2nd Edition

# Mathematics Manual for Water and Wastewater Treatment Plant Operators - Three Volume Set

**Also available as eBook on:**

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.*Basic Mathematics for Water and Wastewater Operators *introduces and reviews fundamental concepts critical to qualified operators. It builds a strong foundation based on theoretical math concepts, which it then applies to solving practical problems for both water and wastewater operations. *Water Treatment Operations: Math Concepts and Calculations *covers computations used in water treatment, and *Wastewater Treatment Operations: Math Concepts and Calculations *covers computations commonly used in wastewater treatment plant operations. The volumes present math operations that progressively advance to higher, more practical applications, 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, the volumes provide illustrative examples for commonly used waterworks and wastewater treatment operations covering unit process operations found in today’s treatment facilities. Readers working through the books systematically will acquire a definitive understanding of and skill in performing the applied water/wastewater calculations that are essential for a successful career in the water industry.

**Volume 1:**

**Introduction**

The 411 on Mathematics

Dimensional Analysis

Basic Units of Measurement and Conversions

Setting the Stage

Units of Measurement

Conversion Factors

Conversions

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**

Fractions

Decimals

Percent

**Rounding and Significant Digits**

Rounding Numbers

Determining Significant Figures

**Powers of Ten and Exponents**

Rules

Powers

Examples

**Averages (Arithmetic Mean) and Median**

Averages

Median

**Solving for the Unknown**

Math Rules of Operation

Equations

Axioms

Solving Equations

Checking the Answer

Setting Up Equations

Summary of Key Points

**Ratios and Proportions**

Ratios

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

Volume

Area Examples

Volume Examples

**Force, Pressure, Head, and Velocity Calculations**

Force and Pressure

Head

Velocity

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

Normality

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**

Index

Volume 2:

Pumping Calculations

Pumping

Index

Volume 2:

Pumping Calculations

Basic Water Hydraulics Calculations

Basic Pumping Calculations

Positive-Displacement Pumps

**Water Source and Storage Calculations**

Water Sources

Water Source Calculations

Water Storage

Water Storage Calculations

Copper Sulfate Dosing

Iron and Manganese Removal

**Coagulation and Flocculation Calculations**

Coagulation

Flocculation

Coagulation and Flocculation Calculations

Coagulation and Flocculation Practice Problems

Chemical Feeders

Chemical Feeder Calculations

**Sedimentation Calculations**

Sedimentation

Tank Volume Calculations

Detention Time

Surface Overflow Rate

Mean Flow Velocity

Weir Loading (Overflow) Rate

Percent Settled Biosolids

Determining Lime Dosage (mg/L)

Determining Lime Dosage (lb/day)

Determining Lime Dosage (g/min)

Sedimentation Practice Problems

**Filtration Calculations**

Water Filtration

Flow Rate through a Filter

Filtration Rate

Unit Filter Run Volume

Backwash Rate

Volume of Backwash Water Required

Required Depth of Backwash Water Tank

Backwash Pumping Rate

Percent Product Water Used for Backwatering

Percent Mud Ball Volume

Filter Bed Expansion

Filter Loading Rate

Filter Medium Size

Mixed Media

Head Loss for Fixed Bed Flow

Head Loss through a Fluidized Bed

Horizontal Washwater Troughs

Filter Efficiency

Water Filtration Practice Problems

References and Recommended Reading

**Water Chlorination Calculations**

Chlorine Disinfection

Determining Chlorine Dosage (Feed Rate)

Calculating Chlorine Dose, Demand, and Residual

Breakpoint Chlorination Calculations

Calculating Dry Hypochlorite Feed Rate

Calculating Hypochlorite Solution Feed Rate

Calculating Percent Strength of Solutions

Chemical Use Calculations

Chlorination Math Practice Problems

**Fluoridation**

Water Fluoridation

Fluoride Compounds

Optimal Fluoride Levels

Fluoridation Process Calculations

Fluoridation Math Practice Problems

**Water Softening**

Water Hardness

Determining Alkalinity

Determining Bicarbonate, Carbonate, and Hydroxide Alkalinity

Lime Dosage Calculation for Removal of Carbonate Hardness

Calculation for Removal of Noncarbonate Hardness

Recarbonation Calculation

Calculating Feed Rates

Ion Exchange Capacity

Water Treatment Capacity

Treatment Time Calculations (Until Regeneration Required)

Salt and Brine Required for Regeneration

**Water Treatment Practice Calculations**

Appendix.Solutions to Chapter 9 Problems

Appendix.

**Index**

Volume 3:

Flow, Velocity, and Pumping Calculations

Velocity and Flow Examples

Volume 3:

Flow, Velocity, and Pumping Calculations

Velocity and Flow Practice Problems

Pumping

Basic Water Hydraulics Calculations

Basic Pumping Calculations

Positive-Displacement Pumps

**Preliminary Treatment Calculations**

Wet Well Capacity and Pumping Rate

Screening

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**

Thickening

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

Normality

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 A.

**Appendix B.**Formulas

### Biography

**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.