Orifice Plates and Venturi Tubes (eBook)

Michael Reader-Harris (Autor)

eBook Download: PDF

2015 | 2015
XVIII, 393 Seiten
Springer International Publishing (Verlag)
978-3-319-16880-7 (ISBN)

Infos

This book gives the background to differential-pressure flow measurement and goes through the requirements explaining the reason for them. For those who want to use an orifice plate or a Venturi tube the standard ISO 5167 and its associated Technical Reports give the instructions required.  However, they rarely tell the users why they should follow certain instructions.  This book helps users of the ISO standards for orifice plates and Venturi tubes to understand the reasons why the standards are as they are, to apply them effectively, and to understand the consequences of deviations from the standards.

Dr Reader-Harris is Principal Consultant in flow measurement at NEL.  He provides technical leadership to projects, carries out consultancy work particularly in the area of differential pressure meters, and undertakes work in support of Standards. 

Inhalt

Preface 6
Contents 8
Notations 15
1 Introduction and History 19
Abstract 19
1.1 Introduction 19
1.2 Theory 20
1.2.1 Bernoulli's Theorem 20
1.2.2 Method of Operation 21
1.2.2.1 General 21
1.2.2.2 Incompressible Flow 21
1.2.2.3 Compressible Flow 22
1.2.2.4 Equation for Practical Use 24
1.3 Essential Requirements 25
1.3.1 General 25
1.3.2 With a Calibration in a Flowing Fluid 25
1.3.3 Without a Calibration in a Flowing Fluid 26
1.4 Introduction to Reynolds Number and Velocity Profile 26
1.5 Pipe Roughness 29
1.6 Accuracy 30
1.7 Pressure Loss 31
1.8 Standards 32
1.9 Advantages and Disadvantages 32
1.10 History 33
1.11 Conclusions 40
Appendix 1.A: Sextus Julius Frontinus 41
References 46
2 Orifice Design 50
Abstract 50
2.1 Introduction 50
2.2 Orifice Plate 51
2.2.1 General 51
2.2.2 Flatness 53
2.2.3 Surface Condition of the Upstream Face of the Plate 54
2.2.4 Edge Sharpness 56
2.2.5 Plate Thickness E and Orifice (Bore) Thickness e 58
2.2.5.1 General 58
2.2.5.2 Plate Thickness E 58
2.2.5.3 Orifice (Bore) Thickness e 59
2.2.5.4 Requirements 61
2.2.6 Circularity 62
2.3 The Pipe 62
2.3.1 General 62
2.3.2 Pressure Tappings 63
2.3.2.1 General 63
2.3.2.2 Flange and D and D/2 Tappings 63
General 63
Tapping Diameter 65
Tapping Location 65
2.3.2.3 Corner Tappings 67
2.3.2.4 Number of Tappings 67
2.3.3 Pipe Roughness 68
2.3.3.1 Uniform Roughness 68
2.3.3.2 Rough Pipes with a Smooth Portion Immediately Upstream of the Orifice 71
2.3.3.3 Non-uniform Roughness 72
2.3.4 Steps and Misalignment 74
2.3.5 Eccentricity 76
2.4 Dimensional Measurements 77
2.5 Orifice Fittings 78
2.6 Pressure Loss 79
2.7 Reversed Orifice Plates 82
2.8 Conclusions 84
Appendix 2.A: Orifice Plates of Small Orifice Diameter 85
2.A.1 Introduction and Test Work 85
2.A.2 Conclusions 89
References 90
3 Venturi Tube Design 94
Abstract 94
3.1 Introduction 94
3.2 Type 96
3.2.1 General 96
3.2.2 Machined Convergent (5.2.9, 5.5.3 and 5.7.2 of ISO 5167-4:2003) 97
3.2.3 Rough-Welded Sheet-Iron Convergent (5.2.10, 5.5.4 and 5.7.3 of ISO 5167-4:2003) 97
3.2.4 `As Cast' Convergent (5.2.8, 5.5.2 and 5.7.1 of ISO 5167-4:2003) 97
3.2.5 Wider Range of Reynolds Number 98
3.3 Angles, Pressure Loss and Truncation 98
3.4 Dimensional Measurements 100
3.5 Steps and Straightness 101
3.6 Pressure Tappings 102
3.7 Effects of Roughness and Reynolds Number 104
3.8 High or Low Reynolds Number 104
3.9 Conclusions 107
Appendix 3.A:‚Effect of Roughness: Computational Fluid Dynamics 107
3.A.1 General 107
3.A.2 Venturi Tube Roughness 107
3.A.2.1 Effect of Venturi Tube Roughness Height 107
3.A.2.2 Effect of Reynolds Number 108
3.A.2.3 Effect of Venturi Tube Roughness Type 108
3.A.3 Pipe Roughness 109
3.A.4 Effect of Rounding the Corner Between the Convergent Section and the Throat 110
References 112
4 General Design 114
Abstract 114
4.1 Introduction 114
4.2 Impulse Lines 114
4.2.1 General 114
4.2.2 Tapping Locations and Slopes of Impulse Lines 116
4.2.3 Density of the Fluids in Two Impulse Lines to Measure the Differential Pressure 118
4.2.4 Length of Impulse Lines 121
4.2.5 Blockage 122
4.2.6 Damping of the Pressure Signal or Resonance 123
4.3 Differential Pressure 123
4.3.1 Differential-Pressure Transmitters 123
4.3.2 Piezometer Rings 126
4.4 Static Pressure 127
4.5 Drain and Vent Holes (Through the Pipe Wall) 128
4.6 Temperature 128
4.6.1 General 128
4.6.2 Temperature Correction from Downstream of the Flowmeter to Upstream of It 129
4.6.3 Using a Densitometer 132
4.6.4 Correction of Dimensions for Temperature 133
4.7 Iteration 134
4.8 Uncertainty 134
4.9 Cavitation 135
4.10 Diagnostics 135
4.11 Mixtures 136
4.12 Conclusions 137
Appendix 4.A: Impulse Lines in Pulsating Flows 137
Appendix 4.B:‚Measuring Low Differential Pressure at High Static Pressure 140
4.B.1‚Introduction 140
4.B.2‚The Problem 140
4.B.3‚A Possible Solution 140
References 141
5 Orifice Discharge Coefficient 143
Abstract 143
5.1 Introduction 143
5.2 History 144
5.3 The EEC/API Database 147
5.4 The Equation 150
5.4.1 Introduction 150
5.4.2 The Tapping Terms 150
5.4.2.1 Introduction 150
5.4.2.2 High Reynolds Number Tapping Terms 152
Total Tapping Terms 152
Upstream Term 152
Downstream Term 154
5.4.2.3 Low Reynolds Number Tapping Terms 156
5.4.3 The C221E and Slope Terms 160
5.4.4 A Term for Small Orifice Meters 162
5.4.5 The Complete Equation 163
5.5 Quality of Fit 164
5.6 Equations and Comparison Between Them on the Basis of Deviations 171
5.6.1 The Reader-Harris/Gallagher (RG) Equation as in API 14.3.1:1990 171
5.6.2 The Stolz Equation in ISO 5167:1980 172
5.6.3 Comparisons 172
5.7 Uncertainty 175
5.8 Conclusions 179
Appendix 5.A: Better Options for Tapping Terms 179
Appendix 5.B: Small Orifice Diameters Within the EEC/API Database 183
Appendix 5.C: The PR14 Equation and an Equation in Terms of Friction Factor 186
5.C.1 The PR14 Equation 186
5.C.2 An Equation in Terms of Friction Factor 187
Appendix 5.D: The Effect on the Discharge-Coefficient Equation of Changing the Expansibility-Factor Equation 188
Appendix 5.E: Orifice Plates in Pipes of Small Diameter or with No Upstream or with No Downstream Pipeline or with No Upstream and No Downstream Pipeline 191
5.E.1 Introduction 191
5.E.2 Orifice Plates in Pipes of Small Diameter 191
5.E.3 Orifice Plates with No Upstream or Downstream Pipeline 192
5.E.4 Orifice Plates with No Upstream Pipeline 194
5.E.5 Orifice Plates with No Downstream Pipeline 195
Appendix 5.F: Lower Reynolds Number Limit for the Reader-Harris/Gallagher (1998) Equation 197
References 199
6 Orifice Expansibility Factor 203
Abstract 203
6.1 Introduction 203
6.2 History and Theory 204
6.3 The Database 205
6.4 Analysis 206
6.5 Theoretical Model 211
6.6 Subsequent Work 214
6.7 Conclusions 215
Appendix 6.A: Data Taken with a Flow Conditioner 7D or 10D from the Orifice Plate 215
References 216
7 Venturi Tube Discharge Coefficient in High-Pressure Gas 218
Abstract 218
7.1 Introduction 218
7.2 Experimental Work: Standard Shape 219
7.2.1 Description of the Venturi Tubes 219
7.2.2 Calibration in Water 220
7.2.3 Calibration in Gas 221
7.3 Interpretation and Analysis of Data 224
7.3.1 Static-Hole Error 224
7.3.2 Measurements of Static-Hole Error at High Tapping-Hole Reynolds Number 225
7.3.3 Measurements of Static-Hole Error at Low Tapping-Hole Reynolds Number 226
7.3.4 The Effect of Tapping Depth on Static-Hole Error 227
7.3.5 The Effect of Tapping Shape on Static-Hole Error 229
7.3.6 The Effect of a Burr or a Protruding Tapping on Static-Hole Error 229
7.3.7 Analysis of the Gas Data in Sect. 7.2.3 229
7.3.8 Conclusions to Sect. 7.3 230
7.4 Improved Shape 232
7.4.1 General 232
7.4.2 Venturi Tube with Convergent Angle 10.5? 232
7.4.3 The Discharge-Coefficient Equation for Venturi Tubes with Convergent Angle 10.5? 234
7.5 Conclusions 236
Appendix 7.A: Shape of Venturi Tubes: Tests at NEL 236
7.A.1 Design 236
7.A.2 Calibration in Water 239
7.A.3 Calibration in Gas 239
7.A.4 Analysis 239
7.A.5 Conclusions on Shape from the 42033 Venturi Tubes 247
7.A.6 Manufacture of Additional Venturi Tubes with 10.5? Convergent Angle and Sharp Corners 247
7.A.7 Calibration of Additional Venturi Tubes in Water and in Gas 248
Appendix 7.B: Depth of Tappings: Tests at NEL 252
Appendix 7.C: Refitting the Data With Convergent Angle 10.5? 254
References 257
8 Installation Effects 259
Abstract 259
8.1 Introduction 259
8.2 Upstream Straight Lengths 260
8.2.1 General 260
8.2.2 Definitions 262
8.2.3 Orifice Plates 262
8.2.3.1 History 262
8.2.3.2 The Pattern of the Data 262
8.2.3.3 The Straight Lengths in ISO 5167-2:2003 267
8.2.4 Venturi Tubes 269
8.2.4.1 Standard Venturi Tubes 269
General 269
Calibrations Downstream of a Contraction and an Expansion 270
Calibrations Downstream of Bends 270
Analysis 273
8.2.4.2 Venturi Tubes with Convergent Angle 10.5? 274
8.2.5 What to Do if a Case is not Covered in Table 3 of ISO 5167-2:2003/Table 1 of ISO 5167-4:2003 276
8.2.5.1 General 276
8.2.5.2 The Upstream Installation is a Combination of Fittings 276
8.2.5.3 A Flow Conditioner Is Used 277
General 277
With an Orifice Plate 278
With a Venturi Tube 282
Damage to Flow Conditioners 284
8.2.5.4 A Specific Test Is Done 284
8.2.5.5 CFD is Carried Out 285
8.2.5.6 Engineering Judgement is Employed 285
8.3 Downstream Straight Length 286
8.3.1 Orifice Plates 286
8.3.2 Venturi Tubes 286
8.4 Pulsations 287
8.4.1 General 287
8.4.2 Orifice Plates 288
8.4.3 Venturi Tubes 288
8.5 Conclusions 288
Appendix 8.A: Swirl Decay 289
References 289
9 Nozzle Discharge Coefficient 295
Abstract 295
9.1 Introduction 295
9.2 Manufacture 297
9.2.1 General 297
9.2.2 Pipework and Nozzles 298
9.2.3 Nozzle Tappings 298
9.2.4 Wall Tappings 300
9.3 Data 300
9.4 Wall-Tapping Data: Analysis 301
9.5 Throat-Tapping Data: Initial Analysis 305
9.6 Hot-Water (NMIJ Throat-Tapping) Data 309
9.7 Throat-Tapping Data: Further Analysis 310
9.7.1 General 310
9.7.2 Analysis of NMIJ Data 312
9.7.3 Application to NEL Data 313
9.7.4 Analysis of NEL Data 315
9.8 Conclusions 316
References 317
10 Orifice Plates with Drain Holes 319
Abstract 319
10.1 Introduction 319
10.2 Experimental Work: Initial Data 322
10.3 Experimental Work: Additional Data 327
10.4 Analysis 330
10.4.1 Bernoulli's Theorem 330
10.4.2 Pressure Tapping Location for Flow Measurement Without Error 332
10.4.3 An Equation for the Corrected Diameter 334
10.4.4 Practical Equations for the Corrected Diameter 338
10.5 Conclusions 339
References 339
11 Wet Gas 341
Abstract 341
11.1 Introduction 341
11.2 Fundamental Equations 343
11.2.1 General 343
11.2.2 Laboratory Test Work 344
11.2.3 Models for Field Use 344
11.2.3.1 General 344
11.2.3.2 Venturi Tube 345
General 345
de Leeuw Equation 345
ISO/TR 11583:2012 Correlation 345
11.2.3.3 Orifice Plate 346
11.2.4 Methods to Obtain the Lockhart-Martinelli Parameter, X (Eq. 11.2) 347
11.2.4.1 General 347
11.2.4.2 Pressure Loss Ratio 348
Venturi Tube 348
Orifice Plate 349
11.3 Venturi Tubes 350
11.3.1 Over-Reading Equations 350
11.3.1.1 Derivation of the ISO/TR 11583:2012 Correlation 350
11.3.1.2 Comparison with the de Leeuw Equation 357
11.3.1.3 Possible Improvement of the ISO/TR 11583:2012 Correlation 357
11.3.2 Using Pressure-Loss Measurements 361
11.3.3 Mixtures of Liquids 365
11.4 Orifice Plates 367
11.4.1 General 367
11.4.2 Derivation of the Equations in ISO/TR 11583:2012 367
11.4.3 Subsequent Work 371
11.5 Conclusions 371
Appendix 11.A: A Brief History of ISO/TR 11583 372
Appendix 11.B: Dependence of the Wet-Gas Correlations for Venturi Tubes on Liquid Viscosity 375
11.B.1 General 375
11.B.2 Deviations from the ISO/TR 11583:2012 Correlation 375
11.B.3 Deviations from the de Leeuw Equation 378
11.B.4 Errors Using ISO/TR 11583:2012 with X Determined from the Pressure Loss Ratio 380
11.B.5 Analysis 380
11.B.6 Horizontal Tappings 388
References 388
12 Standards 390
Abstract 390
12.1 Introduction 390
12.2 ISO Standards 391
12.3 ISO/TC 30 Measurement of Fluid Flow in Closed Conduits 392
12.3.1 General 392
12.3.2 ISO/TC 30/SC 2 Pressure Differential Methods 392
12.3.2.1 General 392
12.3.2.2 Differential-Pressure Flow Measurement Standards: ISO 5167 Etc. 393
12.3.2.3 ISO/TR 9464 Guidelines for Using ISO 5167 395
12.3.2.4 ISO/TR 12767 Differential-Pressure Meters Departing from ISO 5167 395
12.3.2.5 ISO/TR 15377 Differential-Pressure Meters Beyond the Scope of ISO 5167 396
12.3.2.6 ISO/TR 3313 Pulsating Flow 396
12.3.2.7 ISO/TR 11583 Wet Gas 397
12.3.2.8 ISO 2186 Impulse Lines 397
12.3.2.9 Priorities for the Future as Seen in 2014 397
12.3.3 The TC Itself 398
12.3.3.1 General 398
12.3.3.2 Priorities for the Future as Seen in 2014 399
12.4 AGA/API Standards 399
12.5 Conclusions 400
Appendix 12.A: The Standards of ISO/TC 30/SC 2 400
References 401
Index 402

Produkt-Details

• Erscheint lt. Verlag: 29.4.2015
• Reihe/Serie: Experimental Fluid Mechanics
• Reihe/Serie: Experimental Fluid Mechanics
• Zusatzinfo: XVIII, 393 p. 220 illus., 192 illus. in color.
• Verlagsort: Cham
• Sprache: englisch
• Themenwelt: Technik ► Bauwesen
• Themenwelt: Technik ► Maschinenbau
• Schlagworte: ISO 5167 Standards • ISO/TC 30 • Nozzle Tappings • Orifice Discharge Coefficient • Orifice Expansibility Factor • Orifice Plates with Drain Holes • Venturi Tube Discharge • Wet-gas meters
• ISBN-10: 3-319-16880-0 / 3319168800
• ISBN-13: 978-3-319-16880-7 / 9783319168807