5.2 Water Supply Fixture Units (WSFU) & Demand Estimations

Water Supply Fixture Units (WSFU) & Demand Estimations

Designing a potable water distribution network requires calculating how much water the system must deliver simultaneously. If a plumbing engineer simply summed the maximum flow rate of every connected faucet, shower, toilet, and hose bibb, the resulting design would assume that every valve in the building is opened wide at the exact same instant. Such an assumption would produce grotesquely oversized pipes, astronomical construction costs, sluggish water velocities that promote biofilm colonization, and severe water stagnation.

To solve this hydraulic problem, the plumbing industry relies on Water Supply Fixture Units (WSFU) and the empirical probability models developed by Dr. Roy B. Hunter of the National Bureau of Standards (now NIST) in 1940. Adopted within Appendix E of the Florida Plumbing Code (FPC), the WSFU methodology assigns a standardized mathematical weight to each fixture based on its flow rate, frequency of use, and the duration of each flushing or drawing cycle.

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1. Hunter's Curve & Simultaneous Probability Theory

Dr. Hunter recognized that plumbing fixtures operate intermittently. A residential flush tank toilet discharges for approximately 10 to 15 seconds once every several hours; a lavatory faucet flows for 15 to 30 seconds to wash hands.

The Binomial Probability Distribution

Using binomial probability theory, Hunter calculated the statistical likelihood that multiple fixtures would operate at the precise same second. For a system with $n$ identical fixtures, each having a probability $p$ of being in use at any random moment, the probability $P(m)$ that exactly $m$ fixtures will operate concurrently is expressed by:

$P(m) = \frac{n!}{m!(n - m)!} p^m (1 - p)^{n - m}$

From these calculations, Hunter established a design threshold: piping should be sized for a peak load that will not be exceeded more than 1 percent of the time during peak morning or evening demand periods.

The resulting mathematical curve—known as Hunter's Curve—translates a cumulative tally of fixture units into an expected peak volumetric flow rate in Gallons Per Minute (GPM).

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2. Private vs. Public Occupancy Classifications

The Florida Plumbing Code establishes different WSFU values depending on whether a fixture is installed in a private or public facility (FPC Section E103.3):

• Private Application: Plumbing fixtures in residences, apartments, condominiums, private hotel/motel guest rooms, and private executive office suites intended for the exclusive use of an individual or family. These fixtures experience low frequency of use and minimal simultaneous overlap.
• Public Application: Plumbing fixtures in schools, gymnasiums, sports stadiums, restaurants, office building corridors, public restrooms, transportation terminals, and commercial shopping centers. These fixtures experience continuous, intense usage patterns with high probabilities of simultaneous operation.

Because public fixtures are used much more frequently, their assigned WSFU ratings are substantially higher than their residential counterparts.

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3. Code-Prescribed WSFU Values (FPC Table E103.3(2))

FPC Table E103.3(2) assigns standardized fixture unit values for private and public installations. Understanding the distribution between total, cold, and hot loads is essential for Journeyman licensing examinations.

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4. The 75% Allocation Rule for Hot & Cold Branches

When sizing individual water distribution piping branches under FPC Section E103.3, plumbers must observe a critical mathematical principle:

The Branch Allocation Principle

• When a water distribution branch or riser supplies fixtures that require both hot and cold water (such as a lavatory, bathtub, or kitchen sink), the cold water branch and the hot water branch are each sized for 75 percent (3/4) of the total fixture unit rating for that fixture.
• Why 75%? A bather in a shower or someone washing hands does not run 100% full cold water and 100% full hot water simultaneously; they mix the streams to achieve a comfortable temperature (typically 100°F to 105°F). Assigning 75% ensures adequate volume if an occupant shifts the mix heavily toward one side while accounting for diversity.

Dedicated Single-Temperature Fixtures (The 100% Rule)

• Cold-Only Fixtures: Water closets (flush tank or flushometer) and exterior hose bibbs consume only cold water. Therefore, 100 percent of their WSFU rating is assigned directly to the cold water supply.
• Hot-Only Fixtures: Modern domestic dishwashers connect exclusively to the hot water supply. Therefore, 100 percent of the dishwasher's WSFU rating (1.5 WSFU) is assigned to the hot water piping, with 0 WSFU added to the cold branch.

[!WARNING] A frequent trap on the Florida Journeyman Plumber exam is applying the 75% factor to water closets or hose bibbs. Never apply the 75% factor to single-temperature fixtures! Water closets add 100% of their load to the cold branch; dishwashers add 100% of their load to the hot branch.

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5. Converting WSFU to Peak Demand: Flush Tank vs. Flush Valve

Once total fixture units are aggregated, plumbers must convert the WSFU load into peak flow demand in Gallons Per Minute (GPM) using FPC Table E103.3(3). The code provides two separate demand curves:

1. System with Predominantly Flush Tanks (Curve 1)
2. System with Flushometer Valves (Curve 2)

+-----------------------------------------------------------------------------+
|                  HUNTER'S CURVE DEMAND COMPARISON (GPM)                     |
+-----------------------------------------------------------------------------+
| Total WSFU   | Flush Tank System (GPM)     | Flushometer Valve System (GPM) |
+--------------+-----------------------------+--------------------------------+
| 5            | 3.0                         | 15.0                           |
| 10           | 8.0                         | 27.0                           |
| 20           | 14.0                        | 35.0                           |
| 30           | 20.0                        | 42.0                           |
| 40           | 24.0                        | 46.0                           |
| 50           | 28.0                        | 50.0                           |
| 60           | 32.0                        | 53.0                           |
| 80           | 38.0                        | 61.0                           |
| 100          | 43.5                        | 68.0                           |
| 150          | 57.0                        | 80.0                           |
| 200          | 65.0                        | 88.0                           |
| 300          | 81.0                        | 101.0                          |
| 500          | 124.0                       | 140.0                          |
+-----------------------------------------------------------------------------+

Why Do the Curves Diverge at Low Fixture Counts?

The dramatic divergence between the two curves at low fixture counts is a fundamental plumbing concept. A standard flush tank toilet slowly fills over 30 to 60 seconds through a small ballcock/fill valve drawing only 2 to 3 GPM.

In stark contrast, a commercial flushometer valve utilizes no storage tank; it relies on direct supply pipe pressure to deliver 25 to 35 GPM in a massive, instantaneous 4-to-10 second scouring burst. Consequently, a system with even a single flushometer valve must have piping large enough to supply that instantaneous 25+ GPM draw without collapsing the residual water pressure to other building fixtures.

As fixture counts grow into the hundreds, the statistical probability of simultaneous flushometer valve operations averages out, and the two curves gradually converge.

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6. Worked Calculation: Single-Family Residence WSFU & Demand

To solidify the principles, let us execute a complete water demand estimation for a two-story Florida single-family residence.

Plumbing Fixture Schedule

• Master Bathroom: 1 Gravity Flush Tank WC, 2 Lavatories, 1 Soaking Bathtub, 1 Separate Shower Stall.
• Guest Bathroom: 1 Gravity Flush Tank WC, 1 Lavatory, 1 Bathtub/Shower Combination.
• Powder Room (Half Bath): 1 Gravity Flush Tank WC, 1 Lavatory.
• Kitchen: 1 Domestic Kitchen Sink, 1 Domestic Automatic Dishwasher.
• Laundry Room: 1 Automatic Clothes Washer.
• Exterior: 2 Hose Bibbs (Sillcocks).

Step 1: Fixture Unit Tabulation Matrix

Step 2: Analysis of Results

• Total Building Demand (Building Main): 26.0 WSFU.
• Cold Water Main / Distribution Header: 20.5 WSFU.
• Hot Water Main / Water Heater Feed: 9.5 WSFU.

Step 3: Determining Peak Flow Rates in GPM (Hunter's Curve)

Consulting FPC Table E103.3(3) under Curve 1 (Flush Tanks):

• For 26.0 Total WSFU: Interpolating between 20 WSFU (14.0 GPM) and 30 WSFU (20.0 GPM): $\text{Peak Building Demand} = 14.0 + \left(\frac{26.0 - 20}{30 - 20}\right) \times (20.0 - 14.0) = 14.0 + (0.6 \times 6.0) = 17.6\text{ GPM}$
• For 9.5 Hot Water WSFU: Interpolating between 5 WSFU (3.0 GPM) and 10 WSFU (8.0 GPM): $\text{Peak Hot Water Demand} = 3.0 + \left(\frac{9.5 - 5}{10 - 5}\right) \times (8.0 - 3.0) = 3.0 + (0.9 \times 5.0) = 7.5\text{ GPM}$

This calculation establishes that the main water service pipe from the municipal meter must be engineered to deliver a peak demand of 17.6 GPM, while the water heater and hot water distribution main must supply 7.5 GPM.