By Christoph Lohr, P.E., CPD, ASSE 12080
After four grueling years at the Virginia Military Institute, upon graduation as an engineer, I decided to follow my own prudent path: I would find the best paying job in an area with the lowest cost of living that afforded me training opportunities. I knew myself well enough that I didn’t want to be stuck behind a desk; I desired interpersonal contact. I always aspired to be an engineering leader — and felt consulting would be the best route to that end.
As a result, I ended up working for an engineering consulting firm based out of the Midwest that had an in-depth multi-year new engineer training program. At this particular firm, which hired predominantly mechanical and electrical engineers, the incoming mechanical engineers were developed as generalists who designed both HVAC and plumbing systems for a variety of buildings, including universities, healthcare and laboratories. My first buildings, mostly for higher-education institutions, allowed me to begin honing my craft as I learned how to size ducts, select air-handling units and design plumbing systems.
It was the latter of these items that at first gave me much consternation. While my engineering classmates were traveling the world, working on nuclear reactors, going to prestigious graduate schools or importantly serving our country as military officers, I was stuck indoors, while practically arctic conditions seemed to last outdoors for months, designing plumbing systems... for toilets. For a young man who went to college with dreams of flying or designing airplanes, this new reality struck me in the face. I made many “social mistakes” along the way that further ostracized me. In short, I made a bad decision for myself, compounded the mistake, and was now dealing with the consequences: Disliking my work, feeling lonely and uninspired.
I let my emotions get the better of me. However, despite struggling to motivate myself in the challenging conditions, especially as I was engineering “piping for toilets,” I came across the concept that no one could truly explain to me — the fixture unit. For HVAC piping systems, I added gallons per minute. For ductwork systems, I added cubic feet per minute. But for plumbing systems (water or waste), I added fixture units and used “Hunter’s Curve” to convert the fixture units to gallons per minute. But the flows were not additive, nor 100% aligned with the fixture units. What on earth was this fixture unit?
I asked several of the engineers with whom I was working at the time to explain the concept to me — no one could. Answers I received ranged from, “It was just what was used to size plumbing piping systems,” to “That’s the way it was done.” “Besides, you still have to do the ductwork design, which is where the real engineering is.” But my curiosity remained — what exactly was this fixture unit? It wasn’t until years later that I got my answer.
Several years and several thousand miles later, I was working on a hospital bed tower addition project and used code, as I had the preceding half-decade, to size my plumbing system. For this specific hospital, the incoming water was very hard, and in order to keep the plumbing system and equipment efficiencies high, we were going to utilize a water softener system. As I had countless times before, I gave the water softener manufacturer my calculated flow rate, however, unlike previous times, the water softener manufacturer told me my number was not only wrong but grossly oversized and asked what I calculated for the existing hospital and the new hospital. I gave them the numbers. The water softener manufacturer told me both numbers were too high.
This was a first, and even though I explained that I had used the code-mandated sizing criteria, the water softener manufacturer wouldn’t budge. In fact, to prove they were right, they put an ultrasonic flowmeter on the incoming water service to the building and measured the peak flow rate over two weeks. Sure enough, they found that their number was correct, and my calculation was shown to be greatly exaggerated. This re-sparked my curiosity, so I immediately started researching into what the fixture unit truly was. It was during this research that I came across the name of Dr. Steven Buchberger by complete chance. As I was googling Hunter’s Curve, I discovered an ACEEE presentation that Dr. Buchberger had given. In his slides, he had content discussing flow rates, probability and plumbing codes. I decided I had to see if I could speak with the professor, so I found his contact information and then sent him an email. Fortunately, Dr. Buchberger is as kind and generous as he is knowledgeable. He wrote me back immediately and we had a call in which my years of questions about plumbing fixture units and Hunter’s Curve were finally answered.
A flow to a faucet (or any other plumbing fixture) can either be “on” or “off” — and is thus binary. When plumbing systems are operated, flows surge at various rates and stop suddenly as people use toilets, sinks, showers, etc., at various times and places inside a building. Additionally, when water comes out of a faucet, if implemented correctly, will never go back into the plumbing water system — rather, it goes down the drain to the sewer system. Therefore, it can be said that plumbing water systems operate intermittently and are open — as opposed to heating and cooling systems that have constant flow that never leaves the system (making plumbing systems more complex). The challenge then becomes, how does one size a piece of cold water pipe to be able to handle the variations of flow?
Dr. Hunter realized that each plumbing fixture in a building could be “on” or “off.” For example, if someone is washing their hands, the plumbing fixture is on, but then when the faucet is turned off to dry their hands, the fixture is off. But more importantly, Dr. Hunter realized there was some measure of probability of the fixture being “on” or “off” against other fixtures. In a building, the likelihood of every faucet or shower being on is very low, but at a given instance there is a possibility that a certain percentage of plumbing fixtures could be on at the same time. Additionally, Dr. Hunter realized that every plumbing fixture had a different flow rate — a toilet has a higher flow rate than a shower, which, in turn, has a higher flow rate than a faucet. So, the two variables that Dr. Hunter had to balance against each other were the probability of simultaneous usage and the flow rate of the fixture.
Dr. Hunter's brilliant inspiration in 1940 was to create a benchmark unit that consolidated first the probability of a fixture being on and then the flow rate. To create this new unit of measurement, he needed to create a baseline for all the plumbing fixtures against which to be compared. His choice was well thought out: The toilet (or professionally known as a “water closet”). The water closet has the highest peak flow rate of any plumbing fixture. This meant that if Dr. Hunter could determine the worst-case scenario accurately, he could confidently base all other fixtures off of this one unit, saving him immense time while also giving him confidence that he had enough safety factor to mitigate failure based on flow.
So having his base unit of flow identified, Dr. Hunter moved onto trying to identify the correct probability of two or more plumbing fixtures being on at the same time. He didn’t want to underestimate the occurrence of multiple fixtures being on at the same time, as he realized this would cause massive pressure drops inside buildings. Again, going back to his base fixture, the toilet, he ended up using a measure of probability that was very conservative: “Person A” steps up to the plumbing fixture, turns it on and/or uses it, turns it off, steps away from the fixture and is immediately replaced by “Person B,” who steps up to the plumbing fixture, turns it on and/or uses it, turns it off, steps away from the fixture, and is immediately replaced by “Person C,” and so on. In essence, the situation to determine probability Dr. Hunter had in mind was probably an opera house or theater at intermission (In current times, we would probably imagine a sports stadium at halftime). In essence, it was a lot of people wanting to use a small number of bathrooms, all at the same time.
What this type of usage equates, in a mathematical sense, is a 99.9% probability of simultaneous use. Going with a simultaneous usage less than 100% allowed for drastic reduction in plumbing domestic water pipe sizing. For example, assuming 25 gpm of flow per water closet for a bank of 10 water closets, the breakdown in flow and pipe sizing would be as follows:
By reducing the estimated simultaneous usage by this fraction, the pipe size in this instance was able to be reduced to half the original size. The result was significant cost savings due to lower pipe material costs. This was one of the main driving factors, if not the driving factor for the U.S. Commerce Department in hiring Dr. Hunter: To make building construction less expensive.
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Christoph Lohr, P.E., CPD, ASSE 12080, is the vice president of Strategic Initiatives at IAPMO. All views and opinions expressed in this article are his alone. Have some thoughts on this article? Contact Christoph at firstname.lastname@example.org.