The Water Demand Calculator Leaves Home

By Steven Buchberger, PhD, PE

Instantaneous peak water demand is an important consideration when designing a new building. The peak water demand affects the scale and cost of the entire premise plumbing system, including meter size, heater capacity, pipe diameters, valves, and other related hydraulic appurtenances. Determining the peak water demand is a challenge because water use in a building is unpredictable. The diurnal pattern of water use never repeats exactly and, as a consequence, the magnitude of the peak demand varies randomly from day to day.

This problem was first investigated nearly 100 years ago by Dr. Roy Hunter, a research physicist at the National Bureau of Standards. Recognizing that water use is a random process, Hunter applied probability principles to predict peak water demand based on the total number of fixtures in a building and on the flow drawn when a fixture is operated. Hunter’s crowning achievement was development of a design graph, known as “Hunter’s Curve,” giving the 99th percentile water demand versus total fixture units for any combination of indoor end uses (Hunter 1940). Hunter did not attempt to predict the absolute maximum possible water demand. Instead, he defined a threshold for design such that there is only a 1% chance that the actual peak period demand will exceed the load estimated from his curve.

Hunter’s iconic curve is a stunning blend of theoretical rigor and practical simplicity. It quickly became the basis for plumbing codes in the United States and across the globe (Buchberger et al, 2012). Hunter’s work established the standard for satisfactory service of building water supply systems. The problem, however, is that Hunter’s curve is frozen in time. It is a snapshot of peak water use in 1940.

In recent years, a growing consensus has emerged among practicing engineers that Hunter’s curve leads to overdesign of the premise plumbing system in new buildings. There are a couple reasons for this. First, Hunter’s assumption of congested service (i.e., users que at fixtures) often does not hold. Second, flow rates based on plumbing fixtures from the 1930s do not apply to the new generation of water-conserving fixtures, especially those imposed by passage of the 1992 Energy Policy Act and other green plumbing codes.

There have been many attempts to salvage Hunter’s curve by tweaking fixture-unit values for contemporary end use applications. Often these modifications stemmed from engineering judgment rather than observable data. These ad hoc adjustments frequently resulted in discrepancies among fixture-unit values posted in various plumbing codes (Cole 2012).

In 2011, the International Association of Plumbing and Mechanical Officials (IAPMO) and the American Society of Plumbing Engineers (ASPE) in collaboration with the Water Quality Research Foundation (WQRF) convened a task group to review methods for estimating peak demands in buildings fitted with water-conserving plumbing fixtures. Researchers from the University of Cincinnati also joined the team.

The task group acquired a large database of high resolution indoor water use measurements taken between 1996 and 2011 at nearly 1,100 single-family homes in 62 cities across the United States. Because the dataset provided statistics for residential end use only, the scope of work was narrowed to single and multi-family residential dwellings. Residential indoor fixtures considered in the database were bathtubs, showers, dishwashers, clothes washers, faucets, and toilets.

The task group was charged with developing a probability model to predict the peak water demand for single and multi-family dwellings having water-conserving plumbing fixtures. In other words, the goal was to bring Hunter’s curve into the 21st century. Not surprisingly, analysis of the modern residential database led to several significant changes in the parameters of the binomial probability model that underpins Hunter’s method. Most notably, for tank toilets, the peak hour probability of fixture use dropped from 20% to 1% and the fixture flow rate decreased from 4 to 3 GPM (Omaghomi et al 2020). A complete listing of all recalibrated parameter values for water-conserving residential fixtures is available in the summary report (Buchberger et al 2017).

Rather than create a new design curve that essentially would be a snapshot of peak water use in 2020, the task group opted to employ a digital-age resource. Keeping with the spirit of Hunter’s probabilistic approach, a set of three algorithms was coded into a user-friendly excel spreadsheet called the Water Demand Calculator (WDC). The user simply provides the itemized fixture count for their residential building. Then, armed with information about the probability of fixture use and flow of an operating fixture (the p and q values, respectively), the WDC computes the 99th percentile of the peak period water demand. The WDC program is available at no charge from the IAPMO website (www.iapmo.org/water-demand-calculator). Figure 1 shows the WDC input template and computed results for a multi-family building with 10 apartments.

For single family homes, where the total fixture count is generally under 30, the WDC uses exhaustive enumeration (ExEn) to delineate all possible water use combinations. While offering an exact solution, ExEn carries a high computational burden. For instance, in a home with 15 fixtures, ExEn involves 215 = 32,768 calculations. For large residential buildings with hundreds of fixtures, ExEn is intractable. In this case, the WDC estimates the 99th percentile of the water demand using the normal approximation to the Poisson-binomial distribution, as first proposed by ASPE engineer Robert Wistort (1994). In the region between these household extremes, the WDC uses a new modified Wistort method to predict peak demands during the transition from single family homes to large residential buildings.

Extensive beta testing of the WDC at several residential locations across the United States and Australia has yielded very reasonable results. Based on this encouraging performance, the WDC has been incorporated into the Uniform Plumbing Code (IAPMO 2018). Next year with the release of the fourth edition of AWWA’s M22 Manual of Water Supply Practice, the WDC will be endorsed as the preferred method for estimating peak water demands in all residential buildings.

Like Hunter’s seminal work from 1940, the theoretical basis for the WDC has a rock solid foundation. With proof of concept clearly demonstrated, the WDC is now poised to leave home and serve as a design aid for estimating peak demands in non-residential buildings. To punch this ticket, one major hurdle remains: we must assemble and analyze a national database of water use measurements from buildings in the non-residential sector, as outlined in the recent NIST report on research needs for premise plumbing systems (Persily et al., 2020). This final step is essential to estimate values for the probability of fixture use, the elusive p-values that lie at the heart of Hunter’s curve and the WDC.

References

• Buchberger, S.G., E.M.J. Blokker, D.P. Cole (2012) “Estimating Peak Water Demands in Hydraulic Systems I – Current Practice”, in Proc of WDSA2012 Symposium, Adelaide, South Australia, Sept 24-27, 2012.
• Buchberger, S.G., T. Omaghomi, T. Wolfe, J. Hewitt, D.P. Cole (2017) “Peak Water Demand Study – Probability Estimates for Efficient Fixtures in Single and Multi-Family Residential Buildings”, Executive Summary, IAPMO, Chicago, IL
• Cole, D.P. (2012) “Determining fixture units for high efficiency fixtures,” IAPMO.
• Hunter, R. B. (1940). “Methods of Estimating Loads on Plumbing Systems.” Rep. No. BMS65, US National Bureau of Standards, Washington DC. IAPMO (2018). “Uniform Plumbing Code.” IAPMO, Ontario, CA, Volume 1.
• Omaghomi, T., S.G. Buchberger, D. Cole, J. Hewitt, and T. Wolfe, (2020) “Probability of Water Fixture Use during Peak Hour in Residential Buildings”, ASCE J. Water Resources Planning and Management, 146(5). DOI: 10.1061/(ASCE)WR.1943-5452.001207.
• Persily, A., D. Yashar, N.M. Ferretti, T. Ullah, W. Healy (2020) “Measurement Science Research Needs for Premise Plumbing Systems”, NIST Technical Note 2088, U.S. Department of Commerce, https://doi.org/10.6028/NIST.TN.2088.
• Wistort, R. A. (1994). “A new look at determining water demands in building: ASPE direct analytic method.” Technical Proceedings; ASPE 1994 Convention, American Society of Plumbing Engineers, Kansas City, MO, 17-34.

Article courtesy of Working Pressure magazine

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Last modified: December 30, 2022