Table Of ContentWATER SCIENCE & ENGINEERING S Mathematics Manual for Water and Wastewater Treatment Plant Operators
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Mathematics Manual for Water and Wastewater Treatment Plant Operators
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Water Treatment Operations
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To properly operate a waterworks or wastewater treatment plant and to pass the examination e
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for a waterworks/wastewater operator’s license, it is necessary to know how to perform certain tio
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calculations. All operators, at all levels of licensure, need a basic understanding of arithmetic and s
problem-solving techniques to solve the problems they typically encounter in the workplace.
Mathematics Manual for Water and Wastewater Treatment Plant Operators was hailed on its first
publication as a masterly account written in an engaging, highly readable, user-friendly style. It
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has now been expanded and divided into three specialized texts that contain hundreds of worked th
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examples presented in a step-by-step format. They are ideal for all levels of water treatment operators a
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in training and practitioners studying for advanced licensure. In addition, they provide a handy s M
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desk reference and handheld guide for daily use in making operational math computations. n
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Mathematics Manual for Water and Wastewater Treatment Plant Operators, Second Edition: Water r W
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Treatment Operations: Math Concepts and Calculations covers computations commonly used in water r a
treatment with applied math problems specific to waterworks operations, allowing operators of specific unit nd W
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processes to focus on their area of specialty. It explains calculations for pumping, water source and storage, ste and Calculations
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coagulation and flocculation, sedimentation, filtration, chlorination, fluoridation, and water softening. The text a
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presents math operations that progressively advance to higher, more practical applications of mathematical r T
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calculations, including math operations that operators at the highest level of licensure would be expected tm
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to know and perform. To ensure correlation to modern practice and design, this book provides illustrative nt P
problems for commonly used waterworks treatment operations found in today’s treatment facilities. lan
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K22360 Frank R. Spellman
6000 Broken Sound Parkway, NW
Suite 300, Boca Raton, FL 33487
711 Third Avenue
New York, NY 10017
an informa business
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K22360_cover.indd 1 4/7/14 1:52 PM
Mathematics Manual for Water and Wastewater Treatment Plant Operators
Second Edition
Water Treatment Operations
Math Concepts and Calculations
Mathematics Manual for Water and Wastewater
Treatment Plant Operators, Second Edition
Basic Mathematics for Water and Wastewater Operators
Water Treatment Operations: Math Concepts and Calculations
Wastewater Treatment Operations: Math Concepts and Calculations
Mathematics Manual for Water and Wastewater Treatment Plant Operators
Second Edition
Water Treatment Operations
Math Concepts and Calculations
Frank R. Spellman
Boca Raton London New York
CRC Press is an imprint of the
Taylor & Francis Group, an informa business
CRC Press
Taylor & Francis Group
6000 Broken Sound Parkway NW, Suite 300
Boca Raton, FL 33487-2742
© 2014 by Taylor & Francis Group, LLC
CRC Press is an imprint of Taylor & Francis Group, an Informa business
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Version Date: 20140114
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Contents
Preface.......................................................................................................................ix
Author .......................................................................................................................xi
Chapter 1 Pumping Calculations ..........................................................................1
Pumping ...............................................................................................1
Basic Water Hydraulics Calculations ...................................................1
Weight of Water ...............................................................................1
Weight of Water Related to the Weight of Air ................................2
Water at Rest ....................................................................................2
Gauge Pressure ................................................................................3
Water in Motion ...............................................................................3
Discharge ....................................................................................4
The Law of Continuity ................................................................5
Pipe Friction ....................................................................................5
Basic Pumping Calculations.................................................................6
Pumping Rates .................................................................................6
Calculating Head Loss ....................................................................8
Calculating Head .............................................................................8
Calculating Horsepower and Efficiency ..........................................9
Hydraulic Horsepower ................................................................9
Pump Efficiency and Brake Horsepower ..................................10
Specific Speed ...............................................................................12
Positive-Displacement Pumps ............................................................12
Volume of Biosolids Pumped (Capacity) .......................................13
Chapter 2 Water Source and Storage Calculations .............................................15
Water Sources .....................................................................................15
Water Source Calculations .................................................................16
Well Drawdown .............................................................................16
Well Yield ......................................................................................17
Specific Yield.................................................................................18
Well Casing Disinfection ...............................................................18
Deep-Well Turbine Pump Calculations .........................................19
Vertical Turbine Pump Calculations .............................................19
Water Storage .....................................................................................24
Water Storage Calculations ................................................................25
Copper Sulfate Dosing .......................................................................26
Iron and Manganese Removal ............................................................29
Precipitation ..............................................................................29
Oxidation ..................................................................................30
v
vi Contents
Ion Exchange ............................................................................30
Sequestering..............................................................................31
Aeration ....................................................................................31
Potassium Permanganate Oxidation and Manganese
Greensand .................................................................................31
Chapter 3 Coagulation and Flocculation Calculations .......................................35
Coagulation ........................................................................................35
Flocculation ........................................................................................35
Coagulation and Flocculation Calculations .......................................36
Chamber and Basin Volume Calculations .....................................36
Detention Time ..............................................................................37
Determining Dry Chemical Feeder Setting ..................................37
Determining Chemical Solution Feeder Setting (lb/day) ..............38
Determining Chemical Solution Feeder Setting (mL/min) ...........39
Determining Percent Strength of Solutions ...................................40
Determining Percent Strength of Liquid Solutions .......................41
Determining Percent Strength of Mixed Solutions .......................41
Dry Chemical Feeder Calibration .................................................42
Chemical Solution Feeder Calibration ..........................................43
Determining Chemical Usage .......................................................44
Coagulation and Flocculation Practice Problems ..............................46
Chemical Feeders ...............................................................................51
Solution Feeders ............................................................................51
Dry Feeders ...................................................................................51
Chemical Feeder Calibration .........................................................52
Chemical Feeder Calculations ...........................................................52
Chapter 4 Sedimentation Calculations ................................................................57
Sedimentation .....................................................................................57
Tank Volume Calculations .................................................................57
Calculating Tank Volume ..............................................................57
Detention Time ...................................................................................58
Surface Loading (Overflow) Rate.......................................................59
Mean Flow Velocity ...........................................................................60
Weir Loading (Overflow) Rate ...........................................................61
Percent Settled Biosolids ....................................................................62
Determining Lime Dosage (mg/L) .....................................................62
Step 1 .............................................................................................63
Step 2 .............................................................................................64
Step 3 .............................................................................................64
Determining Lime Dosage (lb/day) ....................................................66
Determining Lime Dosage (g/min) ....................................................66
Sedimentation Practice Problems.......................................................67
Contents vii
Chapter 5 Filtration Calculations ........................................................................75
Water Filtration ..................................................................................75
Flow Rate through a Filter .................................................................75
Filtration Rate .....................................................................................78
Unit Filter Run Volume ......................................................................79
Backwash Rate ...................................................................................80
Backwash Rise Rate ......................................................................81
Volume of Backwash Water Required ...............................................82
Required Depth of Backwash Water Tank .........................................83
Backwash Pumping Rate ....................................................................83
Percent Product Water Used for Backwashing ...................................84
Percent Mud Ball Volume ..................................................................85
Filter Bed Expansion ..........................................................................86
Filter Loading Rate ............................................................................86
Filter Medium Size .............................................................................87
Mixed Media ......................................................................................88
Head Loss for Fixed Bed Flow ...........................................................89
Head Loss through a Fluidized Bed ...................................................90
Horizontal Wastewater Troughs .........................................................92
Filter Efficiency ..................................................................................93
Water Filtration Practice Problems ....................................................93
References and Recommended Reading ............................................99
Chapter 6 Water Chlorination Calculations ......................................................101
Chlorine Disinfection .......................................................................101
Determining Chlorine Dosage (Feed Rate) .....................................101
Calculating Chlorine Dose, Demand, and Residual ........................103
Breakpoint Chlorination Calculations ..............................................104
Calculating Dry Hypochlorite Feed Rate.........................................106
Calculating Hypochlorite Solution Feed Rate ..................................108
Calculating Percent Strength of Solutions ........................................109
Calculating Percent Strength Using Dry Hypochlorite ...............110
Calculating Percent Strength Using Liquid Hypochlorite ...........110
Chemical Use Calculations ..............................................................111
Chlorination Math Practice Problems ..............................................112
Chapter 7 Fluoridation ......................................................................................115
Water Fluoridation............................................................................115
Fluoride Compounds ........................................................................115
Sodium Fluoride ..........................................................................116
Fluorosilicic Acid ........................................................................117
Sodium Fluorosilicate ..................................................................117
Optimal Fluoride Levels ..................................................................118
viii Contents
Fluoridation Process Calculations ....................................................119
Percent Fluoride Ion in a Compound ...........................................119
Fluoride Feed Rate ......................................................................120
Fluoride Feed Rates for Saturator ...............................................122
Calculated Dosages .....................................................................123
Calculated Dosage Examples ......................................................125
Fluoridation Practice Problems ........................................................127
Chapter 8 Water Softening ................................................................................131
Water Hardness ................................................................................131
Calculating Calcium Hardness (as CaCO) .................................131
3
Calculating Magnesium Hardness (as CaCO) ............................132
3
Calculating Total Hardness .........................................................133
Calculating Carbonate and Noncarbonate Hardness...................133
Determining Alkalinity ....................................................................135
Determining Bicarbonate, Carbonate, and Hydroxide Alkalinity .....136
Lime Dosage Calculation for Removal of Carbonate Hardness ......138
Calculation for Removal of Noncarbonate Hardness .......................139
Recarbonation Calculation ...............................................................141
Calculating Feed Rates .....................................................................142
Ion Exchange Capacity .....................................................................143
Water Treatment Capacity ................................................................143
Treatment Time Calculations (Until Regeneration Required) .........145
Salt and Brine Required for Regeneration .......................................145
Chapter 9 Water Treatment Practice Calculations ............................................147
Appendix: Solutions to Chapter 9 Problems .....................................................191
