Guest Column | May 27, 2016

Math Solutions: Combining Concentrations

Wastewater Dan Theobald

By Daniel Theobald, "Wastewater Dan"


“Wastewater Dan” instructs operators on how to perform calculations for combining concentrations.

During my 24-plus years of training experience in wastewater, I learned that many operators were held back from advancing their operating license because they struggled with the mathematics portion of wastewater operator certification examinations.

This tool for operators — represented through video tutorials — offers mathematical templates for performing accurate wastewater calculations. It also provides definitions, explanations, and alternative applications for the calculations beyond the specific examples presented. In addition to operators, it may also serve educators, engineers, regulators, and others.

Some common calculations needed for combining concentrations are accessible below. Your specific calculations may have different requirements such as expressing the results as square feet, cubic feet, increment of millions, or even incorporating a time element in calculation solutions.

Combining Percent (%) Concentrations Calculation:

Calculate combined percentage concentration:

mg/L Concentrations Calculation And  The Supporting Math Solutions:

Calculate plant influent flow mass:


Calculate press filtrate mass:


Calculate digester supernate mass:


Calculate combined mg/L (ppm) concentration, consolidating three flows streams into one:


Playlist of 20-plus process control calculations

Playlist of all 125-plus Math Solutions

This is the ‘Combining Concentrations’ presentation in my series of “Math Solutions.” If you have specific wastewater math queries, please submit a question.  

About Dan Theobald:

Known in the industry as “Wastewater Dan,” Daniel L. Theobald, proprietor of Environmental Services (, is a professional wastewater and safety consultant/trainer. He has more than 24 years of hands-on industry experience operating many variants of wastewater treatment processing units and is eager to share with others his knowledge about water conservation.

Theobald serves as an active consultant for industries looking to achieve and maintain improved wastewater treatment at reduced cost. He is a Lifetime Member of the Who’s Who Registry of Professionals and holds numerous certifications from wastewater management regulatory boards and professional organizations. Theobald contributed one chapter to the Water Environment Federation’s ( Manual of Practice # 37 (MOP-37), a technical manual resource guide for biological nutrient removal, published in 2013.

Image credit: "Drainage Pipe," Chad Cooper © 2013, used under an Attribution 2.0 Generic license: