Dynamic Stresses, and Piping Design
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1 Fluid Mechanics, Water Hammer, Dynamic Stresses, and Piping Design Robert A. Leishear, FhJD., P. E. Savannah River National Laboratory On the cover: Steam plume due to a pipe explosion caused by water hammer in a New York City Steam System, This manuscript has been authored by Savannah River Nuclear Solutions, LLC under Contract No. DE-AC09-08SR22470 with the U.S. Department of Energy. The United States Government retains and publisher, by ac cepting this article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this work, or allow others to do so, for United States Government purposes. twe PRESS SAVANNAH KKt KATWHAi. IA8MATMY Op«MlrSMni*RwlMwMMlMiU We Put Science To Work
2 Contents Preface xviii Friction Factors from Churchill's Equation 28 CHAPTER 1 Introduction Pipe Friction Losses for Bingham 1.1 Model of a Valve Closure and Fluid Plastic Fluids and Power Law Fluids 34 Transient Friction Losses in Series Pipes Pipe Stresses Flow and Friction Losses in Static Stresses 2 Parallel Pipes Dynamic Stresses Inlets, Outlets, and Orifices Failure Theories Fitting Construction Valve Closure Model Summary Valve Designs Gate Valves CHAPTER 2 Steady-State Fluid Mechanics Globe Valves 55 and Pipe System Components Ball Valves Conservation of Mass and Bernoulli's Butterfly Valves 56 Equation Plug Valves Conservation of Mass Diaphragm Valves Bernoulli's Equation Check Valves Limitations of Bernoulli's Equation Relief Valves 62 Due to Localized Flow Characteristics Safety Valves Hydraulic and Energy Grade Lines Needle Valves Friction Losses for Pipes Pinch Valves Types of Fluids Traps Viscosity Definition Pressure Regulators Properties of Newtonian and 2.4 Friction Losses for Fittings and Non-Newtonian Fluids 14 Open Valves Laminar Flow in Newtonian and Graphic Method for Friction Losses Non-Newtonian Fluids 15 in Fittings and Valves Pipe Friction Losses for Crane's Method for Friction Losses Newtonian Fluids 16 in Steel Fittings and Valves Friction Factors from the Moody Modified Crane's Method for Friction Diagram Surface Roughness 19 Materials and Pipe Losses in Fittings and Valves of Other Diameters Pipe and Tubing Dimensions Darby's Method for Friction Losses Density and Viscosity Data and Their Effects on Pressure Drops in Fittings and Valves for Newtonian and Non-Newtonian Fluids 69 Due to Flow Tabulated Resistance Coefficients for Tabulated Pressure Drops for Water Fittings and Valves Using Crane's, Flow in Steel Pipe 26 Darby's, and Hooper's Methods Effects of Aging on Water-Filled 2.5 Valve Performance and Friction Losses Steel Pipes 26 for Throttled Valves 74
3 viii Contents Valve Flow Characteristics Other Codes and Standards Throttled Valve Characteristics ASME B31.3, Process Piping Resistance Coefficients for Throttled 3.2 Pipe Material Properties 121 Valves Tensile Tests Valve Actuators Ductile Materials Flow Control True Stress and True Strain PTD' Control Strain Hardening Design Flow Rates Loss of Ductility Operation of Centrifugal Pumps in Strain Rate Effects on Material Pipe Systems 88 Properties Types of Centrifugal Pumps Brittle Materials Pump Curves Elastic Modulus Data Affinity Laws Yield Strength and Ultimate Impeller Diameter 90 Strength Data Impeller Speed Charpy Impact Test Acoustic Vibrations in Pumps and Fatigue Testing and Fatigue Limit 128 Pipe Systems Fatigue Limit Accuracy Power and Efficiency Fatigue-Testing Methods and Effects of Other Fluids on Pump Fatigue Data 129 Performance Relationship of Fatigue to Vibrations Net Positive Suction Head and Environmental and Surface Effects Cavitation 92 on Fatigue Motor Speed Control Summary of Fatigue Testing Induction Motors Fatigue Testing for Pipe Components Motor Starters Fatigue Curves for B31.3 Piping VFDs Pressure Cycling Fatigue Data Pump Shutdown and Inertia of Fatigue Data for Pressure Vessel Pumps and Motors 100 Design Pump Performance as a Function of Poisson's Ratio 136 Specific Speed Material Densities Pump Heating Due to Flow Through Thermal Expansion and Thermal the Pump 102 Stresses 136 ^ System Curves 102 Thermal Stresses Parallel and Series Pumps Longitudinal Thermal Expansion Parallel and Series Pipes 107 of a Pipe Jet Pumps Bending Due to Thermal Expansion Two Phase Flow Characteristics Pipe System Design Stresses Liquid/Gas Flows Stress Calculations 153 2:9.1.1 Air Entrainment and Dissolved Gas Load-Controlled and Displacement Air Binding in Pipes 113 Controlled Stresses Open Channel Flow Maximum Stresses Liquid/Vapor Flows Internal Pressure Stresses, Hoop Stresses Liquid/Solid Flows Corrosion and Erosion Allowances Siphons Hoop 2.10 Design Summary for How in Limits for Sustained Longitudinal Steady-State Systems 116 Stress and Maximum Pressure 156 Stresses, Occasional Stresses, and Displacement Stresses 157 CHAPTER 3 Pipe System Design Allowable Stresses Piping and Pressure Vessel Codes Pipe Stresses and Reactions at and Standards 119 Pipe Supports ASME Piping and Pressure Vessel Axial Stresses and Reactions Due Codes 119 to Pressure and Flow 164
4 FLUID MECHANICS, WATER HAMMER, DYNAMIC STRESSES, AND PIPING DESIGN ix Restraint and Control of Forces Reactions and Pipe Stresses Torsional Stresses and Moments Pipe Stresses Due to Pipe and Fluid Weights Stress Intensification Factors Flexibility Calculation Example Comparison of Code Stress Calculations Pipe Stresses Due to Wind and Earthquake Pipe Supports and Anchor Designs Structural Requirements for Fittings, Flanges, and Valves Pipe Schedule and Pressure Ratings for Fittings, Flanges, and Valves Flange Stresses Limiting Stresses for Rotary Pump Nozzles Hydrostatic Pressure Tests Summary of Piping Design 185 CHAPTER 4 Pipe Failure Analysis and Damage Mechanisms Failure Theories State of Stress at a Point, Multiaxial Stresses Maximum Stresses Principal Stresses Maximum Shear Stresses Stresses Due to Pipe Restraint Failure Stresses Comparison of Failure Stress Theories Maximum Normal Stress Theory (Rankine) Maximum Shear Stress Theory (Tresca, Guest) Distortion Energy/Octahedral Shear Stress Theory (Von Mises, Huber, Henckey) Structural Damage Mechanisms/ Failure Criteria Overload Failure or Rupture Burst Pressure for a Pipe External Pressure Stresses Plastic Deformation Plasticity Models for Tension Cyclic Plasticity Elastic Follow-Up Cyclic, Plastic Deformation Plastic Cycling for Piping Design Limit Load Analysis for Bending Limit Load Analysis for Equations for Bending of a Pipe Comparison of Limit Load Analysis to Cyclic Plasticity Plastic Deformation Due to Pressure, Hoop Stress Autofrettage Combined Stresses for Plasticity Comparison of Limit Load Analysis to the Bree Diagram Summary of Plastic Failure Analysis Fatigue Failure High-Cycle Fatigue Mechanism High-Cycle Fatigue Life of Materials Triaxial Fatigue Theories Maximum Normal Stress Theory, Triaxial Stresses Maximum Shear Stress Theory, Triaxial Stresses Octahedral Shear Stress Theory, Triaxial Stresses Cumulative Damage Rain Flow Counting Technique Use of Fatigue Theory and Equations Pressure Vessel Code, Fatigue Calculations Method 1: Elastic Stress Method for Fatigue Method 2: Elastic-Plastic Stress Method for Fatigue Method 3: Structural Stress Method for Fatigue Fatigue Summary Fracture Mechanics Fracture Mechanics History Applications of Fracture Mechanics and Fitness for Service LEFM Elastic-Plastic Analysis Elastic-Plastic Fracture Mechanisms Crack Propagation Stress Raisers Fracture Mechanics Summary Corrosion, Erosion, and Stress Corrosion Cracking Flow-Assisted Corrosion (FAC) Leak Before Break Thermal Fatigue Creep Examples of Creep-Induced Failures Creep in Plastic and Rubber Materials 228
5 x Contents Failures Other Causes of Piping 4.13 Summary of Piping Design and Failure Analysis 229 CHAPTER 5 Fluid Transients in Liquid-Filled Systems Slug Flow During System Startup Slug Flow Due to Pump Operation Slug Flow During Series Pump Operation Pump Runout Effects on Slug Flow Draw Down of Systems Fluid Transients Due to Flow Rate Changes Examples of Pipe System Damages in Liquid-Filled Systems Hydroelectric Power Plants Valve Closure Vapor Collapse in a Liquid-Filled System Damages Due to Combined Valve and Pump Flow Rate Changes Types of Fluid Transient Models for Valve Closure Rigid Water Column Theory Basic Water Hammer Equation, Elastic Water Column Theory Arithmetic Water Hammer Equation Shock Waves in Piping Wave Speeds in Thin Wall Metallic Pipes Wave Speeds in Thick Wall Metallic Pipes Wave Speeds in Nonmetallic Pipes Effects of Entrained Solids on Wave Speed Effects of Air Entrainment on Wave Speed Uncertainty of the Water Hammer Equation Computer Simulations/Method of Characteristics Differential Equations Describing Fluid Motion Shock Wave Speed Equation MOC Equations Valve Actuation Reflected Shock Waves Reflected Waves in a Dead-End Pipe Series Pipes and Transitions in Pipe Material Parallel Pipes/Intersections Centrifugal Pump OperationDuring Transients Graphic Water Hammer Solution for Pumps Reverse Pump Operation Due to Flow Reversal Transient Radial Pump Operation MOC Water Hammer Solution for Pumps Use of Valve Closure Speeds to 268 Control Pump Transients Column Separation and Vapor Collapse Column Separation and Vapor Collapse at a High Point in a System With Both Pipe Ends Submerged Column Separation and Vapor Collapse at a High Point in a Pipe With One End Submerged Column Separation and Vapor Collapse at a Valve Solution Methods to Describe Column Separation and Vapor Collapse Positive Displacement Pumps Effect of Trapped Air Pockets on Fluid Transients Additional Corrective Actions for Fluid Transients Valve Stroking Relief Valves Surge Tanks and Air Chambers Fluid Resonance Example Water Hammer Arrestors Surge Suppressors Check Valves Flow Rate Control for Fluid Transients Summary of Fluid Transients in CHAPTER 6 Liquid-Filled Systems 283 Fluid Transients in Steam Systems Examples of Water Hammer Accidents in Steam/Condensate Systems Brookhaven Fatalities Hanford Fatality Savannah River Site Pipe Damages Pipe Failure During Initial System Startup Pipe Damages During System Restart Pipe Failures Due to Condensate- Induced Water Hammer 291
6 FLUID MECHANICS, WATER HAMMER, DYNAMIC STRESSES, AND PIPING DESIGN xi 6.2 Water Hammer Mechanisms in Steam/Condensate Systems Water Cannon Steam and Water Counterflow Condensate-Induced Water Hammer in a Horizontal Pipe Steam Pocket Collapse and Filling of Voided Lines Low-Pressure Discharge and Column Separation Steam-Propelled Water Slug Sudden Valve Closure and Pump Operations Blowdown Sonic Velocity at Discharge Nozzles Piping Loads During Blowdown Steam/Water Flow Pressures in Closed Vessels and Thrust During Blowdown Appropriate Operation of Steam Systems for Personnel Safety System Startup Steam Traps Summary of Fluid Transients 301 CHAPTER 7 Shock Waves, Vibrations, and Dynamic Stresses in Elastic Solids Strain Waves and Vibrations One-Dimensional Strain Waves in a Rod Three-Dimensional Strain Waves in a Solid Vibration Terms Vibrations in a Rod Due to Strain Waves Dilatational Strain Waves in a Rod Wave Reflections in a Rod Strain Wave Examples for Rods Inelastic Damage Due to Wave Reflections Single Degree of Freedom Models SDOF Oscillators SDOF Equation of Motion SDOF, Free Vibrations Damping Effects Damping Ratio Log Decrement Phase Angle Effects SDOF Responses to Applied Forces Step Response for a SDOF Oscillator Homogeneous Solution to the Equation of Motion for a Step Response Particular Solution to the Equation of Motion for a Step Response General Solution to the Equation of Motion for a Step Response Impulse Response for a SDOF Oscillator Ramp Response for a SDOF Oscillator SDOF Harmonic Response SDOF Load Control Steady-State, SDOF Load-Controlled Vibration Frequency Effects on the DMF During SDOF Load-Controlled Vibration DMF for SDOF Load Control Multi-DOF Harmonic Response Multi-DOF Load Control Modal Contributions for Multi-DOF Vibrations Participation Factors for SDOF Vibrations Resonance for Multi-DOF Vibrations Load-Controlled Vibrations for Rods Load-Controlled Vibrations for Beams Dynamic Stress Equations Triaxial Vibrations Damping Proportional Damping Structural Damping for Pipe Systems Fluid Damping and Damping for Hoop Summary of Dynamic Stresses in CHAPTER 8 Elastic Solids 330 Water Hammer Effects on Breathing Stresses for Pipes and Other Components Examples of Piping Fatigue Failures FEA Model of Breathing Stresses for a Short Pipe FEA Assumptions Model Geometry and Dynamic Pressure Loading FEA Model for a Pipe With Fixed Ends Stress Waves and Through-Wall Radial Stresses Hoop Stresses for a Pipe With Fixed Ends 336
7 xii Contents Axial Stresses for a Pipe with Effects of the Wave Speed 354 Fixed Ends Maximum Damped Precursor Stress Impulse Loads Aftershock-Free-Vibration Stresses Stresses for a Pipe with One Free End Damping FEA Summary Maximum Stress When the Critical is Not Considered Theory and Experimental Results for Velocity Breathing Stresses Comparison of Theory to Experimental 8.4 Flexural Resonance 340 Results for a Gas-Filled Tube Flexural Resonance Theory Comparison of Theory to Moment in a Differential Element 340 Experimental Results for a Membrane Forces in a Cylindrical Liquid-Filled Pipe 356 and Raw Data 358 Shell Test Setup Axial Displacement in a Cylindrical Test Results and Discussion 359 Shell Breathing Stress Frequency Equation of Motion for a Cylindrical Wave Velocities 363 Shell Pressure Surge Magnitude Evaluation of Flexural Resonance Equivalent Axial and Hoop Strains DMF and the Critical Velocity Example of Corrective Actions and Critical Velocity 344 Fitness for Service Breathing-Mode Frequency Corrective Actions Flexural Resonance Assuming Fixed Fitness for Service 365 Pipe Ends Comparison of Flexural Resonance Flexural Resonance Examples 345 Theory to Dynamic Stress Theory Strains in Gun Tubes Valves and Fittings Strains Due to Internal Shocks 8.7 Pressure Vessels 369 in a Tube Plastic Hoop Stresses Summary of Flexural Resonance FEA Results for a Shock Wave in a Theory 348 Short Pipe Dynamic Hoop Stresses Experimental Results for Explosions Bounded Hoop Stresses from in a Thin-Wall Tube 371 Beam Equations Explosions in Pipes Precursor and Aftershock Vibrations 350 / 89 Summary of Elastic and Plastic Hoop Pipe Wall Displacement Derivation 350 Stress Responses to Step Pressure Pipe Wall Displacement Equation 350 Transients Critical Velocity DMF and Maximum Stresses from CHAPTER 9 Dynamic Stresses Due to Beam Theory 351 Bending Dynamic Stress Theory Deformations, Stresses, and Derivation of Dynamic Stress Equations Frequencies for Elastic Frames Static Deflections and Reactions for Static Stress 352 Simply Supported Beams and Equation of Motion for a SDOF Elastic Frames 379 Oscillator Frequencies for Simple Beams 379 for Elastic Frames Equation of Motion for a Cylinder Frequencies Subjected to a Sudden Internal 9.2 Elastic Stresses Due to Bending 383 Pressure Step Response Calculation for Pipe Stresses Due to a Shock Wave 353 Bending Precursor Stresses Calculation Assumptions Effects of the Arbitrary Selection Axial Stresses 385 of r = Bending Stresses 386
8 FLUID MECHANICS, WATER HAMMER, DYNAMIC STRESSES, AND PIPING DESIGN xiii Hoop Stresses 387 CHAPTER 10 Summary of Water Comparison of Calculated Bending Hammer-Induced Pipe Failures 395 Stress to an FEA Pipe Stress Model Troubleshooting a Pipe Failure Ramp Response for Bending Suggested References Impulse Response for Bending Recommended Future Research Multiple Bend FEA Models FEA Model of Bending Stresses 393 Appendix A: Notation and Units Plastic Deformation and Stresses A.1 Systems of Units 399 Due to Bending 393 A.2 Conversion Factors Consideration of Earthquake A.3 Notation: Variables, Constants, Damages to Pipe Systems 393 and Dimensions Summary of Stresses During Water References 409 Hammer 393 Index 419
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