Hunter’s Horizontal Drain Capacities and the Uniform Plumbing Code, Part 2
Having demonstrated how Dr. Hunter derived capacities for horizontal drains in fixture units, we will now turn our attention to the UPC table for horizontal drains and compare it with BH13. The earliest archived edition of the UPC we have is from 1946. Table 7 compares the 1946 edition with Report BH13 showing UPC modifications in red. Notice that the corresponding values are for slopes at ½-inch per foot according to BH13. We will come back to this when considering UPC modifications.
The UPC diverges significantly from BH13 with respect to 4-inch pipe capacity, which will be discussed momentarily. The Western Plumbing Officials (now the International Association of Plumbing & Mechanical Officials, or IAPMO) did not allow any drainage flow into 1¼-inch-diameter pipe (until the 1973 committee permitted 1 fixture unit) and had limited 1½-inch pipe diameters to 1 fixture unit. The UPC fixture unit value for 2½-inch-diameter pipe is an interpolated value since BH13 did not list that size in its table.
Although the discrepancies between fixture units for 5-inch pipe (a difference of one toilet) and for 8-inch pipe (a difference of three toilets) is insignificant, the explanation for the UPC modifications eludes us. These values do not round to a whole number when translating into number of toilets as do the other values as explained previously. If the fixture unit value for 8-inch pipe was rounded to the nearest hundredth place, then there is no explanation why this didn’t occur for the fixture unit values for 12-inch pipe. Since the fixture unit values match exactly for pipe diameters of 6 inches, 10 inches, and 12 inches, we may postulate that the UPC fixture unit value for 8-inch pipe should reflect the same as BH13.
The discrepancy in fixture unit values for 4-inch pipe is problematic and significant. It reflects a difference of 11 toilets between BH13 and the UPC. We do not find this fixture unit value in the 1931 revision of BH13, but we do find it in BMS66 (1940) as well as in the ASA A40 National Plumbing Code (a tentative draft was proposed in the early 1940s by a committee that included three representatives from the Western Plumbing Officials Association). However, the 180 fixture unit value in both BMS66 and ASA A40 is only for a primary branch or building drains and sewers at 1/8-inch per foot slope, which does not correspond with the other fixture unit values that are at ½-inch per foot. This explanation would only deepen the mystery and does not explain why no other fixture unit values from BMS66 or the ASA A40 code were adopted in the UPC if indeed this value was borrowed from either one of them. Unfortunately, we must leave this fixture unit value unresolved and without explanation.
Further modifications in fixture units were made for horizontal drains between 1950 and 1973, when the last modifications were made for horizontal drains. These modifications are presented in Table 8 and displayed in red. It is readily observable that the most significant changes to the UPC horizontal pipe size table were made in 1973.
We have no archived information why the capacity for 3-inch pipe in fixture units was increased to either 27 or 35 fixture units. The UPC continued to limit the number of toilets to two for a 3-inch horizontal drain (until 1970), so the increase was not for a greater allowance of toilets, but only to allow additional fixtures such as sinks, tubs, and showers. How the actual fixture unit values were derived is unknown.
In 1961, the clause “Based on ¼ inch per foot Slope” was added to the title of Table 4-3 and remains in the current edition of the UPC as a footnote. The fixture unit values remained the same as those for 1950. This added clause is a significant error, which was exacerbated in 1973 as shall be discussed below. We have already demonstrated that the fixture unit values for horizontal drains were based on ½-inch per foot slope according to BH13. The 1961 mistake surfaced because the UPC has never provided fixture unit values for differing slopes. We can only surmise that the code committee lost awareness of where and how horizontal pipe sizing was derived. How the committee incorrectly decided on the ¼-inch per foot slope is unknown. The fixture unit values do not even remotely compare with sizing tables at ¼-inch per foot slope in other codes.
In 1964 we see the fixture unit value for 5-inch pipe increasing by 100 fixture units. This is a very odd modification unless the hundredth digit is an error and it should have remained 256. However, this modification remained in place up to 1973. No explanation can be discovered for this increase, which also is incomparable with other codes.
We find the most significant modifications to the horizontal pipe sizing in 1973. During the 1973 code cycle, the technical committee agreed that the fixture unit values for pipes sizes 4 inches and greater were not based on ¼-inch per foot slope, but rather 1/8-inch per foot! This added error upon error. The committee removed the ¼-inch per foot reference from the title of the table and moved it to a footnote. The footnote additionally provided a multiplier that purportedly reduced the fixture unit values for 1/8-inch per foot slope.
Wrongfully assuming that the fixture unit values for pipe diameters 4 inches and larger were based on 1/8-inch per foot slope instead of ¼-inch per foot slope (when in fact they were based on ½-inch per foot slope), the fixture unit values were increased by a diversity factor of 1.2. This diversity factor was determined by the ratio in fixture unit values between 1/8-inch per foot slope and ¼-inch per foot slope according to BMS66 (the ratios are the same for the ASA Code as adopted by the two other model codes). Table 9 demonstrates how this diversity factor was derived.
To decrease the fixture unit values from ¼-inch per foot slope to 1/8-inch per foot slope, the diversity factor is 0.833, which is the factor noted in the UPC footnote (rounded to 0.8). Using the diversity factor of 0.833 to modify the fixture unit values in the 1973 table will actually reduce the fixture unit values to ½-inch per foot slope and not 1/8-inch per foot slope. The present fixture unit values in the UPC for pipe sizes 4 inches and larger have been significantly increased based on mistaken assumptions. Furthermore, the constant slope ratios in the Plumbing Manual differ from the slope ratios in BH13 as displayed in Table 5, which are not constant.
The resulting 1973 UPC horizontal pipe capacities in fixture units for pipe diameters of 8 inches and greater is unprecedented and significantly transcends pipe capacities by 34 to 46 percent when compared to any other model plumbing code, including BMS66, which was a significant advancement from BH13. When applying the diversity factor of 0.8 toward the 1973 4-inch to 6-inch pipe sizes, the resulting capacities are less than any other model plumbing code capacities for 1/8-inch per foot slope by 4 to 18 percent.
The UPC sizing table for horizontal drains has progressed no further since the 1973 modifications. Perhaps the saving grace for the exaggerated capacities for larger pipes is that Hunter’s 1928 estimates were soon dated. Like the original probability model for drainage stacks, Dr. Hunter also abandoned this model for horizontal drains. Hunter continued to modify the tables as we have previously noted, and by 1940 he provided completely new drainage capacity tables that were published in BMS66 based on a new probability model and a better understanding of surge flows and continuous flows in a drainage system. In BMS66, we already see Dr. Hunter increasing the capacity in fixture units for horizontal pipe diameters of 4 to 6 inches that are greater than the UPC 1973 modifications.
Dr. Hunter’s pioneering work published in Report BH13 is one of the most significant contributions toward applied science in plumbing system hydraulics, laying the foundation for the formulation of essential regulations and sound rules of practice for plumbing design. When originally published, letters to the National Bureau of Standards urged its continued publication for use as a textbook in institutions of higher learning for plumbing engineers. Today, this publication is rarely known or referenced, yet the model codes are still built upon this foundation.
It seems apparent from Dr. Hunter’s work that Report BH13, though foundational, was expected to be under constant revision in accordance with the progress of research. In fact, the National Bureau of Standards continued such investigations many decades after Hunter’s final work in 1940, and the published results are still advantageous for plumbing engineers and code bodies as markers pointing to the next needed research for continual development of the plumbing code.
If nothing else, this article serves as a marker pointing to needed research on drainage systems designed with low water consumption fixtures that could influence the development of new pipe sizing tables for vertical and horizontal drains. Flow rates, water volumes, and the duration of toilet discharges have decreased, affecting the probability of overlapping surge discharges and the mean flow rate in building drains and sewers. Also, consumer awareness is increasing, resulting in behavioral changes tending toward water conservation and less demand upon the plumbing system. How does this impact pipe capacity in terms of fixture units? Can there be increased groupings of fixtures in a common branch for a given pipe size if there is less chance of overlapping? Can the venting system be reduced if the discharge load is decreased?
These are only a few questions encouraging further research. Until a path is forged for such plumbing research, code development for system pipe sizing design will remain stagnant. Therein lays the present challenge facing the plumbing code.
Daniel Cole is the Technical Services Supervisor for the International Association of Plumbing & Mechanical Officials (IAPMO), which publishes the Uniform Plumbing Code. He can be reached at firstname.lastname@example.org.