Preface ..................................................... xviii
CHAPTER 1 Introduction ......................................... 1
1.1 Model of a Valve Closure and Fluid Transient ............... 1
1.2 Pipe Stresses .............................................. 2
1.2.1 Static Stresses ..................................... 2
1.2.2 Dynamic Stresses .................................... 2
1.3 Failure Theories ........................................... 3
1.4 Valve Closure Model Summary ................................ 3
CHAPTER 2 Steady-State Fluid Mechanics and Pipe System
Components ...................................................... 5
2.1 Conservation of Mass and Bernoulli's Equation .............. 5
2.1.1 Conservation of Mass ................................ 5
2.1.2 Bernoulli's Equation ................................ 6
2.1.3 Limitations of Bernoulli's Equation Due to
Localized Flow Characteristics ...................... 7
2.2 Hydraulic and Energy Grade Lines .......................... 11
2.3 Friction Losses for Pipes ................................. 11
2.3.1 Types of Fluids .................................... 13
2.3.2 Pipe Friction Losses for Newtonian Fluids .......... 16
2.3.3 Friction Factors from the Moody Diagram ............ 16
2.3.4 Tabulated Pressure Drops for Water Flow in Steel
Pipe ............................................... 26
2.3.5 Effects of Aging on Water-Filled Steel Pipes ....... 26
2.3.6 Friction Factors from Churchill's Equation ......... 28
2.3.7 Pipe Friction Losses for Bingham Plastic Fluids
and Power Law Fluids ............................... 34
2.3.8 Friction Losses in Series Pipes .................... 38
2.3.9 Flow and Friction Losses in Parallel Pipes ......... 40
2.3.10 Inlets, Outlets, and Orifices ...................... 41
2.3.11 Fitting Construction ............................... 41
2.3.12 Valve Designs ...................................... 43
2.4 Friction Losses for Fittings and Open Valves .............. 68
2.4.1 Graphic Method for Friction Losses in Fittings
and Valves ......................................... 69
2.4.2 Crane's Method for Friction Losses in Steel
Fittings and Valves ................................ 69
2.4.3 Modified Crane's Method for Friction Losses in
Fittings and Valves of Other Materials and Pipe
Diameters .......................................... 69
2.4.4 Darby's Method for Friction Losses in Fittings
and Valves for Newtonian and Non-Newtonian Fluids .. 69
2.4.5 Tabulated Resistance Coefficients for
Fittings and Valves Using Crane's, Darby's, and
Hooper's Methods ................................... 74
2.5 Valve Performance and Friction Losses for Throttled
Valves .................................................... 74
2.5.1 Valve Flow Characteristics ......................... 75
2.5.2 Throttled Valve Characteristics .................... 75
2.5.3 Resistance Coefficients for Throttled Valves ....... 75
2.5.4 Valve Actuators .................................... 77
2.5.5 Flow Control ....................................... 83
2.5.6 P'FD' Control ...................................... 84
2.6 Design Flow Rates ......................................... 88
2.7 Operation of Centrifugal Pumps in Pipe Systems ............ 88
2.7.1 Types of Centrifugal Pumps ......................... 88
2.7.2 Pump Curves ........................................ 89
2.7.3 Motor Speed Control ................................ 99
2.7.4 Pump Performance as a Function of Specific Speed .. 100
2.7.5 Pump Heating Due to Flow Through the Pump ......... 102
2.7.6 System Curves ..................................... 102
2.7.7 Parallel and Series Pumps ......................... 107
2.7.8 Parallel and Series Pipes ......................... 107
2.8 Jet Pumps ................................................ 107
2.9 Two Phase Flow Characteristics ........................... 108
2.9.1 Liquid/Gas Flows .................................. 108
2.9.2 Open Channel Flow ................................. 113
2.9.3 Liquid/Vapor Flows ................................ 114
2.9.4 Liquid/Solid Flows ................................ 114
2.9.5 Siphons ........................................... 114
2.10 Design Summary for Flow in Steady-State Systems .......... 116
CHAPTER 3 Pipe System Design ................................. 119
3.1 Piping and Pressure Vessel Codes and Standards ........... 119
3.1.1 ASME Piping and Pressure Vessel Codes ............. 119
3.1.2 Other Codes and Standards ......................... 120
3.1.3 ASME B31.3, Process Piping ........................ 120
3.2 Pipe Material Properties ................................. 121
3.2.1 Tensile Tests ..................................... 121
3.2.2 Charpy Impact Test ................................ 127
3.2.3 Fatigue Testing and Fatigue Limit ................. 128
3.2.4 Poisson's Ratio ................................... 136
3.2.5 Material Densities ................................ 136
3.2.6 Thermal Expansion and Thermal Stresses ............ 136
3.3 Pipe System Design Stresses .............................. 152
3.3.1 Stress Calculations ............................... 153
3.3.2 Load-Controlled and Displacement-Controlled
Stresses .......................................... 154
3.3.3 Maximum Stresses .................................. 154
3.3.4 Internal Pressure Stresses, Hoop Stresses ......... 154
3.3.5 Limits for Sustained Longitudinal Stresses,
Occasional Stresses, and Displacement Stresses .... 157
3.3.6 Allowable Stresses ................................ 161
3.3.7 Pipe Stresses and Reactions at Pipe Supports ...... 164
3.3.8 Structural Requirements for Fittings, Flanges,
and Valves ........................................ 180
3.3.9 Pipe Schedule and Pressure Ratings for Fittings,
Flanges, and Valves ............................... 181
3.3.10 Flange Stresses ................................... 182
3.3.11 Limiting Stresses for Rotary Pump Nozzles ......... 182
3.5 Summary of Piping Design ................................. 185
CHAPTER 4 Pipe Failure Analysis and Damage Mechanisms ........ 193
4.1 Failure Theories ......................................... 193
4.1.1 State of Stress at a Point, Multiaxial Stresses ... 193
4.1.2 Maximum Stresses .................................. 194
4.1.3 Failure Stresses .................................. 197
4.1.4 Comparison of Failure Stress Theories ............. 197
4.1.5 Maximum Normal Stress Theory (Rankine) ............ 199
4.1.6 Maximum Shear Stress Theory (Tresca, Guest) ....... 200
4.1.7 Distortion Energy/Octahedral Shear Stress Theory
(Von Mises, Huber, Henckey) ....................... 201
4.2 Structural Damage Mechanisms/Failure Criteria ............ 201
4.3 Overload Failure or Rupture .............................. 201
4.3.1 Burst Pressure for a Pipe ......................... 201
4.3.2 External Pressure Stresses ........................ 202
4.4 Plastic Deformation ...................................... 202
4.4.1 Plasticity Models for Tension ..................... 202
4.4.2 Cyclic Plasticity ................................. 203
4.4.3 Elastic Follow-Up ................................. 203
4.4.4 Cyclic, Plastic Deformation ....................... 203
4.4.5 Plastic Cycling for Piping Design ................. 206
4.4.6 Limit Load Analysis for Bending ................... 207
4.4.7 Limit Load Analysis for Equations for Bending of
a Pipe ............................................ 207
4.4.8 Comparison of Limit Load Analysis to Cyclic
Plasticity ........................................ 208
4.4.9 Plastic Deformation Due to Pressure, Hoop Stress .. 208
4.4.10 Autofrettage ...................................... 209
4.4.11 Combined Stresses for Plasticity .................. 209
4.4.12 Comparison of Limit Load Analysis to the Bree
Diagram ........................................... 209
4.4.13 Summary of Plastic Failure Analysis ............... 210
4.5 Fatigue Failure .......................................... 210
4.5.1 High-Cycle Fatigue Mechanism ...................... 210
4.5.2 High-Cycle Fatigue Life of Materials .............. 211
4.5.3 Triaxial Fatigue Theories ......................... 212
4.5.4 Cumulative Damage ................................. 214
4.5.5 Rain Flow Counting Technique ...................... 214
4.5.6 Use of Fatigue Theory and Equations ............... 215
4.5.7 Pressure Vessel Code, Fatigue Calculations ........ 217
4.5.8 Fatigue Summary ................................... 218
4.6 Fracture Mechanics ....................................... 218
4.6.1 Fracture Mechanics History ........................ 219
4.6.2 Applications of Fracture Mechanics and Fitness
for Service ....................................... 219
4.6.3 LEFM .............................................. 219
4.6.4 Elastic-Plastic Analysis .......................... 221
4.6.5 Elastic-Plastic Fracture Mechanisms ............... 221
4.6.6 Crack Propagation ................................. 221
4.6.7 Stress Raisers .................................... 224
4.6.8 Fracture Mechanics Summary ........................ 224
4.7 Corrosion, Erosion, and Stress Corrosion Cracking ........ 225
4.8 Flow-Assisted Corrosion (FAC) ............................ 226
4.9 Leak Before Break ........................................ 226
4.10 Thermal Fatigue .......................................... 227
4.11 Creep .................................................... 227
4.11.1 Examples of Creep-Induced Failures ................ 227
4.11.2 Creep in Plastic and Rubber Materials ............. 228
4.12 Other Causes of Piping Failures .......................... 228
4.13 Summary of Piping Design and Failure Analysis ............ 229
CHAPTER 5 Fluid Transients in Liquid-Filled Systems .......... 233
5.1 Slug Flow During System Startup .......................... 233
5.1.1 Slug Flow Due to Pump Operation ................... 234
5.1.2 Slug Flow During Series Pump Operation ............ 234
5.1.3 Pump Runout Effects on Slug Flow .................. 234
5.2 Draw Down of Systems ..................................... 235
5.3 Fluid Transients Due to Flow Rate Changes ................ 235
5.3.1 Examples of Pipe System Damages in Liquid-Filled
Systems ........................................... 235
5.4 Types of Fluid Transient Models for Valve Closure ........ 239
5.5 Rigid Water Column Theory ................................ 239
5.5.1 Вasic Water Hammer Equation, Elastic Water
Column Theory ..................................... 242
5.5.2 Arithmetic Water Hammer Equation .................. 245
5.6 Shock Waves in Piping .................................... 247
5.6.1 Wave Speeds in Thin Wall Metallic Pipes ........... 248
5.6.2 Wave Speeds in Thick Wall Metallic Pipes .......... 249
5.6.3 Wave Speeds in Nonmetallic Pipes .................. 250
5.6.4 Effects of Entrained Solids on Wave Speed ......... 250
5.6.5 Effects of Air Entrainment on Wave Speed .......... 250
5.7 Uncertainty of the Water Hammer Equation ................. 252
5.8 Computer Simulations/Method of Characteristics ........... 253
5.8.1 Differential Equations Describing Fluid Motion .... 253
5.8.2 Shock Wave Speed Equation ......................... 254
5.8.3 MOC Equations ..................................... 254
5.9 Valve Actuation .......................................... 257
5.10 Reflected Shock Waves .................................... 261
5.11 Reflected Waves in a Dead-End Pipe ....................... 261
5.12 Series Pipes and Transitions in Pipe Material ............ 262
5.13 Parallel Pipes/Intersections ............................. 262
5.14 Centrifugal Pump Operation During Transients ............. 266
5.14.1 Graphic Water Hammer Solution for Pumps ........... 266
5.14.2 Reverse Pump Operation Due to Flow Reversal ....... 266
5.14.3 Transient Radial Pump Operation ................... 268
5.14.4 MOC Water Hammer Solution for Pumps ............... 268
5.14.5 Use of Valve Closure Speeds to Control Pump
Transients ........................................ 269
5.15 Column Separation and Vapor Collapse ..................... 269
5.15.1 Column Separation and Vapor Collapse at a High
Point in a System With Both Pipe Ends Submerged ... 270
5.15.2 Column Separation and Vapor Collapse at a High
Point in a Pipe With One End Submerged ............ 273
5.15.3 Column Separation and Vapor Collapse at a Valve ... 275
5.15.4 Solution Methods to Describe Column Separation
and Vapor Collapse ................................ 275
5.16 Positive Displacement Pumps .............................. 276
5.17 Effect of Trapped Air Pockets on Fluid Transients ........ 277
5.18 Additional Corrective Actions for Fluid Transients ....... 278
5.18.1 Valve Stroking .................................... 278
5.18.2 Relief Valves ..................................... 278
5.18.3 Surge Tanks and Air Chambers ...................... 278
5.18.4 Water Hammer Arrestors ............................ 280
5.18.5 Surge Suppressors ................................. 280
5.18.6 Check Valves ...................................... 280
5.18.7 Flow Rate Control for Fluid Transients ............ 280
5.19 Summary of Fluid Transients in Liquid-Filled Systems ..... 283
CHAPTER 6 Fluid Transients in Steam Systems .................. 287
6.1 Examples of Water Hammer Accidents in Steam/Condensate
Systems .................................................. 287
6.1.1 Brookhaven Fatalities ............................. 287
6.1.2 Hanford Fatality .................................. 287
6.1.3 Savannah River Site Pipe Damages .................. 289
6.1.4 Pipe Failures Due to Condensate-Induced Water
Hammer ............................................ 291
6.2 Water Hammer Mechanisms in Steam/Condensate Systems ...... 291
6.2.1 Water Cannon ...................................... 292
6.2.2 Steam and Water Counterflow ....................... 292
6.2.3 Condensate-Induced Water Hammer in a Horizontal
Pipe .............................................. 292
6.2.4 Steam Pocket Collapse and Filling of Voided
Lines ............................................. 293
6.2.5 Low-Pressure Discharge and Column Separation ...... 295
6.2.6 Steam-Propelled Water Slug ........................ 295
6.2.7 Sudden Valve Closure and Pump Operations .......... 295
6.3 Blowdown ................................................. 295
6.3.1 Sonic Velocity at Discharge Nozzles ............... 296
6.3.2 Piping Loads During Blowdown ...................... 297
6.3.3 Steam/Water Flow .................................. 298
6.3.4 Pressures in Closed Vessels and Thrust During
Blowdown .......................................... 298
6.4 Appropriate Operation of Steam Systems for Personnel
Safety ................................................... 300
6.4.1 System Startup .................................... 300
6.4.2 Steam Traps ....................................... 301
6.5 Summary of Fluid Transients .............................. 301
CHAPTER 7 Shock Waves, Vibrations, and Dynamic Stresses in
Elastic Solids ................................................ 303
7.1 Strain Waves and Vibrations .............................. 303
7.1.1 One-Dimensional Strain Waves in a Rod ............. 303
7.1.2 Three-Dimensional Strain Waves in a Solid ......... 304
7.1.3 Vibration Terms ................................... 304
7.1.4 Vibrations in a Rod Due to Strain Waves ........... 305
7.1.5 Dilatational Strain Waves in a Rod ................ 305
7.1.6 Wave Reflections in a Rod ......................... 305
7.1.7 Strain Wave Examples for Rods ..................... 306
7.1.8 Inelastic Damage Due to Wave Reflections .......... 308
7.2 Single Degree of Freedom Models .......................... 308
7.2.1 SDOF Oscillators .................................. 308
7.2.2 Step Response for a SDOF Oscillator ............... 311
7.2.3 Impulse Response for a SDOF Oscillator ............ 312
7.2.4 Ramp Response for a SDOF Oscillator ............... 313
7.2.5 SDOF Harmonic Response ............................ 313
7.2.6 Multi-DOF Harmonic Response ....................... 317
7.3 Dynamic Stress Equations ................................. 324
7.3.1 Triaxial Vibrations ............................... 324
7.3.2 Damping ........................................... 325
7.4 Summary of Dynamic Stresses in Elastic Solids ............ 330
CHAPTER 8 Water Hammer Effects on Breathing Stresses for
Pipes and Other Components .................................... 331
8.1 Examples of Piping Fatigue Failures ...................... 331
8.2 FEA Model of Breathing Stresses for a Short Pipe ......... 331
8.2.1 FEA Assumptions ................................... 332
8.2.2 Model Geometry and Dynamic Pressure Loading ....... 334
8.2.3 FEA Model for a Pipe With Fixed Ends .............. 335
8.2.4 Stress Waves and Through-Wall Radial Stresses ..... 336
8.2.5 Hoop Stresses for a Pipe With Fixed Ends .......... 336
8.2.6 Axial Stresses for a Pipe with Fixed Ends ......... 337
8.2.7 Impulse Loads ..................................... 337
8.2.8 Stresses for a Pipe with One Free End ............. 338
8.2.9 FEA Summary ....................................... 339
8.3 Theory and Experimental Results for Breathing Stresses ... 340
8.4 Flexural Resonance ....................................... 340
8.4.1 Flexural Resonance Theory ......................... 340
8.4.2 Flexural Resonance Examples ....................... 345
8.5 Dynamic Hoop Stresses .................................... 348
8.5.1 Bounded Hoop Stresses from Beam Equations ......... 348
8.5.2 Dynamic Stress Theory ............................. 351
8.5.3 Comparison of Theory to Experimental Results for
a Gas-Filled Tube ................................. 355
8.5.4 Comparison of Theory to Experimental Results for
a Liquid-Filled Pipe .............................. 356
8.5.5 Comparison of Flexural Resonance Theory to
Dynamic Stress Theory ............................. 367
8.6 Valves and Fittings ...................................... 369
8.7 Pressure Vessels ......................................... 369
8.8 Plastic Hoop Stresses .................................... 370
8.8.1 FEA Results for a Shock Wave in a Short Pipe ...... 370
8.8.2 Experimental Results for Explosions in a Thin-
Wall Tube ......................................... 371
8.8.3 Explosions in Pipes ............................... 372
8.9 Summary of Elastic and Plastic Hoop Stress Responses to
Step Pressure Transients ................................. 373
CHAPTER 9 Dynamic Stresses Due to Bending .................... 379
9.1 Deformations, Stresses, and Frequencies for Elastic
Frames ................................................... 379
9.1.1 Static Deflections and Reactions for Simply
Supported Beams and Elastic Frames ................ 379
9.1.2 Frequencies for Simple Beams ...................... 379
9.1.3 Frequencies for Elastic Frames .................... 381
9.2 Elastic Stresses Due to Bending .......................... 383
9.2.1 Step Response Calculation for Bending ............. 384
9.2.2 Ramp Response for Bending ......................... 388
9.2.3 Impulse Response for Bending ...................... 390
9.2.4 Multiple Bend FEA Models .......................... 392
9.3 FEA Model of Bending Stresses ............................ 393
9.4 Plastic Deformation and Stresses Due to Bending .......... 393
9.4.1 Consideration of Earthquake Damages to Pipe
Systems ........................................... 393
9.5 Summary of Stresses During Water Hammer .................. 393
CHAPTER 10 Summary of Water Hammer-Induced Pipe Failures ...... 395
10.1 Troubleshooting a Pipe Failure ........................... 396
10.2 Suggested References ..................................... 396
10.3 Recommended Future Research .............................. 397
Appendix A: Notation and Units ................................ 399
A.l Systems of Units ..................................... 399
A.2 Conversion Factors ................................... 400
A.3 Notation: Variables, Constants, and Dimensions ....... 402
References .................................................... 409
Index ......................................................... 419
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