ENVIRONMENTAL ENGINEER’S MATHEMATICS HANDBOOK Frank R. Spellman and Nancy E. Whiting CRC PR E S S Boca Raton London New York Washington, D. © 2005 by CRC Press LLC L1681_C00.fm Page iv Tuesday, October 5, 2004 2:12 PM Library of Congress Cataloging-in-Publication Data Spellman, Frank R.
Environmental engineer’s mathematics handbook / by Frank R. Spellman, Nancy Whiting. Includes bibliographical references and index. Environmental engineering--Mathematics--Handbooks, manuals, etc.8′95--dc22 2004051872 This book contains information obtained from authentic and highly regarded sources.
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Visit the CRC Press Web site at www.com © 2005 by CRC Press LLC No claim to original U. Government works International Standard Book Number 1-56670-681-5 Library of Congress Card Number 2004051872 Printed in the United States of America 1 2 3 4 5 6 7 8 9 0 © 2005 by CRC Press LLC L1681_C00.fm Page v Tuesday, October 5, 2004 2:12 PM Preface Environmental Engineer’s Mathematics Handbook brings together and integrates in a single text the more practical math operations of environmental engineering for air, water, wastewater, biosolids and stormwater. Taking an unusual approach to the overall concept of environmental engineering math concepts, this offers the reader an approach that emphasizes the relationship between the principles in natural processes and those employed in engineered processes. The text covers in detail the engineering principles, practices, and math operations involved in the design and operation of conventional environmental engineering works and presents engineering modeling tools and environmental algorithm examples.
The arrangement of the material lends itself to several different specific environmental specialties and several different formal course formats. Major subjects covered in this book include: • Math concepts review • Modeling • Algorithms • Air pollution control calculations • Water assessment and control calculations • Stormwater engineering math calculations In our approach, we emphasize concepts, definitions, descriptions, and derivations, as well as a touch of common sense. This book is intended to be a combination textbook and reference tool for practitioners involved in the protection of the three environmental media: air, water, and land resources. Spellman Norfolk, Virginia Nancy E.
Whiting Columbia, Pennsylvania © 2005 by CRC Press LLC L1681_C00.fm Page vii Tuesday, October 5, 2004 2:12 PM Acknowledgments This text would not have been possible without the tireless efforts of Mimi Williams. We appreciate her astute sense of sensibility and correctness. © 2005 by CRC Press LLC L1681_C00.fm Page ix Tuesday, October 5, 2004 2:12 PM Contents PART I: FUNDAMENTAL COMPUTATION AND MODELING .1 Chapter 1 Conversion Factors and SI Units .3 Conversion Factors: Practical Examples .1 Weight, Concentration, and Flow.2 Water/Wastewater Conversion Examples.4 Conversion Factors: Air Pollution Measurements.1 Conversion from Parts per Million to Micrograms per Cubic Meter .2 Conversion Tables for Common Air Pollution Measurements.5 Soil Test Results Conversion Factors .26 Chapter 2 Basic Math Operations.2 Basic Math Terminology and Definitions .3 Sequence of Operations .1 Sequence of Operations — Rules .2 Sequence of Operations — Examples .6 Powers and Exponents .10 Threshold Odor Number (TON).1 Perimeter and Circumference.12 Force, Pressure, and Head Calculations .1 Force and Pressure .4 Total Dynamic Head (Total System Head).13 Review of Advanced Algebra Key Terms and Concepts .71 © 2005 by CRC Press LLC L1681_C00.fm Page x Tuesday, October 5, 2004 2:12 PM Chapter 3 Environmental Modeling .2 Media Material Content .1 Material Content: Liquid Phases.3 Phase Equilibrium and Steady State.4 Math Operations and Laws of Equilibrium.1 Solving Equilibrium Problems .2 Laws of Equilibrium.1 Ideal Gas Law .5 Chemical Transport Systems .6 A Final Word on Environmental Modeling.85 Chapter 4 Algorithms and Environmental Engineering .2 Algorithms: What Are They?.4 General Algorithm Applications .5 Environmental Engineering Algorithm Applications .92 PART II: FUNDAMENTAL SCIENCE AND STATISTICS REVIEW .93 Chapter 5 Fundamental Chemistry and Hydraulics .1 Density and Specific Gravity .2 Water Chemistry Fundamentals .1 The Water Molecule .8 Simple Solutions and Dilutions .1 Principles of Water Hydraulics .1 Weight of Air.2 Weight of Water .3 Weight of Water Related to the Weight of Air .4 Water at Rest .128 © 2005 by CRC Press LLC L1681_C00.fm Page xi Tuesday, October 5, 2004 2:12 PM 5.6 Water in Motion .8 The Law of Continuity.2 Basic Pumping Calculations .3 Calculating Head Loss .5 Calculating Horsepower and Efficiency.2 Pump Efficiency and Brake Horsepower (bhp).138 Chapter 6 Statistics Review .2 Measure of Central Tendency .3 Basic Statistical Terms.2 Monthly Average Loading Calculations .3 30-Day Average Calculation .2 Nth Root Calculation Method.147 PART III: MATH CONCEPTS: AIR POLLUTION CONTROL .149 Chapter 7 Air Pollution Fundamentals .1 Six Common Air Pollutants .1 Ground-Level Ozone .1 The Gas Laws.3 Gay–Lussac’s Law .4 The Combined Gas Law .5 The Ideal Gas Law.6 Composition of Air .159 © 2005 by CRC Press LLC L1681_C00.fm Page xii Tuesday, October 5, 2004 2:12 PM 7.4 Pollution Emission Measurement Parameters .162 Chapter 8 Gaseous Emission Control.2 Equilibrium Solubility and Henry’s Law.4 Sizing Packed Column Diameter and Height of an Absorber .1 Packed Tower Absorber Diameter .2 Sizing the Packed Tower Absorber Height.3 Sizing the Plate (Tray) Tower .4 Theoretical Number of Absorber Plates or Trays.2 Adsorption Forces — Physical and Chemical.3 Adsorption Equilibrium Relationships.4 Factors Affecting Adsorption .1 Factors Affecting Incineration for Emission Control .2 Incineration Example Calculations .1 Contact Condenser Calculations .2 Surface Condenser Calculations.206 Chapter 9 Particulate Emission Control .1 Particulate Emission Control Basics.1 Interaction of Particles with Gas.2 Particulate Size Characteristics and General Characteristics.209 © 2005 by CRC Press LLC L1681_C00.fm Page xiii Tuesday, October 5, 2004 2:12 PM 9.5 Dynamic Shape Factor .3 Flow Regime of Particle Motion .4 Particulate Emission Control Equipment Calculations .2 Gravity Settling Chamber Theoretical Collection Efficiency.3 Minimum Particle Size.1 Factors Affecting Cyclone Performance.2 Precipitator Example Calculations.1 Air-to-Filter (Media) Ratio .2 Baghouse Example Calculations.247 Chapter 10 Wet Scrubbers for Emission Control.2 Wet Scrubber Collection Mechanisms and Efficiency (Particulates) .5 Calculation of Venturi Scrubber Efficiency .2 Infinite Throat Model .3 Cut Power Method .4 Contact Power Theory.3 Wet Scrubber Collection Mechanisms and Efficiency (Gaseous Emissions).4 Assorted Venturi Scrubber Example Calculations .1 Scrubber Design of a Venturi Scrubber .4 Packed Column Height and Diameter .5 Summary of Key Points.285 PART IV: MATH CONCEPTS: WATER QUALITY .287 Chapter 11 Running Waters .1 Balancing the “Aquarium”.1 Sources of Stream Pollution.2 Is Dilution the Solution?.1 Dilution Capacity of Running Waters.292 © 2005 by CRC Press LLC L1681_C00.fm Page xiv Tuesday, October 5, 2004 2:12 PM 11.4 Time of Travel.1 DO Correction Factor.6 Biochemical Oxygen Demand .1 BOD Test Procedure.2 Practical BOD Calculation Procedure .1 Unseeded BOD Procedure .2 Seeded BOD Procedure .8 Stream Purification: A Quantitative Analysis.304 Chapter 12 Still Waters .2 Still Water Systems .3 Still Water System Calculations .1 Still Water Body Morphometry Calculations .2 Shoreline Development Index (DL).4 Still Water Surface Evaporation.1 Water Budget Model .2 Energy Budget Model .3 Priestly–Taylor Equation .5 DeBruin–Keijman Equation .1 Groundwater and Aquifers.5 Hydraulic Gradient and Head .6 Flow Lines and Flow Nets .4 General Equations of Groundwater Flow.1 Steady Flow in a Confined Aquifer .2 Steady Flow in an Unconfined Aquifer .322 Chapter 14 Basic Hydraulics .325 © 2005 by CRC Press LLC L1681_C00.fm Page xv Tuesday, October 5, 2004 2:12 PM 14.2 Density and Specific Gravity .3 Force and Pressure .4 Total Dynamic Head (Total System Head).3 Flow/Discharge Rate: Water in Motion.5 Calculating Major Head Loss .6 Characteristics of Open-Channel Flow.1 Laminar and Turbulent Flow.2 Uniform and Varied Flow.4 Parameters Used in Open Channel Flow.7 Open-Channel Flow Calculations .341 Chapter 15 Water Treatment Process Calculations .2 Water Source and Storage Calculations .1 Water Source Calculations .4 Well Casing Disinfection .5 Deep-Well Turbine Pump Calculations .3 Vertical Turbine Pump Calculations .1 Water Storage Calculations .2 Copper Sulfate Dosing .4 Coagulation, Mixing, and Flocculation .4 Coagulation and Flocculation General Calculations .1 Chamber and Basin Volume Calculations .3 Determining Dry Chemical Feeder Setting (Pounds per Day) .362 © 2005 by CRC Press LLC L1681_C00.fm Page xvi Tuesday, October 5, 2004 2:12 PM 15.4Determining Chemical Solution Feeder Setting (Gallons per Day).5 Determining Chemical Solution Feeder Setting (Milliliters per Minute) .5 Determining Percent of Solutions.1 Determining Percent Strength of Liquid Solutions .2 Determining Percent Strength of Mixed Solutions .6 Dry Chemical Feeder Calibration .1 Solution Chemical Feeder Calibration.7 Determining Chemical Usage .1 Paddle Flocculator Calculations.1 Tank Volume Calculations.1 Calculating Tank Volume .3 Surface Overflow Rate .4 Mean Flow Velocity .5 Weir Loading Rate (Weir Overflow Rate) .6 Percent Settled Biosolids.7 Determining Lime Dosage (Milligrams per Liter) .8 Determining Lime Dosage (Pounds per Day) .9 Determining Lime Dosage (Grams per Minute) .6 Water Filtration Calculations .1 Flow Rate through a Filter (Gallons per Minute) .3 Unit Filter Run Volume (UFRV).5 Backwash Rise Rate .6 Volume of Backwash Water Required (Gallons).7 Required Depth of Backwash Water Tank (Feet) .8 Backwash Pumping Rate (Gallons per Minute) .9 Percent Product Water Used for Backwashing.10 Percent Mud Ball Volume .11 Filter Bed Expansion.12 Filter Loading Rate .13 Filter Medium Size.15 Head Loss for Fixed Bed Flow.16 Head Loss through a Fluidized Bed .17 Horizontal Washwater Troughs .7 Water Chlorination Calculations.2 Determining Chlorine Dosage (Feed Rate) .3 Calculating Chlorine Dose, Demand, and Residual .4 Breakpoint Chlorination Calculations.5 Calculating Dry Hypochlorite Feed Rate .6 Calculating Hypochlorite Solution Feed Rate .7 Calculating Percent Strength of Solutions.423 © 2005 by CRC Press LLC L1681_C00.fm Page xvii Tuesday, October 5, 2004 2:12 PM 15.8 Calculating Percent Strength Using Dry Hypochlorite .9 Calculating Percent Strength Using Liquid Hypochlorite.8 Chemical Use Calculations.428 PART V: MATH CONCEPTS: WASTEWATER ENGINEERING.429 Chapter 16 Wastewater Calculations .2 Preliminary Treatment Calculations .2 Screenings Removal Calculations .3 Screenings Pit Capacity Calculations .4 Headloss through Bar Screen.6 Grit Removal Calculations .7 Grit Channel Velocity Calculation .1 Required Settling Time .2 Required Channel Length .3 Velocity of Scour.3 Primary Treatment Calculations .1 Process Control Calculations .2 Surface Loading Rate (Surface Settling Rate/Surface Overflow Rate).3 Weir Overflow Rate (Weir Loading Rate) .4 Primary Sedimentation Basins .1 Percent Total Solids (% TS).2 BOD and SS Removed, Pounds per Day .5 Trickling Filter Calculations .1 Trickling Filter Process Calculations .3 Organic Loading Rate .4 BOD and SS Removed.6 Trickling Filter Design .6 Rotating Biological Contactors (RBCs) .1 RBC Process Control Calculations .2 Hydraulic Loading Rate .4 Organic Loading Rate .5 Total Media Area .6 Modeling RBC Performance.7 RBC Performance Parameter .1 Activated Biosolids Process Control Calculations .3 BOD or COD Loading .5 Food-to-Microorganism Ratio (F/M Ratio) .459 © 2005 by CRC Press LLC L1681_C00.fm Page xviii Tuesday, October 5, 2004 2:12 PM 16.6 Gould Biosolids Age .7 Mean Cell Residence Time (MCRT) .8 Estimating Return Rates from SBV60 (SSV60) .10 Mass Balance: Settling Tank Suspended Solids .11 Mass Balance Calculation .12 Biosolids Waste Based Upon Mass Balance .13 Aeration Tank Design Parameters.14 Lawrence and McCarty Design Model.1 Complete Mix with Recycle .15 Effluent Microorganism and Substrate Concentrations .1 Process Design and Control Relationships.8 Oxidation Ditch Detention Time .1 Treatment Pond Parameters.2 Treatment Pond Process Control Calculations .1 Hydraulic Detention Time, Days .3 Organic Loading Rate .4 BOD Removal Efficiency.6 Hydraulic Loading, Inches/Day (Overflow Rate).10 Chemical Dosage Calculations .2 Chemical Feed Rate .3 Chlorine Dose, Demand, and Residual.6 Mixing Solutions of Different Strengths .7 Solution Mixtures Target Percent Strength.8 Solution Chemical Feeder Setting, GPD .