Reader-Harris Orifice Plates and Venturi Tubes

1. Auflage 2015
ISBN: 978-3-319-16880-7
Verlag: Springer International Publishing
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 393 Seiten

Reihe: Experimental Fluid Mechanics

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.

Zielgruppe

Professional/practitioner

Autoren/Hrsg.

Reader-Harris, Michael

Inhaltsverzeichnis

1;Preface;6
2;Contents;8
3;Notations;15
4;1 Introduction and History;19
4.1;Abstract;19
4.2;1.1 Introduction;19
4.3;1.2 Theory;20
4.3.1;1.2.1 Bernoulli's Theorem;20
4.3.2;1.2.2 Method of Operation;21
4.3.2.1;1.2.2.1 General;21
4.3.2.2;1.2.2.2 Incompressible Flow;21
4.3.2.3;1.2.2.3 Compressible Flow;22
4.3.2.4;1.2.2.4 Equation for Practical Use;24
4.4;1.3 Essential Requirements;25
4.4.1;1.3.1 General;25
4.4.2;1.3.2 With a Calibration in a Flowing Fluid;25
4.4.3;1.3.3 Without a Calibration in a Flowing Fluid;26
4.5;1.4 Introduction to Reynolds Number and Velocity Profile;26
4.6;1.5 Pipe Roughness;29
4.7;1.6 Accuracy;30
4.8;1.7 Pressure Loss;31
4.9;1.8 Standards;32
4.10;1.9 Advantages and Disadvantages;32
4.11;1.10 History;33
4.12;1.11 Conclusions;40
4.13;Appendix 1.A: Sextus Julius Frontinus;41
4.14;References;46
5;2 Orifice Design;50
5.1;Abstract;50
5.2;2.1 Introduction;50
5.3;2.2 Orifice Plate;51
5.3.1;2.2.1 General;51
5.3.2;2.2.2 Flatness;53
5.3.3;2.2.3 Surface Condition of the Upstream Face of the Plate;54
5.3.4;2.2.4 Edge Sharpness;56
5.3.5;2.2.5 Plate Thickness E and Orifice (Bore) Thickness e;58
5.3.5.1;2.2.5.1 General;58
5.3.5.2;2.2.5.2 Plate Thickness E;58
5.3.5.3;2.2.5.3 Orifice (Bore) Thickness e;59
5.3.5.4;2.2.5.4 Requirements;61
5.3.6;2.2.6 Circularity;62
5.4;2.3 The Pipe;62
5.4.1;2.3.1 General;62
5.4.2;2.3.2 Pressure Tappings;63
5.4.2.1;2.3.2.1 General;63
5.4.2.2;2.3.2.2 Flange and D and D/2 Tappings;63
5.4.2.2.1;General;63
5.4.2.2.2;Tapping Diameter;65
5.4.2.2.3;Tapping Location;65
5.4.2.3;2.3.2.3 Corner Tappings;67
5.4.2.4;2.3.2.4 Number of Tappings;67
5.4.3;2.3.3 Pipe Roughness;68
5.4.3.1;2.3.3.1 Uniform Roughness;68
5.4.3.2;2.3.3.2 Rough Pipes with a Smooth Portion Immediately Upstream of the Orifice;71
5.4.3.3;2.3.3.3 Non-uniform Roughness;72
5.4.4;2.3.4 Steps and Misalignment;74
5.4.5;2.3.5 Eccentricity;76
5.5;2.4 Dimensional Measurements;77
5.6;2.5 Orifice Fittings;78
5.7;2.6 Pressure Loss;79
5.8;2.7 Reversed Orifice Plates;82
5.9;2.8 Conclusions;84
5.10;Appendix 2.A: Orifice Plates of Small Orifice Diameter;85
5.10.1;2.A.1 Introduction and Test Work;85
5.10.2;2.A.2 Conclusions;89
5.11;References;90
6;3 Venturi Tube Design;94
6.1;Abstract;94
6.2;3.1 Introduction;94
6.3;3.2 Type;96
6.3.1;3.2.1 General;96
6.3.2;3.2.2 Machined Convergent (5.2.9, 5.5.3 and 5.7.2 of ISO 5167-4:2003);97
6.3.3;3.2.3 Rough-Welded Sheet-Iron Convergent (5.2.10, 5.5.4 and 5.7.3 of ISO 5167-4:2003);97
6.3.4;3.2.4 `As Cast' Convergent (5.2.8, 5.5.2 and 5.7.1 of ISO 5167-4:2003);97
6.3.5;3.2.5 Wider Range of Reynolds Number;98
6.4;3.3 Angles, Pressure Loss and Truncation;98
6.5;3.4 Dimensional Measurements;100
6.6;3.5 Steps and Straightness;101
6.7;3.6 Pressure Tappings;102
6.8;3.7 Effects of Roughness and Reynolds Number;104
6.9;3.8 High or Low Reynolds Number;104
6.10;3.9 Conclusions;107
6.11;Appendix 3.A:‚Effect of Roughness: Computational Fluid Dynamics;107
6.11.1;3.A.1 General;107
6.11.2;3.A.2 Venturi Tube Roughness;107
6.11.2.1;3.A.2.1 Effect of Venturi Tube Roughness Height;107
6.11.2.2;3.A.2.2 Effect of Reynolds Number;108
6.11.2.3;3.A.2.3 Effect of Venturi Tube Roughness Type;108
6.11.3;3.A.3 Pipe Roughness;109
6.11.4;3.A.4 Effect of Rounding the Corner Between the Convergent Section and the Throat;110
6.12;References;112
7;4 General Design;114
7.1;Abstract;114
7.2;4.1 Introduction;114
7.3;4.2 Impulse Lines;114
7.3.1;4.2.1 General;114
7.3.2;4.2.2 Tapping Locations and Slopes of Impulse Lines;116
7.3.3;4.2.3 Density of the Fluids in Two Impulse Lines to Measure the Differential Pressure;118
7.3.4;4.2.4 Length of Impulse Lines;121
7.3.5;4.2.5 Blockage;122
7.3.6;4.2.6 Damping of the Pressure Signal or Resonance;123
7.4;4.3 Differential Pressure;123
7.4.1;4.3.1 Differential-Pressure Transmitters;123
7.4.2;4.3.2 Piezometer Rings;126
7.5;4.4 Static Pressure;127
7.6;4.5 Drain and Vent Holes (Through the Pipe Wall);128
7.7;4.6 Temperature;128
7.7.1;4.6.1 General;128
7.7.2;4.6.2 Temperature Correction from Downstream of the Flowmeter to Upstream of It;129
7.7.3;4.6.3 Using a Densitometer;132
7.7.4;4.6.4 Correction of Dimensions for Temperature;133
7.8;4.7 Iteration;134
7.9;4.8 Uncertainty;134
7.10;4.9 Cavitation;135
7.11;4.10 Diagnostics;135
7.12;4.11 Mixtures;136
7.13;4.12 Conclusions;137
7.14;Appendix 4.A: Impulse Lines in Pulsating Flows;137
7.15;Appendix 4.B:‚Measuring Low Differential Pressure at High Static Pressure;140
7.15.1;4.B.1‚Introduction;140
7.15.2;4.B.2‚The Problem;140
7.15.3;4.B.3‚A Possible Solution;140
7.16;References;141
8;5 Orifice Discharge Coefficient;143
8.1;Abstract;143
8.2;5.1 Introduction;143
8.3;5.2 History;144
8.4;5.3 The EEC/API Database;147
8.5;5.4 The Equation;150
8.5.1;5.4.1 Introduction;150
8.5.2;5.4.2 The Tapping Terms;150
8.5.2.1;5.4.2.1 Introduction;150
8.5.2.2;5.4.2.2 High Reynolds Number Tapping Terms;152
8.5.2.2.1;Total Tapping Terms;152
8.5.2.2.2;Upstream Term;152
8.5.2.2.3;Downstream Term;154
8.5.2.3;5.4.2.3 Low Reynolds Number Tapping Terms;156
8.5.3;5.4.3 The C221E and Slope Terms;160
8.5.4;5.4.4 A Term for Small Orifice Meters;162
8.5.5;5.4.5 The Complete Equation;163
8.6;5.5 Quality of Fit;164
8.7;5.6 Equations and Comparison Between Them on the Basis of Deviations;171
8.7.1;5.6.1 The Reader-Harris/Gallagher (RG) Equation as in API 14.3.1:1990;171
8.7.2;5.6.2 The Stolz Equation in ISO 5167:1980;172
8.7.3;5.6.3 Comparisons;172
8.8;5.7 Uncertainty;175
8.9;5.8 Conclusions;179
8.10;Appendix 5.A: Better Options for Tapping Terms;179
8.11;Appendix 5.B: Small Orifice Diameters Within the EEC/API Database;183
8.12;Appendix 5.C: The PR14 Equation and an Equation in Terms of Friction Factor;186
8.12.1;5.C.1 The PR14 Equation;186
8.12.2;5.C.2 An Equation in Terms of Friction Factor;187
8.13;Appendix 5.D: The Effect on the Discharge-Coefficient Equation of Changing the Expansibility-Factor Equation;188
8.14;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
8.14.1;5.E.1 Introduction;191
8.14.2;5.E.2 Orifice Plates in Pipes of Small Diameter;191
8.14.3;5.E.3 Orifice Plates with No Upstream or Downstream Pipeline;192
8.14.4;5.E.4 Orifice Plates with No Upstream Pipeline;194
8.14.5;5.E.5 Orifice Plates with No Downstream Pipeline;195
8.15;Appendix 5.F: Lower Reynolds Number Limit for the Reader-Harris/Gallagher (1998) Equation;197
8.16;References;199
9;6 Orifice Expansibility Factor;203
9.1;Abstract;203
9.2;6.1 Introduction;203
9.3;6.2 History and Theory;204
9.4;6.3 The Database;205
9.5;6.4 Analysis;206
9.6;6.5 Theoretical Model;211
9.7;6.6 Subsequent Work;214
9.8;6.7 Conclusions;215
9.9;Appendix 6.A: Data Taken with a Flow Conditioner 7D or 10D from the Orifice Plate;215
9.10;References;216
10;7 Venturi Tube Discharge Coefficient in High-Pressure Gas;218
10.1;Abstract;218
10.2;7.1 Introduction;218
10.3;7.2 Experimental Work: Standard Shape;219
10.3.1;7.2.1 Description of the Venturi Tubes;219
10.3.2;7.2.2 Calibration in Water;220
10.3.3;7.2.3 Calibration in Gas;221
10.4;7.3 Interpretation and Analysis of Data;224
10.4.1;7.3.1 Static-Hole Error;224
10.4.2;7.3.2 Measurements of Static-Hole Error at High Tapping-Hole Reynolds Number;225
10.4.3;7.3.3 Measurements of Static-Hole Error at Low Tapping-Hole Reynolds Number;226
10.4.4;7.3.4 The Effect of Tapping Depth on Static-Hole Error;227
10.4.5;7.3.5 The Effect of Tapping Shape on Static-Hole Error;229
10.4.6;7.3.6 The Effect of a Burr or a Protruding Tapping on Static-Hole Error;229
10.4.7;7.3.7 Analysis of the Gas Data in Sect. 7.2.3;229
10.4.8;7.3.8 Conclusions to Sect. 7.3;230
10.5;7.4 Improved Shape;232
10.5.1;7.4.1 General;232
10.5.2;7.4.2 Venturi Tube with Convergent Angle 10.5?;232
10.5.3;7.4.3 The Discharge-Coefficient Equation for Venturi Tubes with Convergent Angle 10.5?;234
10.6;7.5 Conclusions;236
10.7;Appendix 7.A: Shape of Venturi Tubes: Tests at NEL;236
10.7.1;7.A.1 Design;236
10.7.2;7.A.2 Calibration in Water;239
10.7.3;7.A.3 Calibration in Gas;239
10.7.4;7.A.4 Analysis;239
10.7.5;7.A.5 Conclusions on Shape from the 42033 Venturi Tubes;247
10.7.6;7.A.6 Manufacture of Additional Venturi Tubes with 10.5? Convergent Angle and Sharp Corners;247
10.7.7;7.A.7 Calibration of Additional Venturi Tubes in Water and in Gas;248
10.8;Appendix 7.B: Depth of Tappings: Tests at NEL;252
10.9;Appendix 7.C: Refitting the Data With Convergent Angle 10.5?;254
10.10;References;257
11;8 Installation Effects;259
11.1;Abstract;259
11.2;8.1 Introduction;259
11.3;8.2 Upstream Straight Lengths;260
11.3.1;8.2.1 General;260
11.3.2;8.2.2 Definitions;262
11.3.3;8.2.3 Orifice Plates;262
11.3.3.1;8.2.3.1 History;262
11.3.3.2;8.2.3.2 The Pattern of the Data;262
11.3.3.3;8.2.3.3 The Straight Lengths in ISO 5167-2:2003;267
11.3.4;8.2.4 Venturi Tubes;269
11.3.4.1;8.2.4.1 Standard Venturi Tubes;269
11.3.4.1.1;General;269
11.3.4.1.2;Calibrations Downstream of a Contraction and an Expansion;270
11.3.4.1.3;Calibrations Downstream of Bends;270
11.3.4.1.4;Analysis;273
11.3.4.2;8.2.4.2 Venturi Tubes with Convergent Angle 10.5?;274
11.3.5;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
11.3.5.1;8.2.5.1 General;276
11.3.5.2;8.2.5.2 The Upstream Installation is a Combination of Fittings;276
11.3.5.3;8.2.5.3 A Flow Conditioner Is Used;277
11.3.5.3.1;General;277
11.3.5.3.2;With an Orifice Plate;278
11.3.5.3.3;With a Venturi Tube;282
11.3.5.3.4;Damage to Flow Conditioners;284
11.3.5.4;8.2.5.4 A Specific Test Is Done;284
11.3.5.5;8.2.5.5 CFD is Carried Out;285
11.3.5.6;8.2.5.6 Engineering Judgement is Employed;285
11.4;8.3 Downstream Straight Length;286
11.4.1;8.3.1 Orifice Plates;286
11.4.2;8.3.2 Venturi Tubes;286
11.5;8.4 Pulsations;287
11.5.1;8.4.1 General;287
11.5.2;8.4.2 Orifice Plates;288
11.5.3;8.4.3 Venturi Tubes;288
11.6;8.5 Conclusions;288
11.7;Appendix 8.A: Swirl Decay;289
11.8;References;289
12;9 Nozzle Discharge Coefficient;295
12.1;Abstract;295
12.2;9.1 Introduction;295
12.3;9.2 Manufacture;297
12.3.1;9.2.1 General;297
12.3.2;9.2.2 Pipework and Nozzles;298
12.3.3;9.2.3 Nozzle Tappings;298
12.3.4;9.2.4 Wall Tappings;300
12.4;9.3 Data;300
12.5;9.4 Wall-Tapping Data: Analysis;301
12.6;9.5 Throat-Tapping Data: Initial Analysis;305
12.7;9.6 Hot-Water (NMIJ Throat-Tapping) Data;309
12.8;9.7 Throat-Tapping Data: Further Analysis;310
12.8.1;9.7.1 General;310
12.8.2;9.7.2 Analysis of NMIJ Data;312
12.8.3;9.7.3 Application to NEL Data;313
12.8.4;9.7.4 Analysis of NEL Data;315
12.9;9.8 Conclusions;316
12.10;References;317
13;10 Orifice Plates with Drain Holes;319
13.1;Abstract;319
13.2;10.1 Introduction;319
13.3;10.2 Experimental Work: Initial Data;322
13.4;10.3 Experimental Work: Additional Data;327
13.5;10.4 Analysis;330
13.5.1;10.4.1 Bernoulli's Theorem;330
13.5.2;10.4.2 Pressure Tapping Location for Flow Measurement Without Error;332
13.5.3;10.4.3 An Equation for the Corrected Diameter;334
13.5.4;10.4.4 Practical Equations for the Corrected Diameter;338
13.6;10.5 Conclusions;339
13.7;References;339
14;11 Wet Gas;341
14.1;Abstract;341
14.2;11.1 Introduction;341
14.3;11.2 Fundamental Equations;343
14.3.1;11.2.1 General;343
14.3.2;11.2.2 Laboratory Test Work;344
14.3.3;11.2.3 Models for Field Use;344
14.3.3.1;11.2.3.1 General;344
14.3.3.2;11.2.3.2 Venturi Tube;345
14.3.3.2.1;General;345
14.3.3.2.2;de Leeuw Equation;345
14.3.3.2.3;ISO/TR 11583:2012 Correlation;345
14.3.3.3;11.2.3.3 Orifice Plate;346
14.3.4;11.2.4 Methods to Obtain the Lockhart-Martinelli Parameter, X (Eq. 11.2);347
14.3.4.1;11.2.4.1 General;347
14.3.4.2;11.2.4.2 Pressure Loss Ratio;348
14.3.4.2.1;Venturi Tube;348
14.3.4.2.2;Orifice Plate;349
14.4;11.3 Venturi Tubes;350
14.4.1;11.3.1 Over-Reading Equations;350
14.4.1.1;11.3.1.1 Derivation of the ISO/TR 11583:2012 Correlation;350
14.4.1.2;11.3.1.2 Comparison with the de Leeuw Equation;357
14.4.1.3;11.3.1.3 Possible Improvement of the ISO/TR 11583:2012 Correlation;357
14.4.2;11.3.2 Using Pressure-Loss Measurements;361
14.4.3;11.3.3 Mixtures of Liquids;365
14.5;11.4 Orifice Plates;367
14.5.1;11.4.1 General;367
14.5.2;11.4.2 Derivation of the Equations in ISO/TR 11583:2012;367
14.5.3;11.4.3 Subsequent Work;371
14.6;11.5 Conclusions;371
14.7;Appendix 11.A: A Brief History of ISO/TR 11583;372
14.8;Appendix 11.B: Dependence of the Wet-Gas Correlations for Venturi Tubes on Liquid Viscosity;375
14.8.1;11.B.1 General;375
14.8.2;11.B.2 Deviations from the ISO/TR 11583:2012 Correlation;375
14.8.3;11.B.3 Deviations from the de Leeuw Equation;378
14.8.4;11.B.4 Errors Using ISO/TR 11583:2012 with X Determined from the Pressure Loss Ratio;380
14.8.5;11.B.5 Analysis;380
14.8.6;11.B.6 Horizontal Tappings;388
14.9;References;388
15;12 Standards;390
15.1;Abstract;390
15.2;12.1 Introduction;390
15.3;12.2 ISO Standards;391
15.4;12.3 ISO/TC 30 Measurement of Fluid Flow in Closed Conduits;392
15.4.1;12.3.1 General;392
15.4.2;12.3.2 ISO/TC 30/SC 2 Pressure Differential Methods;392
15.4.2.1;12.3.2.1 General;392
15.4.2.2;12.3.2.2 Differential-Pressure Flow Measurement Standards: ISO 5167 Etc.;393
15.4.2.3;12.3.2.3 ISO/TR 9464 Guidelines for Using ISO 5167;395
15.4.2.4;12.3.2.4 ISO/TR 12767 Differential-Pressure Meters Departing from ISO 5167;395
15.4.2.5;12.3.2.5 ISO/TR 15377 Differential-Pressure Meters Beyond the Scope of ISO 5167;396
15.4.2.6;12.3.2.6 ISO/TR 3313 Pulsating Flow;396
15.4.2.7;12.3.2.7 ISO/TR 11583 Wet Gas;397
15.4.2.8;12.3.2.8 ISO 2186 Impulse Lines;397
15.4.2.9;12.3.2.9 Priorities for the Future as Seen in 2014;397
15.4.3;12.3.3 The TC Itself;398
15.4.3.1;12.3.3.1 General;398
15.4.3.2;12.3.3.2 Priorities for the Future as Seen in 2014;399
15.5;12.4 AGA/API Standards;399
15.6;12.5 Conclusions;400
15.7;Appendix 12.A: The Standards of ISO/TC 30/SC 2;400
15.8;References;401
16;Index;402

Über Autor(innen)

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.