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Summary
Summary
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.
Author Notes
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.
Table of Contents
Preface | p. xi |
Author | p. xv |
Chapter 1 Introduction | p. 1 |
The 411 on Mathematics | p. 1 |
Math Terminology and Definitions | p. 1 |
Calculation Steps | p. 3 |
Key Words | p. 3 |
Calculators | p. 3 |
Dimensional Analysis | p. 4 |
Basic Operation 1 | p. 4 |
Basic Operation 2 | p. 5 |
Basic Operation 3 | p. 5 |
Chapter 2 Basic Units of Measurement and Conversions | p. 9 |
Setting the Stage | p. 9 |
Units of Measurement | p. 9 |
Conversion Factors | p. 10 |
Weight, Concentration, and Flow | p. 11 |
Conversions | p. 13 |
Typical Water/Wastewater Conversion Examples | p. 14 |
Temperature Conversions | p. 21 |
Population Equivalent or Unit Loading Factor | p. 25 |
Specific Gravity and Density | p. 26 |
Flow | p. 30 |
Key Factors in Calculating Flow Problem Solutions | p. 31 |
Flow through a Channel | p. 31 |
Flow through a Pipeline | p. 32 |
Detention Time | p. 39 |
Chemical Addition Conversions | p. 42 |
Required Amount of Chemical (Active Ingredient) | p. 42 |
Required Amount of Chemical (Inactive Ingredient) | p. 43 |
Dry Chemical Feed Rate | p. 43 |
Liquid Chemical Feed Rate | p. 43 |
Wire-to-Water Calculations | p. 44 |
Horsepower and Energy Costs | p. 45 |
Water Horsepower | p. 45 |
Brake Horsepower | p. 46 |
Motor Horsepower | p. 46 |
Electrical Power | p. 46 |
Power Factor | p. 47 |
Advanced Units of Measurement and Conversions | p. 49 |
Conversion Factors and SI Units | p. 49 |
Conversion Factor Tables | p. 51 |
Water/Wastewater Conversion Examples | p. 51 |
Temperature Conversion Examples | p. 69 |
Conversion Factors for Air Pollution Measurements | p. 72 |
Conversion from ppm to ¿g/m 3 | p. 72 |
Conversion Tables for Common Air Pollution Measurements | p. 74 |
Soil Test Results Conversion Factors | p. 75 |
Greenhouse Gas Emission Numbers to Equivalent Units and Carbon Sequestration | p. 78 |
Electricity Reductions (Kilowatt-Hours) | p. 78 |
Emission Factor | p. 79 |
Passenger Vehicles per Year | p. 79 |
Gallons of Gasoline Consumed | p. 79 |
Therms of Natural Gas | p. 80 |
Barrels of Oil Consumed | p. 80 |
Tanker Trucks Filled with Gasoline | p. 80 |
Number of Tree Seedlings Grown for 10 Years | p. 81 |
Acres of U.S. Forests Storing Carbon for One Year | p. 82 |
Conversion Factors for Carbon Sequestered Annually by One Acre of Average U.S. Forest | p. 83 |
Acres of U.S. Forest Preserved from Conversion to Cropland | p. 83 |
Propane Cylinders Used for Home Barbecues | p. 85 |
Railcars of Coal Burned | p. 86 |
Tons of Waste Recycled Instead of Landfilled | p. 86 |
Coal-Fired Power Plant Emissions for One Year | p. 86 |
References and Recommended Reading | p. 87 |
Chapter 3 Sequence of Operations | p. 89 |
Sequence of Operations Rules | p. 89 |
Rule 1 p. 89 | |
Rule 2 p. 89 | |
Rule 3 p. 89 | |
Rule 4 p. 89 | |
Rule 5 p. 90 | |
Rule 6 p. 90 | |
Sequence of Operations Examples | p. 90 |
Chapter 4 Fractions, Decimals, and Percent | p. 95 |
Fractions | p. 95 |
Decimals | p. 98 |
Percent | p. 100 |
Chapter 5 Rounding and Significant Digits | p. 105 |
Rounding Numbers | p. 105 |
Determining Significant Figures | p. 105 |
Chapter 6 Powers of Ten and Exponents | p. 107 |
Rules | p. 107 |
Powers | p. 108 |
Examples | p. 108 |
Chapter 7 Averages (Arithmetic Mean) and Median | p. 109 |
Averages | p. 109 |
Median | p. 110 |
Chapter 8 Solving for the Unknown | p. 113 |
Math Rules of Operation | p. 113 |
Equations | p. 113 |
Axioms | p. 115 |
Solving Equations | p. 115 |
Checking the Answer | p. 125 |
Setting Up Equations | p. 126 |
Summary of Key Points | p. 127 |
Chapter 9 Ratios and Proportions | p. 129 |
Ratios | p. 129 |
Proportions | p. 129 |
Working with Ratios and Proportions | p. 129 |
Chapter 10 Electrical Calculations | p. 133 |
Electrical Circuits and Power | p. 133 |
Ohm's Law | p. 133 |
Electrical Power | p. 138 |
Electrical Power Calculations | p. 138 |
Electrical Energy | p. 140 |
Series DC Circuit Characteristics | p. 140 |
Series Circuit Resistance | p. 141 |
Series Circuit Current | p. 142 |
Series Circuit Voltage | p. 143 |
Series Circuit Power | p. 145 |
General Series Circuit Analysis | p. 147 |
Parallel DC Circuits | p. 149 |
Parallel Circuit Characteristics | p. 149 |
Voltage in Parallel Circuits | p. 149 |
Current in Parallel Circuits | p. 151 |
Parallel Circuit Resistance | p. 153 |
Reciprocal Method | p. 156 |
Product over the Sum Method | p. 157 |
Power in Parallel Circuits | p. 157 |
Chapter 11 Circumference, Area, and Volume | p. 159 |
Perimeter and Circumference | p. 161 |
Perimeter | p. 161 |
Circumference | p. 162 |
Area | p. 163 |
Area of a Rectangle | p. 163 |
Area of a Circle | p. 164 |
Area of a Circular or Cylindrical Tank | p. 165 |
Volume | p. 166 |
Volume of a Rectangular Basin | p. 166 |
Volume of Round Pipe and Round Surface Areas | p. 167 |
Volume of a Cone and Sphere | p. 168 |
Volume of a Cone | p. 168 |
Volume of a Sphere | p. 168 |
Volume of a Circular or Cylindrical Tank | p. 169 |
Volume in Gallons | p. 169 |
Volume of Pipes | p. 170 |
Area Examples | p. 170 |
Volume Examples | p. 172 |
Chapter 12 Force, Pressure, Head, and Velocity Calculations | p. 175 |
Force and Pressure | p. 175 |
Head | p. 177 |
Static Head | p. 178 |
Friction Head | p. 178 |
Velocity Head | p. 178 |
Total Dynamic Head (Total System Head) | p. 179 |
Pressure and Head | p. 179 |
Head and Pressure | p. 179 |
Velocity | p. 180 |
Force, Pressure, Head, and Velocity Examples | p. 181 |
Chapter 13 Mass Balance and Measuring Plant Performance | p. 187 |
Mass Balance for Settling Tanks | p. 187 |
Mass Balance Using BOD Removal | p. 188 |
Measuring Plant Performance | p. 190 |
Plant Performance/Efficiency | p. 190 |
Unit Process Performance and Efficiency | p. 191 |
Percent Volatile Matter Reduction in Sludge | p. 192 |
Chapter 14 Pumping Calculations | p. 193 |
Basic Water Hydraulics Calculations | p. 193 |
Weight of Water | p. 193 |
Weight of Water Related to the Weight of Air | p. 194 |
Water at Rest | p. 195 |
Gauge Pressure | p. 195 |
Water in Motion | p. 196 |
Discharge | p. 196 |
Law of Continuity | p. 197 |
Pipe Friction | p. 197 |
Basic Pumping Calculations | p. 198 |
Pumping Rates | p. 198 |
Calculating Head Loss | p. 200 |
Calculating Head | p. 200 |
Calculating Horsepower and Efficiency | p. 201 |
Hydraulic Horsepower | p. 201 |
Pump Efficiency and Brake Horsepower | p. 201 |
Specific Speed | p. 204 |
Positive-Displacement Pumps | p. 204 |
Volume of Biosolids Pumped (Capacity) | p. 205 |
Pumping Examples | p. 206 |
Chapter 15 Water Source and Storage Calculations | p. 219 |
Water Source Calculations | p. 219 |
Well Drawdown | p. 219 |
Well Yield | p. 221 |
Specific Yield | p. 221 |
Well Casing Disinfection | p. 222 |
Deep-Well Turbine Pump Calculations | p. 222 |
Vertical Turbine Pump Calculations | p. 223 |
Water Storage | p. 228 |
Water Storage Calculations | p. 228 |
Copper Sulfate Dosing | p. 229 |
Chapter 16 Water/Wastewater Laboratory Calculations | p. 231 |
Faucet Flow Estimation | p. 231 |
Service Line Flushing Time | p. 232 |
Composite Sampling Calculation (Proportioning Factor) | p. 233 |
Composite Sampling Procedure and Calculation | p. 234 |
Biochemical Oxygen Demand Calculations | p. 235 |
BOD 5 (Unseeded) | p. 235 |
BOD 5 (Seeded) | p. 235 |
BOD 7-Day Moving Average | p. 236 |
Moles and Molarity | p. 237 |
Moles | p. 237 |
Normality | p. 238 |
Settleability (Activated Biosolids Solids) | p. 239 |
Settleable Solids | p. 240 |
Total Solids, Fixed Solids, and Volatile Solids | p. 241 |
Wastewater Suspended Solids and Volatile Suspended Solids | p. 243 |
Biosolids Volume Index and Biosolids Density Index | p. 244 |
Chemical Dosage Calculations | p. 245 |
Dosage Formula Pie Chart | p. 246 |
Chlorine Dosage | p. 247 |
Hypochlorite Dosage | p. 249 |
Laboratory Examples | p. 254 |
Chapter 17 Basic Mathemathics Practice Problems | p. 259 |
Basic Math Operations | p. 259 |
Decimal Operations | p. 259 |
Percentage Calculations | p. 260 |
Solving for an Unknown | p. 260 |
Ratio and Proportion | p. 261 |
Area of Rectangles | p. 261 |
Circumference and Area of Circles | p. 261 |
Fundamental Water/Wastewater Operations | p. 261 |
Tank Volume Calculations | p. 261 |
Channel and Pipeline Capacity Calculations | p. 262 |
Miscellaneous Volume Calculations | p. 262 |
Flow, Velocity, and Conversion Calculations | p. 263 |
Average Flow Rates | p. 265 |
Flow Conversions | p. 265 |
General Flow and Velocity Calculations | p. 265 |
Chemical Dosage Calculations | p. 267 |
Appendix: Solutions to Chapter 17 Problems | p. 269 |
Index | p. 273 |