2nd Edition
Mathematics Manual for Water and Wastewater Treatment Plant Operators - Three Volume Set
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
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
Index
Volume 3:
Flow, Velocity, and Pumping Calculations
Velocity and Flow Examples
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 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.
