A. Kayode Coker, PhD, is an engineering consultant for AKC Technology, an honorary research fellow at the University of Wolverhampton, UK, a former engineering coordinator at Saudi Aramco Shell Refinery Company, and chairman of the Department of Chemical Engineering Technology at Jubail Industrial College, Saudi Arabia. He has been a chartered chemical engineer for more than 30 years. He is a fellow of the Institution of Chemical Engineers, UK, and a senior member of the American Institute of Chemical Engineers. He holds a BSc honors degree in chemical engineering, a master of science degree in process analysis and development and PhD in chemical engineering, all from Aston University, Birmingham, UK, and a Teacher’s Certificate in Education at the University of London, UK. He has directed and conducted short courses extensively throughout the world and has been a lecturer at the university level. His articles have been published in several international journals. He is an author of seven books in chemical engineering, a contributor to the Encyclopedia of Chemical Processing and Design, Vol 61 and a certified train-the-mentor trainer. He is also a technical report assessor and interviewer for chartered chemical engineers (IChemE) in the U.K. He is a member of the International Biographical Centre in Cambridge, UK, is in “Leading Engineers of the World for 2008.” He is also a member of “International Who’s Who of ProfessionalsTM” and “Madison Who’s Who in the U.S.” Rahmat Sotudeh–Gharebaagh, PhD, is a full professor of chemical engineering at the University of Tehran. He teaches process modeling and simulation, transport phenomena, plant design and economics and soft skills. His research interests include computer-aided process design and simulation, fluidization, and engineering education. He holds a BEng degree in chemical engineering from Iran’s Sharif University of Technology, plus a MSc and a PhD in fluidization engineering from Canada’s Polytechnique. He has been an invited Professor at Qatar University and Polytechnique de Montréal. Professor Sotudeh has more than 300 publications in major international journals and conferences, plus four books and four book chapters. He is the co-founder and editor-in-chief of the journal, Chemical Product and Process Modeling, a member of the Iranian Elite Foundation, and an official expert (OE) on the oil industry with the Iranian Official Expert Organization.

• Preface xviiAcknowledgments xixAbout the Authors xxi1 Computations with Excel Spreadsheet-UniSim Design Simulation 1Section I - Numerical Analysis 1Introduction 1Excel Spreadsheet 1Functions 2Trendline Coefficients 2Goal Seek 5Solver 6Linear Regression 7Measuring Regression Quality 9Multiple Regression 9Polynomial Regression 11Simultaneous Linear Equations 11Nonlinear Equations 12Interpolations 13Integrations 14The Trapezoidal Rule 14Simpson’s 1/3 Rule 15Simpson’s 3/8 Rule 15Differential Equations 15Nth Order Ordinary Differential Equations 15Solution of First-Order Ordinary Differential Equations 15Runge-Kutta Methods 16Examples and Solutions 17Section II – Process Simulation 28Introduction 28Thermodynamics for Process Simulators 29UNISIM Design Software 30Examples and Solutions 31References 782 Physical Property of Pure Components and Mixtures 81Pure Components 81Density of Liquid 82Viscosity of Liquid 83Heat Capacity of Liquid 85Thermal Conductivity of Liquid 87Volumetric Expansion Rate 90Vapor Pressure 91Viscosity of Gas 93Thermal Conductivity of Gas 94Heat Capacity of Gases 95Mixtures 97Surface Tensions 98Viscosity of Gas Mixture 99Enthalpy of Formation 101Enthalpy of Vaporization 103Gibbs Energy of Reaction 105Henry’s Law Constant for Gases in Water 107Coefficient of Thermal Expansion of Liquid 108Diffusion Coefficients 109Gas-Phase Diffusion Coefficients 109Liquid-Phase Diffusion Coefficients 110Compressibility Z-factor 111Solubility and Adsorption 116Solubility of Hydrocarbons in Water 116Solubility of Gases in Water 117Solubility of Sulfur and Nitrogen Compounds in Water 118Adsorption on Activated Carbon 119References 1193 Fluid Flow 121Introduction 121Flow of Fluids in Pipes 121Equivalent Length of Various Fittings and Valves 123Excess Head Loss 123Pipe Reduction and Enlargement 124Pressure Drop Calculations for Single-phase Incompressible Fluids 124Friction Factor 127Overall Pressure Drop 128Nomenclature 130Compressible Fluid Flow in Pipes 130Maximum Flow and Pressure Drop 131Critical or Sonic Flow and the Mach Number 131Mach Number 132Mathematical Model of Compressible Isothermal Flow 134Flow Rate Through Pipeline 136Pipeline Pressure Drop 138Nomenclature 139Subscripts 139Two-phase Flow in Process Piping 139Flow Patterns 140Flow Regimes 142Pressure Drop 142Erosion-Corrosion 145Nomenclature 145Vapor-liquid Two-phase Vertical Downflow 146The Equations 147The Algorithm 147Nomenclature 147Line Sizes for Flashing Steam Condensate 148The Equations 148Nomenclature 149Flow Through Packed Beds 150The Equations 151Nomenclature 152Examples and Solutions 152References 1624 Equipment Sizing 165Introduction 165Sizing of Vertical and Horizontal Separators 166Vertical Separators 166Calculation Method for a Vertical Drum 168Calculation Method for a Horizontal Drum 170Liquid Holdup and Vapor Space Disengagement 171Wire Mesh Pad 171Standards for Horizontal Separators 172Piping Requirements 172Nomenclature 172Sizing of Partly Filled Vessels and Tanks 173The Equations 173Nomenclature 175Preliminary Vessel Design 176Nomenclature 177Cyclone Design 178Introduction 178Cyclone Design Procedure 178The Equations 179Saltation Velocity 180Pressure Drop 181Troubleshooting Cyclone Maloperations 182Cyclone Collection Efficiency 182Cyclone Design Factor 182Cyclone Design Procedure 183Nomenclature 183Gas Dryer Design 184The Equations 186Pressure Drop 187Desiccant Reactivation 188Nomenclature 188Examples and Solutions 189References 1945 Instrument Sizing 195Introduction 195Variable-Head Meters 195Macroscopic Mechanical Energy Balance 196Variable-Head Meters 196Orifice Sizing for Liquid and Gas Flows 200Orifice Sizing for Liquid Flows 201Orifice Sizing for Gas Flows 202Orifice Sizing for Liquid Flow 204Orifice Sizing for Gas Flow 204Types of Restriction Orifice Plates 205Case Study 1 205Nomenclature 212Control Valve Sizing 221Introduction 221Control Valve Characteristics 223Pressure Drop for Sizing 224Choked Flow 224Flashing and Cavitation 224Control Valve Sizing for Liquid, Gas, Steam and Two-Phase Flows 225Liquid Sizing 226Gas Sizing 227Critical Condition 227Steam Sizing 227Two-Phase Flow 228Installation 229Noise 229Control Valve Sizing Criteria 230Valve Sizing Criteria 230Self-Acting Regulators 231Types of Self-Acting Regulators 231Case Study 2 233Rules of Thumb 246Nomenclature 246References 2476 Pumps and Compressors Sizing 249Pumps 249Introduction 249Pumping of Liquids 249Pump Design Standardization 252Basic Parts of a Centrifugal Pump 253Impellers 253Casing 253Shaft 254Centrifugal Pump Selection 255Single-Stage (Single Impeller) Pumps 256Hydraulic Characteristics for Centrifugal Pumps 260Friction Losses Due to Flow 269Velocity Head 269Friction 271Net Positive Suction Head (npsh) and Pump Suction 271General Suction System 277Reductions in NPSHR 279Corrections to NPSHR for Hot Liquid Hydrocarbons and Water 279Charting NPSHR Values of Pumps 280Net Positive Suction Head (NPSH) 280Specific Speed 282“Type Specific Speed” 285Rotative Speed 286Pumping Systems and Performance 286System Head Using Two Different Pipe Sizes in Same Line 288Power Requirements for Pumping Through Process Lines 291Hydraulic Power 292Relations Between Head, Horsepower, Capacity, Speed 293Brake Horsepower (BHP) Input at Pump 293Affinity Laws 296Pump Parameters 298Specific Speed, Flowrate and Power Required by a Pump 299Pump Sizing of Gas-Oil 301Debutanizer Unit 303Centrifugal Pump Efficiency 306Centrifugal Pump Specifications 311Pump Specifications 311Steps in Pump Sizing 312Reciprocating Pumps 313Significant Features in Reciprocating Pump Arrangements 314Application 316Performance 316Discharge Flow Patterns 317Horsepower 318Pump Selection 318Selection Rules-of-Thumb 318A Case Study 321Pump Simulation on a PFD 321Variables Descriptions 322Simulation Algorithm 322Problem 323Discussion 324Pump Cavitation 332Factors in Pump Selection 333Compressors 334Introduction 334General Application Guide 334Specification Guides 337General Considerations for Any Type of Compressor Flow Conditions 337Fluid Properties 338Compressibility 338Corrosive Nature 338Moisture 339Special Conditions 339Specification Sheet 339Performance Considerations 339Cooling Water to Cylinder Jackets 339Heat Rejected to Water 339Drivers 340Ideal Pressure – Volume Relationship 341Actual Compressor Diagram 343Deviations From Ideal Gas Laws: Compressibility 343Adiabatic Calculations 346Charles’ Law at Constant Pressure 346Amonton’s Law at Constant Volume 346Combined Boyle’s and Charles’ Laws 346Entropy Balance Method 347Isentropic Exponent Method 347Compression Ratio 354Horsepower 356Single Stage 356Theoretical Hp 356Actual Brake Horsepower, Bhp 356Actual Brake Horsepower, Bhp (Alternate Correction for Compressibility) 361Temperature Rise – Adiabatic 363Temperature Rise – Polytropic 365A Case Study Using Unisim Design R460.1 Software for a Two–stage Compression 365Case Study 2 365Solution 3651. Starting UniSim Design Software 3662. Creating a New Simulation 366Saving the Simulation 3673. Adding Components to the Simulation 3674. Selecting a Fluids Package 3685. Select the Units for the Simulation 3696. Enter Simulation Environment 369Accidentally Closing the PFD 371Object Palette 3717. Adding Material Streams 3718. Specifying Material Streams 3729. Adding A Compressor 374Specifications 381Compression Process 385Adiabatic 385Isothermal 385Polytropic 385Efficiency 388Head 390Adiabatic Head Developed Per Single-stage Wheel 390Polytropic Head 391Polytropic 391Brake Horsepower 393Speed of Rotation 396Temperature Rise During Compression 397Sonic or Acoustic Velocity 399Mach Number 402Specific Speed 402Compressor Equations in Si Units 403Polytropic Compressor 405Adiabatic Compressor 408Efficiency 409Mass Flow Rate, w 409Mechanical Losses 410Estimating Compressor Horsepower 411Multistage Compressors 412Multicomponent Gas Streams 414Affinity Laws 422Speed 423Impeller Diameters (Similar) 423Impeller Diameter (Changed) 424Effect of Temperature 424Affinity Law Performance 425Troubleshooting of Centrifugal and Reciprocating Compressors 425Nomenclature 429Greek Symbols 431Subscripts 432Nomenclature 432Subscripts 434Greek Symbols 434References 434Pumps 434Bibliography 435References 435Compressors 435Bibliography 4367 Mass Transfer 437Introduction 437Vapor Liquid Equilibrium 437Bubble Point Calculation 441Dew Point Calculation 442Equilibrium Flash Composition 442Fundamental 443The Equations 444The Algorithm 445Nomenclature 446Tower Sizing for Valve Trays 446Introduction 446The Equations 448Nomenclature 452Greek Letters 465Packed Tower Design 466Introduction 466Pressure Drop 466Flooding 466Operating and Design Conditions 468Design Equations 471Packed Towers versus Trayed Towers 473Economic Trade-Offs 473Nomenclature 474Greek Letters 474Determination of Plates in Fractionating Columns By the Smoker Equations 474Introduction 474The Equations 474Application to a Distillation Column 475Rectifying Section: 475Stripping Section: 476Nomenclature 476Multicomponent Distribution and Minimum Trays In Distillation Columns 477Introduction 477Key Components 477Equations Surveyed 477Fractionating Tray Stability Diagrams 479Areas of Unacceptable Operation 479Foaming 480Flooding 480Entrainment 480Weeping/Dumping 480Fractionation Problem Solving Considerations 481Mathematical Modeling 481The Fenske’s Method for Total Reflux 483The Gilliland Method for Number of Equilibrium Stages 484The Underwood Method 485Equations for Describing Gilliland’s Graph 486Kirkbride’s Feed Plate Location 487Nomenclature 487Greek Letters 488Examples and Solutions 488References 499Index 501

A. Kayode Coker, PhD, is an engineering consultant for AKC Technology, an honorary research fellow at the University of Wolverhampton, UK, a former engineering coordinator at Saudi Aramco Shell Refinery Company, and chairman of the Department of Chemical Engineering Technology at Jubail Industrial College, Saudi Arabia. He has been a chartered chemical engineer for more than 30 years. He is a fellow of the Institution of Chemical Engineers, UK, and a senior member of the American Institute of Chemical Engineers. He holds a BSc honors degree in chemical engineering, a master of science degree in process analysis and development and PhD in chemical engineering, all from Aston University, Birmingham, UK, and a Teacher’s Certificate in Education at the University of London, UK. He has directed and conducted short courses extensively throughout the world and has been a lecturer at the university level. His articles have been published in several international journals. He is an author of seven books in chemical engineering, a contributor to the Encyclopedia of Chemical Processing and Design, Vol 61 and a certified train-the-mentor trainer. He is also a technical report assessor and interviewer for chartered chemical engineers (IChemE) in the U.K. He is a member of the International Biographical Centre in Cambridge, UK, is in “Leading Engineers of the World for 2008.” He is also a member of “International Who’s Who of ProfessionalsTM” and “Madison Who’s Who in the U.S.” Rahmat Sotudeh–Gharebaagh, PhD, is a full professor of chemical engineering at the University of Tehran. He teaches process modeling and simulation, transport phenomena, plant design and economics and soft skills. His research interests include computer-aided process design and simulation, fluidization, and engineering education. He holds a BEng degree in chemical engineering from Iran’s Sharif University of Technology, plus a MSc and a PhD in fluidization engineering from Canada’s Polytechnique. He has been an invited Professor at Qatar University and Polytechnique de Montréal. Professor Sotudeh has more than 300 publications in major international journals and conferences, plus four books and four book chapters. He is the co-founder and editor-in-chief of the journal, Chemical Product and Process Modeling, a member of the Iranian Elite Foundation, and an official expert (OE) on the oil industry with the Iranian Official Expert Organization.

• Preface xviiAcknowledgments xixAbout the Authors xxi1 Computations with Excel Spreadsheet-UniSim Design Simulation 1Section I - Numerical Analysis 1Introduction 1Excel Spreadsheet 1Functions 2Trendline Coefficients 2Goal Seek 5Solver 6Linear Regression 7Measuring Regression Quality 9Multiple Regression 9Polynomial Regression 11Simultaneous Linear Equations 11Nonlinear Equations 12Interpolations 13Integrations 14The Trapezoidal Rule 14Simpson’s 1/3 Rule 15Simpson’s 3/8 Rule 15Differential Equations 15Nth Order Ordinary Differential Equations 15Solution of First-Order Ordinary Differential Equations 15Runge-Kutta Methods 16Examples and Solutions 17Section II – Process Simulation 28Introduction 28Thermodynamics for Process Simulators 29UNISIM Design Software 30Examples and Solutions 31References 782 Physical Property of Pure Components and Mixtures 81Pure Components 81Density of Liquid 82Viscosity of Liquid 83Heat Capacity of Liquid 85Thermal Conductivity of Liquid 87Volumetric Expansion Rate 90Vapor Pressure 91Viscosity of Gas 93Thermal Conductivity of Gas 94Heat Capacity of Gases 95Mixtures 97Surface Tensions 98Viscosity of Gas Mixture 99Enthalpy of Formation 101Enthalpy of Vaporization 103Gibbs Energy of Reaction 105Henry’s Law Constant for Gases in Water 107Coefficient of Thermal Expansion of Liquid 108Diffusion Coefficients 109Gas-Phase Diffusion Coefficients 109Liquid-Phase Diffusion Coefficients 110Compressibility Z-factor 111Solubility and Adsorption 116Solubility of Hydrocarbons in Water 116Solubility of Gases in Water 117Solubility of Sulfur and Nitrogen Compounds in Water 118Adsorption on Activated Carbon 119References 1193 Fluid Flow 121Introduction 121Flow of Fluids in Pipes 121Equivalent Length of Various Fittings and Valves 123Excess Head Loss 123Pipe Reduction and Enlargement 124Pressure Drop Calculations for Single-phase Incompressible Fluids 124Friction Factor 127Overall Pressure Drop 128Nomenclature 130Compressible Fluid Flow in Pipes 130Maximum Flow and Pressure Drop 131Critical or Sonic Flow and the Mach Number 131Mach Number 132Mathematical Model of Compressible Isothermal Flow 134Flow Rate Through Pipeline 136Pipeline Pressure Drop 138Nomenclature 139Subscripts 139Two-phase Flow in Process Piping 139Flow Patterns 140Flow Regimes 142Pressure Drop 142Erosion-Corrosion 145Nomenclature 145Vapor-liquid Two-phase Vertical Downflow 146The Equations 147The Algorithm 147Nomenclature 147Line Sizes for Flashing Steam Condensate 148The Equations 148Nomenclature 149Flow Through Packed Beds 150The Equations 151Nomenclature 152Examples and Solutions 152References 1624 Equipment Sizing 165Introduction 165Sizing of Vertical and Horizontal Separators 166Vertical Separators 166Calculation Method for a Vertical Drum 168Calculation Method for a Horizontal Drum 170Liquid Holdup and Vapor Space Disengagement 171Wire Mesh Pad 171Standards for Horizontal Separators 172Piping Requirements 172Nomenclature 172Sizing of Partly Filled Vessels and Tanks 173The Equations 173Nomenclature 175Preliminary Vessel Design 176Nomenclature 177Cyclone Design 178Introduction 178Cyclone Design Procedure 178The Equations 179Saltation Velocity 180Pressure Drop 181Troubleshooting Cyclone Maloperations 182Cyclone Collection Efficiency 182Cyclone Design Factor 182Cyclone Design Procedure 183Nomenclature 183Gas Dryer Design 184The Equations 186Pressure Drop 187Desiccant Reactivation 188Nomenclature 188Examples and Solutions 189References 1945 Instrument Sizing 195Introduction 195Variable-Head Meters 195Macroscopic Mechanical Energy Balance 196Variable-Head Meters 196Orifice Sizing for Liquid and Gas Flows 200Orifice Sizing for Liquid Flows 201Orifice Sizing for Gas Flows 202Orifice Sizing for Liquid Flow 204Orifice Sizing for Gas Flow 204Types of Restriction Orifice Plates 205Case Study 1 205Nomenclature 212Control Valve Sizing 221Introduction 221Control Valve Characteristics 223Pressure Drop for Sizing 224Choked Flow 224Flashing and Cavitation 224Control Valve Sizing for Liquid, Gas, Steam and Two-Phase Flows 225Liquid Sizing 226Gas Sizing 227Critical Condition 227Steam Sizing 227Two-Phase Flow 228Installation 229Noise 229Control Valve Sizing Criteria 230Valve Sizing Criteria 230Self-Acting Regulators 231Types of Self-Acting Regulators 231Case Study 2 233Rules of Thumb 246Nomenclature 246References 2476 Pumps and Compressors Sizing 249Pumps 249Introduction 249Pumping of Liquids 249Pump Design Standardization 252Basic Parts of a Centrifugal Pump 253Impellers 253Casing 253Shaft 254Centrifugal Pump Selection 255Single-Stage (Single Impeller) Pumps 256Hydraulic Characteristics for Centrifugal Pumps 260Friction Losses Due to Flow 269Velocity Head 269Friction 271Net Positive Suction Head (npsh) and Pump Suction 271General Suction System 277Reductions in NPSHR 279Corrections to NPSHR for Hot Liquid Hydrocarbons and Water 279Charting NPSHR Values of Pumps 280Net Positive Suction Head (NPSH) 280Specific Speed 282“Type Specific Speed” 285Rotative Speed 286Pumping Systems and Performance 286System Head Using Two Different Pipe Sizes in Same Line 288Power Requirements for Pumping Through Process Lines 291Hydraulic Power 292Relations Between Head, Horsepower, Capacity, Speed 293Brake Horsepower (BHP) Input at Pump 293Affinity Laws 296Pump Parameters 298Specific Speed, Flowrate and Power Required by a Pump 299Pump Sizing of Gas-Oil 301Debutanizer Unit 303Centrifugal Pump Efficiency 306Centrifugal Pump Specifications 311Pump Specifications 311Steps in Pump Sizing 312Reciprocating Pumps 313Significant Features in Reciprocating Pump Arrangements 314Application 316Performance 316Discharge Flow Patterns 317Horsepower 318Pump Selection 318Selection Rules-of-Thumb 318A Case Study 321Pump Simulation on a PFD 321Variables Descriptions 322Simulation Algorithm 322Problem 323Discussion 324Pump Cavitation 332Factors in Pump Selection 333Compressors 334Introduction 334General Application Guide 334Specification Guides 337General Considerations for Any Type of Compressor Flow Conditions 337Fluid Properties 338Compressibility 338Corrosive Nature 338Moisture 339Special Conditions 339Specification Sheet 339Performance Considerations 339Cooling Water to Cylinder Jackets 339Heat Rejected to Water 339Drivers 340Ideal Pressure – Volume Relationship 341Actual Compressor Diagram 343Deviations From Ideal Gas Laws: Compressibility 343Adiabatic Calculations 346Charles’ Law at Constant Pressure 346Amonton’s Law at Constant Volume 346Combined Boyle’s and Charles’ Laws 346Entropy Balance Method 347Isentropic Exponent Method 347Compression Ratio 354Horsepower 356Single Stage 356Theoretical Hp 356Actual Brake Horsepower, Bhp 356Actual Brake Horsepower, Bhp (Alternate Correction for Compressibility) 361Temperature Rise – Adiabatic 363Temperature Rise – Polytropic 365A Case Study Using Unisim Design R460.1 Software for a Two–stage Compression 365Case Study 2 365Solution 3651. Starting UniSim Design Software 3662. Creating a New Simulation 366Saving the Simulation 3673. Adding Components to the Simulation 3674. Selecting a Fluids Package 3685. Select the Units for the Simulation 3696. Enter Simulation Environment 369Accidentally Closing the PFD 371Object Palette 3717. Adding Material Streams 3718. Specifying Material Streams 3729. Adding A Compressor 374Specifications 381Compression Process 385Adiabatic 385Isothermal 385Polytropic 385Efficiency 388Head 390Adiabatic Head Developed Per Single-stage Wheel 390Polytropic Head 391Polytropic 391Brake Horsepower 393Speed of Rotation 396Temperature Rise During Compression 397Sonic or Acoustic Velocity 399Mach Number 402Specific Speed 402Compressor Equations in Si Units 403Polytropic Compressor 405Adiabatic Compressor 408Efficiency 409Mass Flow Rate, w 409Mechanical Losses 410Estimating Compressor Horsepower 411Multistage Compressors 412Multicomponent Gas Streams 414Affinity Laws 422Speed 423Impeller Diameters (Similar) 423Impeller Diameter (Changed) 424Effect of Temperature 424Affinity Law Performance 425Troubleshooting of Centrifugal and Reciprocating Compressors 425Nomenclature 429Greek Symbols 431Subscripts 432Nomenclature 432Subscripts 434Greek Symbols 434References 434Pumps 434Bibliography 435References 435Compressors 435Bibliography 4367 Mass Transfer 437Introduction 437Vapor Liquid Equilibrium 437Bubble Point Calculation 441Dew Point Calculation 442Equilibrium Flash Composition 442Fundamental 443The Equations 444The Algorithm 445Nomenclature 446Tower Sizing for Valve Trays 446Introduction 446The Equations 448Nomenclature 452Greek Letters 465Packed Tower Design 466Introduction 466Pressure Drop 466Flooding 466Operating and Design Conditions 468Design Equations 471Packed Towers versus Trayed Towers 473Economic Trade-Offs 473Nomenclature 474Greek Letters 474Determination of Plates in Fractionating Columns By the Smoker Equations 474Introduction 474The Equations 474Application to a Distillation Column 475Rectifying Section: 475Stripping Section: 476Nomenclature 476Multicomponent Distribution and Minimum Trays In Distillation Columns 477Introduction 477Key Components 477Equations Surveyed 477Fractionating Tray Stability Diagrams 479Areas of Unacceptable Operation 479Foaming 480Flooding 480Entrainment 480Weeping/Dumping 480Fractionation Problem Solving Considerations 481Mathematical Modeling 481The Fenske’s Method for Total Reflux 483The Gilliland Method for Number of Equilibrium Stages 484The Underwood Method 485Equations for Describing Gilliland’s Graph 486Kirkbride’s Feed Plate Location 487Nomenclature 487Greek Letters 488Examples and Solutions 488References 499Index 501