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Articles in support of small community water and wastewater operators.

Featured Video: Operator Math

In a lot of ways, the ability to do math is like the ability to use a muscle. You always have muscles, of course, but whether you're able to use a particular muscle or muscle group depends on how developed it is. In other words, it depends on how often you use those muscles, whether you're lifting weights regularly or just hauling around a heavy toolbox on a daily basis. Math is the same way. Sure, on any good day you can probably handle 2 + 2. But for more complicated problems, regular practice and a thorough understanding of the principles can help those equations go from a headache to a breeze. Since water and wastewater operators often find themselves calculating things like chemical doses, the volume of complicated objects, and rate of flow, keeping in good mathematic shape can go a long way to making your life easier. And of course, being in practice doesn't do any harm when it's time to sit for your exams either!

There are a lot of ways to brush up on your math skills, and sometimes it helps to try a couple until you find what works best for you. Our document database has collected math help in a wide variety of formats under the Certification/Exam Prep category. Use "math" (without the quote marks) in the keyword filter box to narrow it down to just math help. But if you're someone who needs to see someone else work the problem in order to get what's going on, this week's videos might be a particularly good fit.

Indigo Water Group, a water and wastewater operator trainer in Colorado, has created a playlist of videos in which their owner works common water and wastewater math problems. Most of these videos are short and broken down by kind of problem. The exception is an hour long video devoted to wastewater math. At the time of this writing, the other videos in the playlist covered unit conversions, geometry, dosing, reducing MLSS concentrations, velocity and HRT, and digester problems. But more topics have been slowly added over time, so there may be more in the future. The video below links the entire playlist, which starts with three short unit conversion videos.

The YouTube channel CAwastewater takes a slightly different approach. Instead of breaking the videos down by topic, the channel owner (who is an operator himself) breaks down the videos by the state exam level where the problems are most likely to appear. He has playlists for the California exam levels 1, 2, and 3, and one playlist that combines the math for 4 and 5. Though these videos are aimed at California wastewater operators, both water and wastewater operators from across the country will likely get something out of them. The individual videos are about 5-10 minutes long, and the playlists are about a half hour to an hour. Choose the playlist that looks most interesting to you.

Hopefully, these operator math videos will help you round out your mathematical fitness routine, leaving you well prepared for operations challenges and certification exams alike. And if there's a great free math resource that we didn't mention here that you want to be sure we know about, let us know in the comments!

Operator Math Part 3: Continuous Education

This is the third and final installment of our operator math series, and we’re closing with an eye to the future. When the exams are done and you’re thrown back into the stress of daily operations, it’s easy for math skills to get a little rusty.

Here are some great videos, blog series, and more to help you test and strengthen your knowledge of commonly—and not so commonly—used formulas and functions. And many of these resources can also double as exam prep, making them something you can turn to again and again.

Beginner Skills Check

Pinpoint your math weak spots with these five sample problems designed to test your familiarity with unit conversions, and calculations related to area, volume, flow rate, chlorine dosage, and pressure. Developed by the engineering firm Souder, Miller & Associates, this skills check also includes an answer sheet.

 

Problem of the Day

Wastewater Technology Trainers gives you a keep your skills sharp and review at your own pace with their Problem of the Day blog series. Each problem is provided in the form of a downloadable document containing a page or two about working in the wastewater treatment industry followed by the sample problem. Although each of the documents appear similar at first, you’ll find the problems generally begin on the second or third page following a schedule of problems provided on earlier dates. 

Indigo Water Group Math Videos

This series of 13 videos walks through the procedures for solving common water or wastewater math problems. Viewers are able to learn how to solve problems in a step-wise process by following along with the video, which demonstrates and explains each step. The series contains three unit conversion tutorials, five geometry tutorials, three dosing tutorials, one that calculates pump run time to reduce MLSS concentration, and one that calculates VSS loading rate to an anaerobic digester.

CAwastewater.org Math Videos

These 19 HD-quality videos were created by operators for operators. They provide instruction, examples, and advice on math topics covered by the Grads 1-5 exams offered in California.

Big Books of Math Problem Generator

Also from Indigo Water Group, this tool gives you a new set of problems with every click. Each set is provided as an Excel spreadsheet, allowing you to easily work through the solutions at your own pace. Click on the “Math Problem Generator” link at the bottom of the page.

 

Skills Builder

This webpage allows you to test your knowledge of wastewater and laboratory topics using Skills Builder—a set of quizzes provided by WEF as a free resource for operator education. The quizzes incorporate math, safety, and a variety of other topics. Skills Builder provides feedback on your answers as well as references for follow-up study sources. Results are completely confidential and are not recorded. 

 

Industry groups and not-for-profits, including our partners at the Rural Community Assistance Partnership, also regularly host operator math training courses and webinars. Learn about these and other training opportunities with our Event Calendar.   

Operator Math Part 2: Online Tools and Apps

Last week, we shared a few basic tips to help you master some of the calculations used in day-to-day operations. Understanding these and other functions and formulas is an integral part of the job, but working through the problems can be intimidating. Fortunately, there is a large bank of online tools and apps geared toward water and wastewater professionals that puts solutions literally at your fingertips. 

Of course, mobile technology is fast-moving and new tools are being released almost daily. Here are just a few of the ones available at no cost right now.

Online tools

From the Pennsylvania Department of Environmental Protection:

From the Missouri Rural Water Association:

Device apps

From the Missouri Rural Water Association:  

From Georg Fischer AG:

From Thermo Fisher Scientific:

  • Process Water Products – Apple

From Hydromantis ESS, Inc.:

From Pipeflowcalculation.com:

  • Pipe Diameter Calculator – Android

From Fleming Training Center:  

Be sure to check back here next week for the last post in our operator math series. We’ll have resources to help you keep your calculation skills sharp.

Operator Math Part 1: Practical Guidelines

Mathematical calculations can be a challenge for even for the most veteran of water and wastewater operators. The formulas for volume, chemical dosage, filtration, pipe velocity, and other daily problems vary of course, but there are a few underlying guidelines that can help you make sure your answer is correct regardless of the calculation you’re working on. 

This is the first in a three-part series dedicated to operator math. The tips below are adapted from information provided by the South Dakota Department of Environmental and Natural Resources.

  1. Learn what a formula means, not just when it is used. This will help you remember when to use πR2H to calculate the volume of a cylinder instead of 2πRH—the formula for measuring the surface area of a cylinder’s sides.
  2. Use unit labels throughout your calculation to help you easily see whether you need to multiply or divide.
  3. Always convert percentages to decimals.
  4. Convert “inches” to “feet” unless you’re trying to solve a pressure problem. Using “inches” in any other problem will almost always leave you with the wrong answer.
  5. Make sure the units you end with match the problem you are trying to solve. If a volume calculation results in a “square feet” or “square yards” answer, something went wrong along the way.
  6. Trust your suspicions. If the answer doesn’t seem right, check that you used the right formula and units before running the problem again.

For those looking for more detailed and specific instruction, our documents database is a great place to start. Here are some of the resources you’ll find if you search “math.”

Basic Math Handbook

This 24-page handbook is a basic math study tool. It provides formulas for basic geometry, velocity & flow rates, and pressure, force & head, and contains several typical water problems that show users how to apply the formulas in real-world scenarios. 

Formula and Conversion Sheet for Drinking Water Treatment and Distribution

This 1 page document provides conversions and formulas for water treatment & distribution operators in studying for a certification exam. 

 

Chlorine Contact Time Calculations

This 7-page document provides guidelines on how to solve math problems that deal with calculating chlorine contact time. It includes important equations and practice problems with solutions. 

 

Industrial Math Formulas

This 7-page document provides a list of valuable formulas and conversion factors important for wastewater operators. 

 

Intermediate Water Math

This 37-page study guide contains 82 intermediate water math questions. Solutions to the problems are provided at the end of the document. 

 

Advanced Wastewater Math

This 29-page study guide contains 35 advanced wastewater math questions. Solutions to the problems are provided at the end of the document. 

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