Mathematics Manual for Water and Wastewater Treatment Plant Operators: Wastewater Treatment Operations: Math Concepts and Calculations, 2nd Edition (Paperback) book cover

Mathematics Manual for Water and Wastewater Treatment Plant Operators: Wastewater Treatment Operations

Math Concepts and Calculations, 2nd Edition

By Frank R. Spellman

CRC Press

258 pages | 30 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 Editionhas 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 third volume, Wastewater Treatment Operations: Math Concepts and Calculations, covers computations commonly used in wastewater treatment with applied math problems specific to wastewater operations, allowing operators of specific unit processes to focus on their area of specialty. It explains calculations for flow, velocity, and pumping; preliminary and primary treatments; trickling filtration; rotating biological contactors; and chemical dosage. It also addresses various aspects of biosolids in wastewater, treatment ponds, and water/wastewater laboratory calculations. The text presents math operations that progressively advance to higher, more practical applications of mathematical calculations, including math operations that operators at the highest level of licensure would be expected to know and perform. To ensure correlation to modern practice and design, this volume provides illustrative problems for commonly used wastewater treatment operations found in today’s treatment facilities.

Table of Contents

Flow, Velocity, and Pumping Calculations

Velocity and Flow Examples

Velocity and Flow Practice Problems


Basic Water Hydraulics Calculations

Basic Pumping Calculations

Positive-Displacement Pumps

Preliminary Treatment Calculations

Wet Well Capacity and Pumping Rate


Grit Removal

Screening and Grit Removal Practice Problems

Primary Treatment Calculations

Process Control Calculations

Primary Treatment Practice Problems

Trickling Filter Calculations

Trickling Filter Process Calculations

Trickling Filter Practice Problems

Rotating Biological Contactors

RBC Process Control Calculations

RBC Practice Problems

Activated Biosolids

Activated Biosolids Process Control Calculations

Activated Biosolids Practice Problems

Treatment Ponds

Treatment Pond Parameters

Treatment Pond Process Control Calculations

Treatment Pond Practice Problems

Chemical Dosage Calculations

Chemical Dosing

Chemical Dosage Practice Problems

Biosolids Production and Pumping Calculations

Process Residuals

Primary and Secondary Solids Production Calculations

Percent Solids

Biosolids Pumping

Biosolids Production and Pumping Practice Calculations

Biosolids Thickening Calculations


Gravity/Dissolved Air Flotation Thickener Calculations

Centrifuge Thickening Calculations

Biosolids Thickening Practice Problems

Biosolids Digestion

Biosolids Stabilization

Aerobic Digestion Process Control Calculations

Anaerobic Digestion Process Control Calculations

Biosolids Digestion Practice Problems

Biosolids Dewatering and Disposal

Biosolids Dewatering

Pressure Filtration Calculations

Rotary Vacuum Filter Dewatering Calculations

Sand Drying Bed Calculations

Biosolids Disposal

Biosolids to Compost

Biosolids Dewatering and Disposal Practice Problems

Water/Wastewater Laboratory Calculations

The Wastewater Lab

Composite Sampling Calculation (Proportioning Factor)

Biochemical Oxygen Demand (BOD) 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

Wastewater Treatment Practice Calculations

Appendix A. Solutions to Chapter 14 Problems

Appendix B. Formulas

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