It’s all about probability — Part 2
Estimating water demand: What are the chances?
We all love simplicity. Simplicity saves time, reduces the margin of error, promotes broader applicability, and is user-friendly. Students today love the simplified “plug and chug” math. This is when you have a ready-made formula complete with the X and Y variables. All you have to do is substitute the X and Y with the right numbers and chug away at the math. Better yet, if you have the formula programmed in your graphing calculator, you just plug in the numbers and let the calculator do the chugging for you.
This is what the Water Demand Calculator that was introduced in the previous article provides for plumbing system designers. In that article, readers already saw a binomial formula that was a bit complicated, and would intimidate those less savvy with numbers from attempting to use. Simplicity was key when choosing an MS Excel spreadsheet as a calculator, where you only need to place your number in the assigned cell and let the calculator produce the odds.
There are four formulas programmed in the Excel spreadsheet. The calculator will select only one formula based on the numbers you place in the spreadsheet. It will then evaluate the number for each kind of fixture with its corresponding frequency of use (the p-value), sum up the values, and place that value within a range determined for one of the formulas. Once the formula is chosen, it chugs out the math and places the answer in the Demand Flow box within seconds. Seriously, all you have to do is place your number and you are guaranteed the winning answer.
Are you ready to place your number? Let’s try this out. If you downloaded the calculator using the link provided in the previous article (also provided at the end of this article), then open it up and follow along.
Figure 1 shows a residential home with one bathroom, kitchen and clothes washer. First, let’s estimate the demand for the whole house at Pipe Section 4. Notice there are six indoor fixtures — a lavatory, combination bath/shower, water closet, kitchen faucet, dishwasher and clothes washer. Since there is only one of each, place the number 1 in Column [B] after each of the six fixtures (see Figure 2). After doing so, click on the box that says Run Water Demand Calculator. The estimated demand for the whole house will appear in the Demand Flow box. In this example, the estimated demand for the whole house is 8.5 gpm.
Easy enough? Let’s try some branch sizing. First, click the Reset button in the Calculator and it will clear Column [B] of the previous numbers you entered. Let’s estimate the demand for the hot water branch at the water heater, Pipe Section 3 in Figure 1. The water closet is the only fixture that does not use hot water, so it would be excluded in the calculator. Enter the number 1 after the other five fixtures and then click Run Water Demand Calculator. The estimated demand for the hot water branch at the water heater is 7.7 gpm (see Figure 3).
Now let’s do a couple on your own for those who downloaded the calculator. Pipe Section 2 in Figure 1 shows a cold and hot water branch. To estimate the cold branch demand, enter the number 1 in Column [B] after the kitchen faucet, the combination bath/shower, lavatory and water closet. These are the fixtures that use cold water. The dishwasher is excluded. Click Run Water Demand Calculator. What is your answer? The cold water branch at Pipe Section 2 has an estimated demand of 7.7 gpm. Now do the hot water demand estimate at Pipe Section 2. Did you exclude the water closet and include the dishwasher? The hot water branch has an estimated demand of 7.0 gpm.
As the number of fixtures on a branch is reduced to one fixture, the remaining fixture supply has a flow rate dictated by that fixture. For example, a fixture supply to a lavatory faucet has a flow rate of 1.5 gpm. There is no need to put a single fixture in the calculator, but if you do, the result will just be the flow rate for that single fixture.
Hopefully you’ve got the hang of this, and now I can introduce some more features of the Water Demand Calculator. By observing the fixture flow rates in Column [D] you may have guessed that these flow rates are for water-conserving fixtures. Notice also that there are blue-colored and white-colored cells. The blue-colored cells are fixed and can’t be changed, but you can change the values in the white-colored cells. However, the flow rates in Column [D] can only be decreased and not increased, depending on the actual flow rate of the water-conserving fixture.
In Column [A] there are additional rows for Other Fixture not included in the calculator. For example, you can add a pot filler and a dog bath to the list of fixtures (see Figure 4). When doing this, find an indoor fixture that has a similar probability of use in Column [C] and add that to the column. Then enter the actual flow rate of additional fixtures in Column [D]. Then click Run Water Demand Calculator. Adding these fixtures slightly increased the estimated demand of the whole house.
There is one caveat that must be observed. The fixtures and appliances applicable to the Water Demand Calculator are those that have an indoor residential frequency-of-use pattern that are recurrent or intermittent. Outdoor water uses such as hose bibbs and landscape irrigation are too variable and infrequent to have an intermittent or recurrent frequency of use. Such water draws are on for a long duration of time and then off for long periods of time, and are considered continuous flows. Continuous flow fixtures are not to be entered into the Water Demand Calculator as Other Fixtures. Rather, continuous flows (in gpm) are to be added to the Demand Flow estimate. For example, Figure 2 shows the whole house demand flow of 8.5 gpm. If there is a hose bibb with a flow rate of 2.0 gpm, then 2.0 gpm would be added to 8.5 gpm for a total whole house estimated demand of 10.5gpm.
The Water Demand Calculator was purposely developed for water-conserving fixtures and appliances. Hence, high-flow Roman tub fillers (exceeding the bathtub flow rates in Column [E] of the calculator) and luxury shower spas fall outside the calculator’s scope. These also should not be included in the Water Demand Calculator, but considered similar to continuous flow fixtures with the high flow rates added to the estimated demand from the Water Demand Calculator.
Now that you know how to use the Water Demand Calculator to find the estimated demand for each pipe segment of a water distribution system, how do you go from the flow rate to finding the pipe size? At this point you must consult your plumbing code and look for an appendix for sizing the water supply system (all the model codes have one). If your adopted plumbing code does not have this appendix, then refer the 2015 Uniform Plumbing Code, Appendix A for a good reference guide.
Generally, the sizing rules begin with estimating the demand in fixture units, and then converting fixture units into flow rates (gpm). This step can be eliminated since the Water Demand Calculator predicts the house’s demand in gallons per minute. The sizing rules will then lay out steps for calculating friction loss and direct you to nomograph charts that include friction loss, velocity and flow rate to determine the appropriate pipe size.
Codified provisions and examples for using this calculator will debut in a new appendix in the 2018 Uniform Plumbing Code as well as the 2017 WEStand.
The Water Demand Calculator may be downloaded at: www.iapmo.org/WEStand/Pages/DocumentInformation.aspx.