Mathematics Manual for Water and Wastewater Treatment Plant Operators: Basic Mathematics for Water and Wastewater Operators, 2nd Edition (Paperback) book cover

Mathematics Manual for Water and Wastewater Treatment Plant Operators

Basic Mathematics for Water and Wastewater Operators, 2nd Edition

By Frank R. Spellman

CRC Press

294 pages | 56 B/W Illus.

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To properly operate a waterworks or wastewater treatment plant and to pass the examination for a waterworks/wastewater operator’s license, it is necessary to know how to perform certain calculations. All operators, at all levels of licensure, need a basic understanding of arithmetic and problem-solving techniques to solve the problems they typically encounter in the workplace.

Hailed on its first publication as a masterly account written in an engaging, highly readable, user-friendly style, the Mathematics Manual for Water and Wastewater Treatment Plant Operators, Second Edition has been expanded and divided into three specialized texts that contain hundreds of worked examples presented in a step-by-step format. They are ideal for all levels of water treatment operators in training and practitioners studying for advanced licensure. In addition, they provide a handy desk reference and handheld guide for daily use in making operational math computations.

This first volume, Basic Mathematics for Water and Wastewater Operators,introduces and reviews fundamental concepts critical to qualified operators. Presented at a basic level, this volume reviews fractions and decimals, rounding numbers, significant digits, raising numbers to powers, averages, proportions, conversion factors, flow and detention time, and the areas and volumes of different shapes. It also explains how to keep track of units of measurement (such as inches, feet, and gallons) during the calculations. After building a strong foundation based on theoretical math concepts, the text moves on to applied math—basic math concepts applied in solving practical problems for both water and wastewater operations. The material is presented using clear explanations in manageable portions to make learning quick and easy, and illustrative real-world problems are provided that correlate to modern practice and design.

Table of Contents


The 411 on Mathematics

Dimensional Analysis

Basic Units of Measurement and Conversions

Setting the Stage

Units of Measurement

Conversion Factors


Wire-to-Water Calculations

Advanced Units of Measurement and Conversions

Sequence of Operations

Sequence of Operations Rules

Sequence of Operations Examples

Fractions, Decimals, and Percent




Rounding and Significant Digits

Rounding Numbers

Determining Significant Figures

Powers of Ten and Exponents




Averages (Arithmetic Mean) and Median



Solving for the Unknown

Math Rules of Operation



Solving Equations

Checking the Answer

Setting Up Equations

Summary of Key Points

Ratios and Proportions



Working with Ratios and Proportions

Electrical Calculations

Electrical Circuits and Power

Series DC Circuit Characteristics

Parallel DC Circuits

Circumference, Area, and Volume

Perimeter and Circumference



Area Examples

Volume Examples

Force, Pressure, Head, and Velocity Calculations

Force and Pressure



Force, Pressure, Head, and Velocity Examples

Mass Balance and Measuring Plant Performance

Mass Balance for Settling Tanks

Mass Balance Using BOD Removal

Measuring Plant Performance

Plant Performance/Efficiency

Unit Process Performance and Efficiency

Percent Volatile Matter Reduction in Sludge

Pumping Calculations

Basic Water Hydraulics Calculations

Basic Pumping Calculations

Positive-Displacement Pumps

Pumping Examples

Water Source and Storage Calculations

Water Source Calculations

Water Storage

Water Storage Calculations

Copper Sulfate Dosing

Water/Wastewater Laboratory Calculations

Faucet Flow Estimation

Service Line Flushing Time

Composite Sampling Calculation (Proportioning Factor)

Biochemical Oxygen Demand Calculations

Moles and Molarity


Settleability (Activated Biosolids Solids)

Settleable Solids

Biosolids Total Solids, Fixed Solids, and Volatile Solids

Wastewater Suspended Solids and Volatile Suspended Solids

Biosolids Volume Index and Biosolids Density Index

Chemical Dosage Calculations

Laboratory Examples

Basic Mathemathics Practice Problems

Basic Math Operations

Fundamental Water/Wastewater Operations

Appendix. Solutions to Chapter 17 Problems


About the Author

Frank R. Spellman, PhD, is a retired assistant professor of environmental health at Old Dominion University, Norfolk, Virginia, and the author of more than 90 books covering topics ranging from concentrated animal feeding operations (CAFOs) to all areas of environmental science and occupational health. He consults on homeland security vulnerability assessments for critical infrastructures, including water/wastewater facilities, and conducts audits for Occupational Safety and Health Administration and Environmental Protection Agency inspections throughout the country. Dr. Spellman lectures on sewage treatment, water treatment, and homeland security, as well as on safety topics, throughout the country and teaches water/wastewater operator short courses at Virginia Tech in Blacksburg.

Subject Categories

BISAC Subject Codes/Headings:
TECHNOLOGY & ENGINEERING / Environmental / General
TECHNOLOGY & ENGINEERING / Environmental / Water Supply