PIPE FLOW -- CONTENTS -- PREFACE -- NOMENCLATURE -- PART I: METHODOLOGY -- PROLOGUE -- 1: FUNDAMENTALS -- 1.1 SYSTEMS OF UNITS -- 1.2 FLUID PROPERTIES -- 1.2.1 Pressure -- 1.2.2 Density -- 1.2.3 Velocity -- 1.2.4 Energy -- 1.2.5 Viscosity -- 1.2.6 Temperature -- 1.2.7 Heat -- 1.3 IMPORTANT DIMENSIONLESS RATIOS -- 1.3.1 Reynolds Number -- 1.3.2 Relative Roughness -- 1.3.3 Loss Coefficient -- 1.3.4 Mach Number -- 1.3.5 Froude Number -- 1.3.6 Reduced Pressure -- 1.3.7 Reduced Temperature -- 1.4 EQUATIONS OF STATE -- 1.4.1 Equation of State of Liquids -- 1.4.2 Equation of State of Gases -- 1.5 FLUID VELOCITY -- 1.6 FLOW REGIMES -- REFERENCES -- FURTHER READING -- 2: CONSERVATION EQUATIONS -- 2.1 CONSERVATION OF MASS -- 2.2 CONSERVATION OF MOMENTUM -- 2.3 THE MOMENTUM FLUX CORRECTION FACTOR -- 2.4 CONSERVATION OF ENERGY -- 2.4.1 Potential Energy -- 2.4.2 Pressure Energy -- 2.4.3 Kinetic Energy -- 2.4.4 Heat Energy -- 2.4.5 Mechanical Work Energy -- 2.5 GENERAL ENERGY EQUATION -- 2.6 HEAD LOSS -- 2.7 THE KINETIC ENERGY CORRECTION FACTOR -- 2.8 CONVENTIONAL HEAD LOSS -- 2.9 GRADE LINES -- REFERENCES -- FURTHER READING -- 3: INCOMPRESSIBLE FLOW -- 3.1 CONVENTIONAL HEAD LOSS -- 3.2 SOURCES OF HEAD LOSS -- 3.2.1 Surface Friction Loss -- 3.2.1.1 Laminar Flow -- 3.2.1.2 Turbulent Flow -- 3.2.1.3 Reynolds Number -- 3.2.1.4 Friction Factors -- 3.2.2 Induced Turbulence -- 3.2.3 Summing Loss Coefficients -- REFERENCES -- FURTHER READING -- 4: COMPRESSIBLE FLOW -- 4.1 PROBLEM SOLUTION METHODS -- 4.2 APPROXIMATE COMPRESSIBLE FLOW USING INCOMPRESSIBLE FLOW EQUATIONS -- 4.2.1 Using Inlet or Outlet Properties -- 4.2.2 Using Average of Inlet and Outlet Properties -- 4.2.2.1 Simple Average Propertie -- 4.2.2.2 Comprehensive Average Properties -- 4.2.3 Using Expansion Factors -- 4.3 ADIABATIC COMPRESSIBLE FLOW WITH FRICTION: IDEAL EQUATION.

4.3.1 Using Mach Number as a Parameter -- 4.3.1.1 Solution when Static Pressure and Static Temperature Are Known -- 4.3.1.2 Solution when Static Pressure and Total Temperature Are Known -- 4.3.1.3 Solution when Total Pressure and Total Temperature Are Known -- 4.3.1.4 Solution when Total Pressure and Static Temperature Are Known -- 4.3.1.5 Treating Changes in Area -- 4.3.2 Using Static Pressure and Temperature as Parameters -- 4.4 ISOTHERMAL COMPRESSIBLE FLOW WITH FRICTION: IDEAL EQUATION -- 4.5 EXAMPLE PROBLEM: COMPRESSIBLE FLOW THROUGH PIPE -- REFERENCES -- FURTHER READING -- 5: NETWORK ANALYSIS -- 5.1 COUPLING EFFECTS -- 5.2 SERIES FLOW -- 5.3 PARALLEL FLOW -- 5.4 BRANCHING FLOW -- 5.5 EXAMPLE PROBLEM: RING SPARGER -- 5.5.1 Ground Rules and Assumptions -- 5.5.2 Input Parameters -- 5.5.3 Initial Calculations -- 5.5.4 Network Equations -- 5.5.4.1 Continuity Equations -- 5.5.4.2 Energy Equations -- 5.5.5 Solution -- 5.6 EXAMPLE PROBLEM: CORE SPRAY SYSTEM -- 5.6.1 New, Clean Steel Pipe -- 5.6.1.1 Ground Rules and Assumptions -- 5.6.1.2 Input Parameters -- 5.6.1.3 Initial Calculations -- 5.6.1.4 Adjusted Parameters -- 5.6.1.5 Network Flow Equations -- 5.6.1.6 Solution -- 5.6.2 Moderately Corroded Steel Pipe -- 5.6.2.1 Ground Rules and Assumptions -- 5.6.2.2 Input Parameters -- 5.6.2.3 Adjusted Parameters -- 5.6.2.4 Network Flow Equations -- 5.6.2.5 Solution -- REFERENCES -- FURTHER READING -- 6: TRANSIENT ANALYSIS -- 6.1 METHODOLOGY -- 6.2 EXAMPLE PROBLEM: VESSEL DRAIN TIMES -- 6.2.1 Upright Cylindrical Vessel -- 6.2.2 Spherical Vessel -- 6.2.3 Upright Cylindrical Vessel with Elliptical Heads -- 6.3 EXAMPLE PROBLEM: POSITIVE DISPLACEMENT PUMP -- 6.3.1 No Heat Transfer -- 6.3.2 Heat Transfer -- 6.4 EXAMPLE PROBLEM: TIME-STEP INTEGRATION -- 6.4.1 Upright Cylindrical Vessel Drain Problem -- 6.4.2 Direct Solution -- 6.4.3 Time-Step Solution -- REFERENCES.

FURTHER READING -- 7: UNCERTAINTY -- 7.1 ERROR SOURCES -- 7.2 PRESSURE DROP UNCERTAINTY -- 7.3 FLOW RATE UNCERTAINTY -- 7.4 EXAMPLE PROBLEM: PRESSURE DROP -- 7.4.1 Input Data -- 7.4.2 Solution -- 7.5 EXAMPLE PROBLEM: FLOW RATE -- 7.5.1 Input Data -- 7.5.2 Solution -- PART II: LOSS COEFFICIENTS -- PROLOGUE -- 8: SURFACE FRICTION -- 8.1 FRICTION FACTOR -- 8.1.1 Laminar Flow Region -- 8.1.2 Critical Zone -- 8.1.3 Turbulent Flow Region -- 8.1.3.1 Smooth Pipes -- 8.1.3.2 Rough Pipes -- 8.2 THE COLEBROOK-WHITE EQUATION -- 8.3 THE MOODY CHART -- 8.4 EXPLICIT FRICTION FACTOR FORMULATIONS -- 8.4.1 Moody's Approximate Formula -- 8.4.2 Wood's Approximate Formula -- 8.4.3 The Churchill 1973 and Swamee and Jain Formulas -- 8.4.4 Chen's Formula -- 8.4.5 Shacham's Formula -- 8.4.6 Barr's Formula -- 8.4.7 Haaland's Formulas -- 8.4.8 Manadilli's Formula -- 8.4.9 Romeo's Formula -- 8.4.10 Evaluation of Explicit Alternatives to the Colebrook-White Equation -- 8.5 ALL-REGIME FRICTION FACTOR FORMULAS -- 8.5.1 Churchill's 1977 Formula -- 8.5.2 Modifications to Churchill's 1977 Formula -- 8.6 SURFACE ROUGHNESS -- 8.6.1 New, Clean Pipe -- 8.6.2 The Relationship between Absolute Roughness and Friction Factor -- 8.6.3 Inherent Margin -- 8.6.4 Loss of Flow Area -- 8.6.5 Machined Surfaces -- 8.7 NONCIRCULAR PASSAGES -- REFERENCES -- FURTHER READING -- 9: ENTRANCES -- 9.1 SHARP-EDGED ENTRANCE -- 9.1.1 Flush Mounted -- 9.1.2 Mounted at a Distance -- 9.1.3 Mounted at an Angle -- 9.2 ROUNDED ENTRANCE -- 9.3 BEVELED ENTRANCE -- 9.4 ENTRANCE THROUGH AN ORIFICE -- 9.4.1 Sharp-Edged Orifice -- 9.4.2 Round-Edged Orifice -- 9.4.3 Thick-Edged Orifice -- 9.4.4 Beveled Orifice -- REFERENCES -- FURTHER READING -- 10: CONTRACTIONS -- 10.1 FLOW MODEL -- 10.2 SHARP-EDGED CONTRACTION -- 10.3 ROUNDED CONTRACTION -- 10.4 CONICAL CONTRACTION -- 10.4.1 Surface Friction Loss -- 10.4.2 Local Loss.

10.5 BEVELED CONTRACTION -- 10.6 SMOOTH CONTRACTION -- 10.7 PIPE REDUCER: CONTRACTING -- REFERENCES -- FURTHER READING -- 11: EXPANSIONS -- 11.1 SUDDEN EXPANSION -- 11.2 STRAIGHT CONICAL DIFFUSER -- 11.3 MULTISTAGE CONICAL DIFFUSERS -- 11.3.1 Stepped Conical Diffuser -- 11.3.2 Two-Stage Conical Diffuser -- 11.4 CURVED WALL DIFFUSER -- 11.5 PIPE REDUCER: EXPANDING -- REFERENCES -- FURTHER READING -- 12: EXITS -- 12.1 DISCHARGE FROM A STRAIGHT PIPE -- 12.2 DISCHARGE FROM A CONICAL DIFFUSER -- 12.3 DISCHARGE FROM AN ORIFICE -- 12.3.1 Sharp-Edged Orifice -- 12.3.2 Round-Edged Orifice -- 12.3.3 Thick-Edged Orifice -- 12.3.4 Bevel-Edged Orifice -- 12.4 DISCHARGE FROM A SMOOTH NOZZLE -- 13: ORIFICES -- 13.1 GENERALIZED FLOW MODEL -- 13.2 SHARP-EDGED ORIFICE -- 13.2.1 In a Straight Pipe -- 13.2.2 In a Transition Section -- 13.2.3 In a Wall -- 13.3 ROUND-EDGED ORIFICE -- 13.3.1 In a Straight Pipe -- 13.3.2 In a Transition Section -- 13.3.3 In a Wall -- 13.4 BEVEL-EDGED ORIFICE -- 13.4.1 In a Straight Pipe -- 13.4.2 In a Transition Section -- 13.4.3 In a Wall -- 13.5 THICK-EDGED ORIFICE -- 13.5.1 In a Straight Pipe -- 13.5.2 In a Transition Section -- 13.5.3 In a Wall -- 13.6 MULTIHOLE ORIFICES -- 13.7 NONCIRCULAR ORIFICES -- REFERENCES -- FURTHER READING -- 14: FLOW METERS -- 14.1 FLOW NOZZLE -- 14.2 VENTURI TUBE -- 14.3 NOZZLE/VENTURI -- REFERENCES -- FURTHER READING -- 15: BENDS -- 15.1 ELBOWS AND PIPE BENDS -- 15.2 COILS -- 15.2.1 Constant Pitch Helix -- 15.2.2 Constant Pitch Spiral -- 15.3 MITER BENDS -- 15.4 COUPLED BENDS -- 15.5 BEND ECONOMY -- REFERENCES -- FURTHER READING -- 16: TEES -- 16.1 DIVERGING TEES -- 16.1.1 Flow through Run -- 16.1.2 Flow through Branch -- 16.1.3 Flow from Branch -- 16.2 CONVERGING TEES -- 16.2.1 Flow through Run -- 16.2.2 Flow through Branch -- 16.2.3 Flow into Branch -- REFERENCES -- FURTHER READING -- 17: PIPE JOINTS.

17.1 WELD PROTRUSION -- 17.2 BACKING RINGS -- 17.3 MISALIGNMENT -- 17.3.1 Misaligned Pipe Joint -- 17.3.2 Misaligned Gasket -- 18: VALVES -- 18.1 MULTITURN VALVES -- 18.1.1 Diaphragm Valve -- 18.1.2 Gate Valve -- 18.1.3 Globe Valve -- 18.1.4 Pinch Valve -- 18.1.5 Needle Valve -- 18.2 QUARTER-TURN VALVES -- 18.2.1 Ball Valve -- 18.2.2 Butterfly Valve -- 18.2.3 Plug Valve -- 18.3 SELF-ACTUATED VALVES -- 18.3.1 Check Valve -- 18.3.2 Relief Valve -- 18.4 CONTROL VALVES -- 18.5 VALVE LOSS COEFFICIENTS -- REFERENCES -- FURTHER READING -- 19: THREADED FITTINGS -- 19.1 REDUCERS: CONTRACTING -- 19.2 REDUCERS: EXPANDING -- 19.3 ELBOWS -- 19.4 TEES -- 19.5 COUPLINGS -- 19.6 VALVES -- REFERENCE -- PART III: FLOW PHENOMENA -- PROLOGUE -- 20: CAVITATION -- 20.1 THE NATURE OF CAVITATION -- 20.2 PIPELINE DESIGN -- 20.3 NET POSITIVE SUCTION HEAD -- 20.4 EXAMPLE PROBLEM: CORE SPRAY PUMP -- 20.4.1 New, Clean Steel Pipe -- 20.4.1.1 Input Parameters -- 20.4.1.2 Solution -- 20.4.1.3 Results -- 20.4.2 Moderately Corroded Steel Pipe -- 20.4.2.1 Input Parameters -- 20.4.2.2 Solution -- 20.4.2.3 Results -- REFERENCE -- FURTHER READING -- 21: FLOW-INDUCED VIBRATION -- 21.1 STEADY INTERNAL FLOW -- 21.2 STEADY EXTERNAL FLOW -- 21.3 WATER HAMMER† -- 21.4 COLUMN SEPARATION -- REFERENCES -- FURTHER READING -- 22: TEMPERATURE RISE -- 22.1 REACTOR HEAT BALANCE -- 22.2 VESSEL HEAT UP -- 22.3 PUMPING SYSTEM TEMPERATURE -- REFERENCES -- 23: FLOW TO RUN FULL -- 23.1 OPEN FLOW -- 23.2 FULL FLOW -- 23.3 SUBMERGED FLOW -- 23.4 REACTOR APPLICATION -- FURTHER READING -- APPENDIX A: PHYSICAL PROPERTIES OF WATER AT 1 ATMOSPHERE -- APPENDIX B: PIPE SIZE DATA -- B.1 COMMERCIAL PIPE DATA -- APPENDIX C: PHYSICAL CONSTANTS AND UNIT CONVERSIONS -- C.1 IMPORTANT PHYSICAL CONSTANTS -- C.2 UNIT CONVERSIONS -- APPENDIX D: COMPRESSIBILITY FACTOR EQUATIONS -- D.1 THE REDLICH-KWONG EQUATION.

D.2 THE LEE-KESLER EQUATION.