org
- 1940 — Report issued; NIST catalogs it as NBS BMS 65, dated 1940. nist.gov
Make it stick
Mnemonic: 'A fixture unit is a vote, not a volume.' Each fixture gets a weighted vote on how big the pipe must be, and the table turns the total votes into a size.
On the exam
Expect MA table lookups (248 CMR 10.15 Table 1: tank WC 4, valve WC 6, lavatory 1, tub 2, residential shower 2, residential kitchen sink 2, laundry connection 3), maximum DFU per pipe size and slope (Table 2 horizontal: 1-1/2 in. 3, 2 in. 6, 3 in. 34 with no more than four water closets, 4 in. 160; Table 3 stacks), adding DFUs for a bathroom group, and the idea that DFU totals are not additive flows. Continuous flows count 2 fixture units per gpm (10.15(2)(b)). WSFU (water supply) and DFU (drainage) are separate tables.
What people get wrong
- 1 DFU equals 7.5 gpm (or 1 cubic foot per minute). UNVERIFIED as a Hunter definition: this equivalence does not appear in BMS 65, which calls the scale 'arbitrary.' Do not teach it as the definition.
- Twice the fixtures means twice the peak flow. Hunter's curve is probabilistic, so peak demand grows more slowly than the number of fixtures.
- Fixture units predict the maximum load. Hunter wrote that it is 'impossible to determine or to estimate closely' the maximum. The method estimates a load with a chosen chance of being exceeded.
- Hunter gave tank and flush-valve toilets the same drainage weight, so they carry the same DFU in Massachusetts. No. That was Hunter's 1940 reasoning. The current MA table (248 CMR 10.15 Table 1) says tank-type = 4 DFU and valve-operated = 6 DFU.
Try it: 3 real practice questions
Q1. Under 248 CMR 10.15 Table 1, what is the drainage fixture unit value of a tank-type toilet?
The Massachusetts table assigns 4 DFU to a tank-type toilet and 6 DFU to a flushometer (valve-operated) toilet. The 3 DFU value is the IPC figure for 1.6 gpf toilets, and 248 CMR does not use it. On the MA exam, size drains from the MA table.
248 CMR 10.15 Table 1Q2. Using 248 CMR 10.15 Table 1, what is the total DFU load of a tank-type toilet, a lavatory (1-1/4" outlet) and a bathtub?
Massachusetts assigns a tank-type toilet 4 DFU, a lavatory 1 DFU and a bathtub or tub/shower 2 DFU, so the total is 7. Unlike the IPC, 248 CMR has no reduced 'bathroom group' value and does not vary the toilet value by flush volume. Add the individual fixture values from the MA table.
248 CMR 10.15 Table 1Q3. What is the maximum number of fixture units (DFU) allowed on a 2-inch horizontal branch?
Branch capacity tables limit fixture units so the pipe runs only partly full, leaving air space above the water. Overloading a branch makes it run full, which slows flow and can siphon the traps connected to it. For a 2 in. horizontal branch the 248 CMR 10.15 limit is 6 DFU.
248 CMR 10.15These come from the PressureTest bank. Start 7 days free for the full bank, timed exam simulations and drawn isometric problems.