The Pounds Formula, Once Again

With the California Water Treatment Operator exam just two weeks from Saturday, it’s time to look at some of the key topics explored on the exam. And no topic is worth more points in your score than our old pal, the Pounds Formula.

We have addressed this formula in an earlier blog — and it is one of the most visited in the archives. As I reviewed that older blog, I realized that we could amplify on this important topic — and that’s just what we have in store today. See:

The Pounds Formula is used for all chemical feed calculations; if you see a math problem that involves chemical feed, you’ll be using your old pal once again! This formula has one constant — 8.34 — plus three variables. That means there are three basic forms of questions you can encounter:
1. Find the Feed Rate, in pounds per day (lb/day)
2. Find the Dosage, in milligrams per liter (mg/L)
3. Find the Flow Rate, in million gallons per day (MGD)

We’ll explore the last one today. It is the least common of the three; because of that, it is often the most confusing. A typical question would be something like this: A 20 MGD treatment plant needs to apply a dosage of 4.0 mg/L of alum for satisfactory treatment. Its lone operational alum feeder can dispense a maximum feed rate of 20 pounds per hour. At what flow rate can this plant be operated?

At first, it looks like they’re asking you “Who is buried in Grant’s tomb?” Duh! A 20 MGD plant can operate at 20 MGD, right? Not always. So don’t automatically select the “20 MGD” answer in the multiple choice!

There are two — unusual — chemical feed circumstances when a plant may not be able to operate at its rated capacity: either, (1) the current dosage requirement is abnormally high; or (2) the current feed rate capability is abnormally low.

In this example, the 4.0 mg/L is not unusual, so it must be case (2). Why does this plant only have one feeder available? Most plants would have at least two, and probably more than two if a single feeder could not deliver normal dosages at the full plant flow rate.

Let’s do the math on this example. First, we have a small “bear trap” to deal with: our feed rate is not in pounds per day — it’s in pounds per hour. Simple enough to fix, right? The 20 pounds per hour is equal to 480 pounds per day. Remember how rigid the units are in the Pounds Formula!

To find the flow rate in MGD, we divide the lb/day (480) by 8.34, and by the mg/L (4.0). My calculator says: 14.4 MGD. Hopefully, that matches up with one of the multiple choice answers!

Note what would happen if we had two feeders available: based on the Pounds Formula, this plant could operate at twice the flow rate, or 28.8 MGD. Could a 20 MGD plant operate at 28.8 MGD? At least two key factors may prevent this from happening. First, a 20 MGD plant is unlikely to have the hydraulic capacity to move that much more water! Second, I think the Department of Public Health would want to discuss this with you first! So, if these circumstances showed up on our exam question, the correct answer would be 20 MGD!

Another thing to consider is that, in an operating plant, we really need to do this same math problem for every single chemical we are feeding! Hopefully, a proper design and effective maintenance will yield a flow rate limitation that is greater than the rated capacity of the plant — for every chemical we can apply.

In this particular case, doing the math is only part of selecting the correct answer; you will also need to interpret your math answer in order to determine the proper flow rate at which your plant can be operated!

One Response to The Pounds Formula, Once Again

  1. avatar Steve McLean says:

    Oops! I previously made a math error in this one. It is now shown correctly above.

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