Environmental Engineer s Mathematics Handbook 1st Edition by Frank Spellman ISBN 978-0367578237 0367578239
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ISBN 10: 0367578239
ISBN 13: 978-0367578237
Author: Frank R. Spellman
Advanced mathematics used in engineering is studied here in this text which examines the relationship between the principles in natural processes and those employed in engineered processes. The text covers principles, practices and the mathematics involved in the design and operation of environmental engineering works. It also presents engineering modelling tools and environmental algorithm examples. Major subjects covered in this book include:* modelling * algorithms * air and water pollution assessment and control calculations Providing concepts, definitions, descriptions, and derivations in an intuitive manner, it is both a textbook and reference tool for practitioners involved in the protection of air, water, and land resources.
Table of contents:
PART I: FUNDAMENTAL COMPUTATION AND MODELING
Chapter 1
Conversion Factors and SI Units
1.1 Introduction
1.2 Conversion Factors..
1.3 Conversion Factors: Practical Examples
1.3.1 Weight, Concentration, and Flow.
1.3.2 Water/Wastewater Conversion Examples.
1.3.3 Temperature Conversions.
1.4 Conversion Factors: Air Pollution Measurements..
1.4.1 Conversion from Parts per Million to Micrograms per Cubic Meter.
1.4.2 Conversion Tables for Common Air Pollution Measurements.
1.5 Soil Test Results Conversion Factors
1.6 Conclusion.
Chapter 2
Basic Math Operations.
2.1 Introduction
2.2 Basic Math Terminology and Definitions
2.3 Sequence of Operations.
2.3.1 Sequence of Operations Rules
2.3.2 Sequence of Operations Examples
2.4 Percent.
2.5 Significant Digits..
2.6 Powers and Exponents
2.7 Averages (Arithmetic Mean).
2.8 Ratio
2.9 Dimensional Analysis
2.10 Threshold Odor Number (TON).
2.11 Geometrical Measurements.
2.11.1 Geometrical Calculations
Perimeter and Circumference.
2.11.1.2 Area
2.11.1.3 Volume.
2.12 Force, Pressure, and Head Calculations
2.12.1 Force and Pressure
2.12.2 Head
2.12.2.1 Static Head
Friction Head.
2.12.2.3 Velocity Head
2.12.2.4 Total Dynamic Head (Total System Head).
2.12.2.5 Pressure/Head
2.12.2.6 Head/Pressure.
2.13 Review of Advanced Algebra Key Terms and Concepts
Chapter 3
Environmental Modeling
3.1 Introduction
3.2 Media Material Content.
3.2.1 Material Content: Liquid Phases…
3.3 Phase Equilibrium and Steady State….
3.4 Math Operations and Laws of Equilibrium.
3.4.1 Solving Equilibrium Problems…
3.4.2 Laws of Equilibrium……..
3.4.2.1 Ideal Gas Law
3.4.2.2 Dalton’s Law
3.4.2.3 Raoult’s Law
3.4.2.4 Henry’s Law
3.5 Chemical Transport Systems
3.6 A Final Word on Environmental Modeling.
References
Chapter 4 Algorithms and Environmental Engineering.
4.1 Introduction
4.2 Algorithms: What Are They?..
4.3 Expressing Algorithms……..
4.4 General Algorithm Applications
4.5 Environmental Engineering Algorithm Applications
4.6 Dispersion Models
4.7 Screening Tools…..
References
Suggested Reading..
PART II: FUNDAMENTAL SCIENCE AND STATISTICS REVIEW
Chapter 5
Fundamental Chemistry and Hydraulics
5.1 Introduction.
5.2 Fundamental Chemistry.
5.2.1 Density and Specific Gravity
5.2.2 Water Chemistry Fundamentals
5.2.2.1 The Water Molecule.
Water Solutions
5.2.2.3 Concentrations……..
5.2.2.4 Predicting Solubility.
5.2.2.5 Colligative Properties
5.2.2.6 Colloids/Emulsions…..
5.2.2.7 Water Constituents
5.2.2.8 Simple Solutions and Dilutions.
5.2.2.9 Chemical Reactions….
5.2.2.10 Chemical Dosages (Water and Wastewater Treatment).
5.3 Fundamental Hydraulics
5.3.1 Principles of Water Hydraulics.
5.3.1.1 Weight of Air……….
5.3.1.2 Weight of Water
5.3.1.3 Weight of Water Related to the Weight of Air..
5.3.1.4 Water at Rest.
5.3.1.5 Gauge Pressure.
5.3.1.6 Water in Motion
5.3.1.7 Discharge…….
5.3.1.8 The Law of Continuity.
5.3.1.9 Pipe Friction
Basic Pumping Calculations
5.3.2.1 Pumping Rates…
5.3.2
5.3.3 Calculating Head Loss
5.3.4 Calculating Head.
5.3.5 Calculating Horsepower and Efficiency…..
5.3.5.1 Hydraulic Horsepower (WHP).
5.3.5.2 Pump Efficiency and Brake Horsepower (bhp).
References
Suggested Reading.
Chapter 6 Statistics Review
6.1 Statistical Concepts.
6.2 Measure of Central Tendency.
6.3 Basic Statistical Terms….
6.4 DMR Calculations……
6.4.1 Loading Calculation
6.4.2 Monthly Average Loading Calculations
6.4.3 30-Day Average Calculation
6.4.4 Moving Average
6.4.5 Geometric Mean.
6.4.5.1 Logarithm (Log) Method
6.4.5.2 Nth Root Calculation Method..
6.5 Standard Deviation…
6.6 Conclusion…..
PART III: MATH CONCEPTS: AIR POLLUTION CONTROL
Chapter 7
Air Pollution Fundamentals.
7.1 Introduction
7.1.1
Six Common Air Pollutants
Ground-Level Ozone.
7.1.1.2 Nitrogen Oxides
7.1.1.3 Particulate Matter.
7.1.1.4 Sulfur Dioxide (SO₂)
7.1.1.5 Carbon Monoxide (CO)
7.1.1.6 Lead
The Gas Laws…..
7.2.1.1 Boyle’s Law.
7.2.1.2 Charles’s Law
7.2.1.3 Gay-Lussac’s Law
7.2.1.4 The Combined Gas Law
7.2.1.5 The Ideal Gas Law..
7.2.1.6 Composition of Air
7.2 Gases
7.2.1
7.3 Particulate Matter.
7.4 Pollution Emission Measurement Parameters.
7.5 Standard Corrections…..
References
Chapter 8
Gaseous Emission Control..
8.1 Introduction.
8.2 Absorption….
8.2.1 Solubility.
8.2.2 Equilibrium Solubility and Henry’s Law….
8.2.3 Material (Mass) Balance
8.2.4
Sizing Packed Column Diameter and Height of an Absorber.
8.2.4.1 Packed Tower Absorber Diameter
8.2.4.2 Sizing the Packed Tower Absorber Height….
8.2.4.3 Sizing the Plate (Tray) Tower…..
8.2.4.4 Theoretical Number of Absorber Plates or Trays.
8.3 Adsorption.
8.3.1 Adsorption Steps
8.3.2 Adsorption Forces Physical and Chemical…
8.3.3 Adsorption Equilibrium Relationships……
8.3.3.1 Isotherm….
8.3.3.2 Isostere…
Isobar.
8.3.4 Factors Affecting Adsorption
8.3.4.1 Temperature.
8.3.4.2 Pressure.
8.3.4.3 Gas Velocity
8.3.4.4 Bed Depth..
8.3.4.5 Humidity……..
8.3.4.6 Contaminants.
8.4 Incineration…..
8.4.1 Factors Affecting Incineration for Emission Control
8.4.1.1 Temperature.
8.4.1.2 Residence Time.
8.4.1.3 Turbulence
8.4.1.4 Oxygen Requirement.
8.4.1.5 Combustion Limit
8.4.1.6 Flame Combustion
8.4.1.7 Heat…..
8.4.2 Incineration Example Calculations
8.5 Condensation……
8.5.1 Contact Condenser Calculations
8.5.2 Surface Condenser Calculations….
References
Chapter 9
Particulate Emission Control
9.1 Particulate Emission Control Basics…
9.1.1 Interaction of Particles with Gas…
9.1.2 Particulate Collection
9.2 Particulate Size Characteristics and General Characteristics….
9.2.1 Aerodynamic Diameter
9.2.2 Equivalent Diameter.
9.2.3 Sedimentation Diameter.
9.2.4 Cut Diameter
9.2.5 Dynamic Shape Factor.
9.3 Flow Regime of Particle Motion
9.4 Particulate Emission Control Equipment Calculations
9.4.1 Gravity Settlers….
9.4.2 Gravity Settling Chamber Theoretical Collection Efficiency.
9.4.3 Minimum Particle Size….
9.4.4 Cyclones
9.4.4.1 Factors Affecting Cyclone Performance.
9.4.6 Electrostatic Precipitator (ESP)…..
9.4.6.1 Collection Efficiency
9.4.6.2 Precipitator Example Calculations…
9.4.7 Baghouse (Fabric) Filters..
9.4.7.1 Air-to-Filter (Media) Ratio
9.4.7.2 Baghouse Example Calculations…
References
Chapter 10 Wet Scrubbers for Emission Control
10.1 Introduction
10.1.1 Wet Scrubbers..
10.2 Wet Scrubber Collection Mechanisms and Efficiency (Particulates)
10.2.1 Collection Efficiency
10.2.2 Impaction
10.2.3 Interception
10.2.4 Diffusion
10.2.5 Calculation of Venturi Scrubber Efficiency
10.2.5.1 Johnstone Equation
10.2.5.2 Infinite Throat Model
10.2.5.3 Cut Power Method
10.2.5.4 Contact Power Theory.
10.2.5.5 Pressure Drop
10.3 Wet Scrubber Collection Mechanisms and Efficiency (Gaseous Emission
10.4 Assorted Venturi Scrubber Example Calculations
10.4.1 Scrubber Design of a Venturi Scrubber
10.4.2 Spray Tower……
10.4.3 Packed Tower…..
10.4.4 Packed Column Height and Diameter
10.5 Summary of Key Points……
References
PART IV: MATH CONCEPTS: WATER QUALITY
Chapter 11 Running Waters
11.1 Balancing the “Aquarium”.
11.1.1 Sources of Stream Pollution….
11.2 Is Dilution the Solution?…
11.2.1 Dilution Capacity of Running Waters…….
11.3 Discharge Measurement………..
11.4 Time of Travel…
11.5 Dissolved Oxygen (DO)
11.5.1 DO Correction Factor.
11.6 Biochemical Oxygen Demand
11.6.1 BOD Test Procedure….
11.6.2 Practical BOD Calculation Procedure
11.6.2.1 Unseeded BOD Procedure
11.6.2.2 Seeded BOD Procedure
11.7 Oxygen Sag (Deoxygenation)….
11.8 Stream Purification: A Quantitative Analysis.
References
Chapter 12 Still Waters
12.1 Introduction…..
12.2 Still Water Systems….
12.3 Still Water System Calculations
12.3.1 Still Water Body Morphometry Calculations
12.3.1.1 Volume….
12.3.1.2 Shoreline Development Index (D)…
12.3.1.3 Mean Depth.
12.4 Still Water Surface Evaporation….
12.4.1 Water Budget Model
12.4.2 Energy Budget Model
12.4.3 Priestly-Taylor Equation.
12.4.4 Penman Equation………
12.4.5 DeBruin-Keijman Equation
12.4.6 Papadakis Equation
References
Chapter 13 Groundwater.
13.1 Groundwater and Aquifers..
13.1.1 Groundwater Quality
13.1.2 GUDISW
13.2 Aquifer Parameters…
13.2.1 Aquifer Porosity
13.2.2 Specific Yield (Storage Coefficient).
13.2.3 Permeability (K)
13.2.4 Transmissivity (T)
13.2.5 Hydraulic Gradient and Head
13.2.6 Flow Lines and Flow Nets.
13.3 Groundwater Flow
13.4 General Equations of Groundwater Flow..
13.4.1 Steady Flow in a Confined Aquifer.
13.4.2 Steady Flow in an Unconfined Aquifer.
References
Chapter 14 Basic Hydraulics.
14.1 Introduction…..
14.2 Basic Concepts.
14.2.1 Stevin’s Law
14.2.2 Density and Specific Gravity
14.2.3 Force and Pressure
14.2.4 Hydrostatic Pressure…
14.2.5 Head…
14.2.5.1 Static Head
14.2.5.2 Friction Head..
14.2.5.3 Velocity Head.
14.2.5.4 Total Dynamic Head (Total System Head).
14.2.5.5 Pressure/Head.
14.2.5.6 Head/Pressure
14.3 Flow/Discharge Rate: Water in Motion.
14.3.1 Area/Velocity
14.3.2 Pressure/Velocity
14.4 Bernoulli’s Theorem…
14.4.1 Bernoulli’s Equation…
14.5 Calculating Major Head Loss.
14.5.1 C Factor
14.6 Characteristics of Open-Channel Flow.
14.6.1 Laminar and Turbulent Flow.
14.6.2 Uniform and Varied Flow..
14.6.3 Critical Flow
14.6.4 Parameters Used in Open Channel Flow.
14.6.4.1 Hydraulic Radius….
14.6.4.2 Hydraulic Depth
14.6.4.3 Slope, S….
14.7 Open-Channel Flow Calculations.
References.
Chapter 15 Water Treatment Process Calculations
15.1 Introduction..
15.2 Water Source and Storage Calculations.
15.2.1 Water Source Calculations
15.2.1.1 Well Drawdown….
15.2.1.2 Well Yield
15.2.1.3 Specific Yield…
15.2.1.4 Well Casing Disinfection
15.2.1.5 Deep-Well Turbine Pump Calculations.
15.2.3 Vertical Turbine Pump Calculations
15.3 Water Storage….
15.3.1 Water Storage Calculations.
15.3.2 Copper Sulfate Dosing…..
15.4 Coagulation, Mixing, and Flocculation…
15.4.1 Coagulation…….
15.4.2 Mixing…….
15.4.3 Flocculation
15.4.4 Coagulation and Flocculation General Calculations.
15.4.4.1 Chamber and Basin Volume Calculations
15.4.4.2 Detention Time…
15.4.4.3 Determining Dry Chemical Feeder Setting (Pounds per Day)
15.7.8 Calculating Percent Strength Using Dry Hypochlorite
15.7.9 Calculating Percent Strength Using Liquid Hypochlorite.
15.8 Chemical Use Calculations….
15.8.1 Chlorination Chemistry
References
PART V: MATH CONCEPTS: WASTEWATER ENGINEERING
Chapter 16 Wastewater Calculations
16.1 Introduction
16.2 Preliminary Treatment Calculations
16.2.1 Screening
16.2.2 Screenings Removal Calculations…..
16.2.3 Screenings Pit Capacity Calculations.
16.2.4 Headloss through Bar Screen……
16.2.5 Grit Removal
16.2.6 Grit Removal Calculations
16.2.7 Grit Channel Velocity Calculation.
16.2.7.1 Required Settling Time
16.2.7.2 Required Channel Length
16.2.7.3 Velocity of Scour..
16.3 Primary Treatment Calculations
16.3.1 Process Control Calculations
16.3.2 Surface Loading Rate (Surface Settling Rate/Surface Overflow Rate)………
16.3.3 Weir Overflow Rate (Weir Loading Rate).
16.3.4 Primary Sedimentation Basins.
16.4 Biosolids Pumping…..
16.4.1 Percent Total Solids (% TS)…
16.4.2 BOD and SS Removed, Pounds per Day
16.5 Trickling Filter Calculations..
16.5.1 Trickling Filter Process Calculations..
16.5.2 Hydraulic Loading..
16.5.3 Organic Loading Rate
16.5.4 BOD and SS Removed…
16.5.5 Recirculation Flow
16.5.6 Trickling Filter Design
16.6 Rotating Biological Contactors (RBCs)
16.6.1 RBC Process Control Calculations.
16.6.2 Hydraulic Loading Rate
16.6.3 Soluble BOD
16.6.4 Organic Loading Rate
16.6.5 Total Media Area……
16.6.6 Modeling RBC Performance..
16.6.7 RBC Performance Parameter
16.7 Activated Biosolids
16.7.1 Activated Biosolids Process Control Calculations
16.7.2 Moving Averages…
16.7.3 BOD or COD Loading
16.7.4 Solids Inventory………
16.7.5 Food-to-Microorganism Ratio (F/M Ratio).
16.7.6 Gould Biosolids Age
16.7.7 Mean Cell Residence Time (MCRT)
16.7.8 Estimating Retum Rates from SBV60 (SSV)
16.7.9 Biosolids (Sludge) Volume Index (BVI)……..
16.7.10 Mass Balance: Settling Tank Suspended Solids.
16.7.11 Mass Balance Calculation
16.7.12 Biosolids Waste Based Upon Mass Balance
16.7.13 Aeration Tank Design Parameters…
16.7.14 Lawrence and McCarty Design Model.
16.7.14.1 Complete Mix with Recycle
16.7.15 Effluent Microorganism and Substrate Concentrations.
16.7.15.1 Process Design and Control Relationships.
16.7.15.2 Sludge Production
16.7.15.3 Oxygen Requirements.
16.8 Oxidation Ditch Detention Time.
16.9 Treatment Ponds……
16.9.1 Treatment Pond Parameters……
16.9.2 Treatment Pond Process Control Calculations
16.9.2.1 Hydraulic Detention Time, Days
16.9.2.2 BOD Loading.
16.9.2.3 Organic Loading Rate.
16.9.2.4 BOD Removal Efficiency.
16.9.2.5 Population Loading.
16.9.2.6 Hydraulic Loading, Inches/Day (Overflow Rate)..
16.9.3 Aerated Ponds…….
16.10 Chemical Dosage Calculations.
16.10.1 Chemical Dosing
16.10.2 Chemical Feed Rate
16.10.3 Chlorine Dose, Demand, and Residual.
16.10.3.1 Chlorine Dose…..
16.10.3.2 Chlorine Demand
16.10.3.3 Chlorine Residual.
16.10.4 Hypochlorite Dosage…..
16.10.5 Chemical Solutions…….
16.10.6 Mixing Solutions of Different Strengths
16.10.7 Solution Mixtures Target Percent Strength.
16.10.8 Solution Chemical Feeder Setting, GPD
16.10.9 Chemical Feed Pump Percent Stroke Setting.
16.10.10 Chemical Solution Feeder Setting, Milliliters per Minute
16.10.11 Chemical Feed Calibration……
16.10.12 Average Use Calculations
16.11 Biosolids Production and Pumping Calculations.
16.11.1 Process Residuals
16.11.2 Primary and Secondary Solids Production Calculations
16.11.3 Primary Clarifier Solids Production Calculations……
16.11.4 Secondary Clarifier Solids Production Calculation.
16.11.5 Percent Solids
16.11.6 Biosolids Pumping
16.11.7 Estimating Daily Biosolids Production……
16.11.8 Biosolids Production (Pounds per Million Gallons).
16.7.6 Gould Biosolids Age
16.7.7 Mean Cell Residence Time (MCRT)
16.7.8 Estimating Retum Rates from SBV60 (SSV60)
16.7.9 Biosolids (Sludge) Volume Index (BVI)…….
16.7.10 Mass Balance: Settling Tank Suspended Solids.
16.7.11 Mass Balance Calculation
16.7.12 Biosolids Waste Based Upon Mass Balance
16.7.13 Aeration Tank Design Parameters….
16.7.14 Lawrence and McCarty Design Model.
16.7.14.1 Complete Mix with Recycle
16.7.15 Effluent Microorganism and Substrate Concentrations.
16.7.15.1 Process Design and Control Relationships.
16.7.15.2 Sludge Production
16.7.15.3 Oxygen Requirements.
16.8 Oxidation Ditch Detention Time
16.9 Treatment Ponds…
16.9.1 Treatment Pond Parameters…
16.9.2 Treatment Pond Process Control Calculations
16.9.2.1 Hydraulic Detention Time, Days
16.9.2.2 BOD Loading
16.9.2.3 Organic Loading Rate.
16.9.2.4 BOD Removal Efficiency.
16.9.2.5 Population Loading.
16.9.2.6 Hydraulic Loading, Inches/Day (Overflow Rate).
16.9.3 Aerated Ponds……..
16.10 Chemical Dosage Calculations.
16.10.1 Chemical Dosing.
16.10.2 Chemical Feed Rate
16.10.3 Chlorine Dose, Demand, and Residual.
16.10.3.1 Chlorine Dose..
16.10.3.2 Chlorine Demand
16.10.3.3 Chlorine Residual.
16.10.4 Hypochlorite Dosage.
16.10.5 Chemical Solutions…..
16.10.6 Mixing Solutions of Different Strengths
16.10.7 Solution Mixtures Target Percent Strength.
16.10.8 Solution Chemical Feeder Setting, GPD
16.10.9 Chemical Feed Pump Percent Stroke Setting.
16.10.10 Chemical Solution Feeder Setting, Milliliters per Minute.
16.10.11 Chemical Feed Calibration……
16.10.12 Average Use Calculations
16.11 Biosolids Production and Pumping Calculations.
16.11.1 Process Residuals.
16.11.2 Primary and Secondary Solids Production Calculations
16.11.3 Primary Clarifier Solids Production Calculations……
16.11.4 Secondary Clarifier Solids Production Calculation.
16.11.5 Percent Solids
16.11.6 Biosolids Pumping
16.11.7 Estimating Daily Biosolids Production……
16.11.8 Biosolids Production (Pounds per Million Gallons).
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