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Preface |
6 |
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Contents |
8 |
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Notations |
15 |
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1 Introduction and History |
19 |
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Abstract |
19 |
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1.1 Introduction |
19 |
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1.2 Theory |
20 |
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1.2.1 Bernoulli's Theorem |
20 |
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1.2.2 Method of Operation |
21 |
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1.2.2.1 General |
21 |
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1.2.2.2 Incompressible Flow |
21 |
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1.2.2.3 Compressible Flow |
22 |
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1.2.2.4 Equation for Practical Use |
24 |
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1.3 Essential Requirements |
25 |
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1.3.1 General |
25 |
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1.3.2 With a Calibration in a Flowing Fluid |
25 |
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1.3.3 Without a Calibration in a Flowing Fluid |
26 |
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1.4 Introduction to Reynolds Number and Velocity Profile |
26 |
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1.5 Pipe Roughness |
29 |
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1.6 Accuracy |
30 |
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1.7 Pressure Loss |
31 |
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1.8 Standards |
32 |
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1.9 Advantages and Disadvantages |
32 |
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1.10 History |
33 |
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1.11 Conclusions |
40 |
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Appendix 1.A: Sextus Julius Frontinus |
41 |
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References |
46 |
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2 Orifice Design |
50 |
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Abstract |
50 |
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2.1 Introduction |
50 |
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2.2 Orifice Plate |
51 |
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2.2.1 General |
51 |
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2.2.2 Flatness |
53 |
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2.2.3 Surface Condition of the Upstream Face of the Plate |
54 |
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2.2.4 Edge Sharpness |
56 |
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2.2.5 Plate Thickness E and Orifice (Bore) Thickness e |
58 |
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2.2.5.1 General |
58 |
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2.2.5.2 Plate Thickness E |
58 |
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2.2.5.3 Orifice (Bore) Thickness e |
59 |
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2.2.5.4 Requirements |
61 |
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2.2.6 Circularity |
62 |
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2.3 The Pipe |
62 |
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2.3.1 General |
62 |
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2.3.2 Pressure Tappings |
63 |
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2.3.2.1 General |
63 |
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2.3.2.2 Flange and D and D/2 Tappings |
63 |
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General |
63 |
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Tapping Diameter |
65 |
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Tapping Location |
65 |
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2.3.2.3 Corner Tappings |
67 |
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2.3.2.4 Number of Tappings |
67 |
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2.3.3 Pipe Roughness |
68 |
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2.3.3.1 Uniform Roughness |
68 |
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2.3.3.2 Rough Pipes with a Smooth Portion Immediately Upstream of the Orifice |
71 |
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2.3.3.3 Non-uniform Roughness |
72 |
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2.3.4 Steps and Misalignment |
74 |
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2.3.5 Eccentricity |
76 |
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2.4 Dimensional Measurements |
77 |
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2.5 Orifice Fittings |
78 |
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2.6 Pressure Loss |
79 |
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2.7 Reversed Orifice Plates |
82 |
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2.8 Conclusions |
84 |
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Appendix 2.A: Orifice Plates of Small Orifice Diameter |
85 |
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2.A.1 Introduction and Test Work |
85 |
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2.A.2 Conclusions |
89 |
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References |
90 |
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3 Venturi Tube Design |
94 |
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Abstract |
94 |
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3.1 Introduction |
94 |
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3.2 Type |
96 |
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3.2.1 General |
96 |
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3.2.2 Machined Convergent (5.2.9, 5.5.3 and 5.7.2 of ISO 5167-4:2003) |
97 |
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3.2.3 Rough-Welded Sheet-Iron Convergent (5.2.10, 5.5.4 and 5.7.3 of ISO 5167-4:2003) |
97 |
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3.2.4 `As Cast' Convergent (5.2.8, 5.5.2 and 5.7.1 of ISO 5167-4:2003) |
97 |
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3.2.5 Wider Range of Reynolds Number |
98 |
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3.3 Angles, Pressure Loss and Truncation |
98 |
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3.4 Dimensional Measurements |
100 |
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3.5 Steps and Straightness |
101 |
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3.6 Pressure Tappings |
102 |
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3.7 Effects of Roughness and Reynolds Number |
104 |
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3.8 High or Low Reynolds Number |
104 |
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3.9 Conclusions |
107 |
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Appendix 3.A:‚Effect of Roughness: Computational Fluid Dynamics |
107 |
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3.A.1 General |
107 |
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3.A.2 Venturi Tube Roughness |
107 |
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3.A.2.1 Effect of Venturi Tube Roughness Height |
107 |
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3.A.2.2 Effect of Reynolds Number |
108 |
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3.A.2.3 Effect of Venturi Tube Roughness Type |
108 |
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3.A.3 Pipe Roughness |
109 |
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3.A.4 Effect of Rounding the Corner Between the Convergent Section and the Throat |
110 |
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References |
112 |
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4 General Design |
114 |
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Abstract |
114 |
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4.1 Introduction |
114 |
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4.2 Impulse Lines |
114 |
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4.2.1 General |
114 |
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4.2.2 Tapping Locations and Slopes of Impulse Lines |
116 |
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4.2.3 Density of the Fluids in Two Impulse Lines to Measure the Differential Pressure |
118 |
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4.2.4 Length of Impulse Lines |
121 |
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4.2.5 Blockage |
122 |
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4.2.6 Damping of the Pressure Signal or Resonance |
123 |
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4.3 Differential Pressure |
123 |
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4.3.1 Differential-Pressure Transmitters |
123 |
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4.3.2 Piezometer Rings |
126 |
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4.4 Static Pressure |
127 |
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4.5 Drain and Vent Holes (Through the Pipe Wall) |
128 |
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4.6 Temperature |
128 |
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4.6.1 General |
128 |
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4.6.2 Temperature Correction from Downstream of the Flowmeter to Upstream of It |
129 |
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4.6.3 Using a Densitometer |
132 |
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4.6.4 Correction of Dimensions for Temperature |
133 |
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4.7 Iteration |
134 |
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4.8 Uncertainty |
134 |
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4.9 Cavitation |
135 |
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4.10 Diagnostics |
135 |
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4.11 Mixtures |
136 |
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4.12 Conclusions |
137 |
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Appendix 4.A: Impulse Lines in Pulsating Flows |
137 |
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Appendix 4.B:‚Measuring Low Differential Pressure at High Static Pressure |
140 |
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4.B.1‚Introduction |
140 |
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4.B.2‚The Problem |
140 |
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4.B.3‚A Possible Solution |
140 |
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References |
141 |
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5 Orifice Discharge Coefficient |
143 |
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Abstract |
143 |
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5.1 Introduction |
143 |
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5.2 History |
144 |
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5.3 The EEC/API Database |
147 |
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5.4 The Equation |
150 |
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5.4.1 Introduction |
150 |
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5.4.2 The Tapping Terms |
150 |
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5.4.2.1 Introduction |
150 |
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5.4.2.2 High Reynolds Number Tapping Terms |
152 |
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Total Tapping Terms |
152 |
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Upstream Term |
152 |
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Downstream Term |
154 |
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|
5.4.2.3 Low Reynolds Number Tapping Terms |
156 |
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5.4.3 The C221E and Slope Terms |
160 |
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5.4.4 A Term for Small Orifice Meters |
162 |
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5.4.5 The Complete Equation |
163 |
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5.5 Quality of Fit |
164 |
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5.6 Equations and Comparison Between Them on the Basis of Deviations |
171 |
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5.6.1 The Reader-Harris/Gallagher (RG) Equation as in API 14.3.1:1990 |
171 |
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5.6.2 The Stolz Equation in ISO 5167:1980 |
172 |
|
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5.6.3 Comparisons |
172 |
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5.7 Uncertainty |
175 |
|
|
5.8 Conclusions |
179 |
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Appendix 5.A: Better Options for Tapping Terms |
179 |
|
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Appendix 5.B: Small Orifice Diameters Within the EEC/API Database |
183 |
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Appendix 5.C: The PR14 Equation and an Equation in Terms of Friction Factor |
186 |
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5.C.1 The PR14 Equation |
186 |
|
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5.C.2 An Equation in Terms of Friction Factor |
187 |
|
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Appendix 5.D: The Effect on the Discharge-Coefficient Equation of Changing the Expansibility-Factor Equation |
188 |
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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 |
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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 |
|
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References |
199 |
|
|
6 Orifice Expansibility Factor |
203 |
|
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Abstract |
203 |
|
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6.1 Introduction |
203 |
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|
6.2 History and Theory |
204 |
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6.3 The Database |
205 |
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6.4 Analysis |
206 |
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6.5 Theoretical Model |
211 |
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6.6 Subsequent Work |
214 |
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6.7 Conclusions |
215 |
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Appendix 6.A: Data Taken with a Flow Conditioner 7D or 10D from the Orifice Plate |
215 |
|
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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 |
|
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7.2.2 Calibration in Water |
220 |
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7.2.3 Calibration in Gas |
221 |
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7.3 Interpretation and Analysis of Data |
224 |
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7.3.1 Static-Hole Error |
224 |
|
|
7.3.2 Measurements of Static-Hole Error at High Tapping-Hole Reynolds Number |
225 |
|
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7.3.3 Measurements of Static-Hole Error at Low Tapping-Hole Reynolds Number |
226 |
|
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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 |
|
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7.3.6 The Effect of a Burr or a Protruding Tapping on Static-Hole Error |
229 |
|
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7.3.7 Analysis of the Gas Data in Sect. 7.2.3 |
229 |
|
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7.3.8 Conclusions to Sect. 7.3 |
230 |
|
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7.4 Improved Shape |
232 |
|
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7.4.1 General |
232 |
|
|
7.4.2 Venturi Tube with Convergent Angle 10.5? |
232 |
|
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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 |
|
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7.A.1 Design |
236 |
|
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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 |
|
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References |
257 |
|
|
8 Installation Effects |
259 |
|
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Abstract |
259 |
|
|
8.1 Introduction |
259 |
|
|
8.2 Upstream Straight Lengths |
260 |
|
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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 |
|
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General |
269 |
|
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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 |
|
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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 |
|
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9.2 Manufacture |
297 |
|
|
9.2.1 General |
297 |
|
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9.2.2 Pipework and Nozzles |
298 |
|
|
9.2.3 Nozzle Tappings |
298 |
|
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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 |
|
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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 |
|
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References |
339 |
|
|
11 Wet Gas |
341 |
|
|
Abstract |
341 |
|
|
11.1 Introduction |
341 |
|
|
11.2 Fundamental Equations |
343 |
|
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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 |
|