ASME PTC 19.5 2022

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ASME PTC-19.5-2022 Flow Measurement

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ASME	2022

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Description

This Supplement describes the techniques and methods of flow measurements required or recommended by ASME PTCs. A variety of commonly used flow measurement devices are included to provide details for the different applications referenced by various PTCs. This is a supplementary document that does not supersede the mandatory requirements of any PTC, unless such an agreement has been expressed in writing prior to testing or a PTC requires that specified sections or paragraphs within this Supplement be used.

PDF Catalog

PDF Pages	PDF Title
4	CONTENTS
12	NOTICE
13	Foreword
15	ASME PTC COMMITTEE ROSTER
16	CORRESPONDENCE WITH THE PTC COMMITTEE
18	Section 1 Object, Scope, and Uncertainty 1-1 OBJECT 1-2 SCOPE 1-3 UNCERTAINTY 1-4 REFERENCES TO ASME STANDARDS
20	Section 2 Definitions, Values, and Descriptions of Terms 2-1 GENERAL 2-2 PRIMARY DEFINITIONS AND SYSTEMS OF UNITS 2-3 SYMBOLS AND DIMENSIONS 2-3.1 Common Conversion Factors 2-4 THERMAL EXPANSION 2-4.1 Linear Thermal Expansion
21	Tables Table 2-3-1 Symbols Typically Used in Flow Measurement
22	2-4.2 Tables of Linear Thermal Expansion for Selected Materials 2-5 REFERENCES
23	Section 3 Differential Pressure Class Meters 3-1 NOMENCLATURE 3-2 GENERAL EQUATION FOR MASS FLOW THROUGH A DIFFERENTIAL PRESSURE CLASS METER 3-3 BASIC PHYSICAL CONCEPTS USED IN THE DERIVATION OF THE GENERAL EQUATION FOR MASS FLOW
24	Table 3-1-1 Symbols Specifically Applied in Sections 3 through 6 (in Addition to Symbols in Table 2-3-1)
25	3-4 THEORETICAL FLOW — LIQUID AS THE FLOWING FLUID Table 3-2-1 Values of Constants in the General Equation for Various Units
26	Figures Figure 3-4-1 Water Leg Correction for Flow Measurement
27	3-5 THEORETICAL FLOW — GAS OR VAPOR AS THE FLOWING FLUID Table 3-4-1 Units and Conversion Factor for Water Leg Correction for Flow Measurement
28	3-6 FACTORS NOT ACCOUNTED FOR IN THEORETICAL MASS FLOW BY IDEALIZED FLOW ASSUMPTIONS 3-7 DISCHARGE COEFFICIENT, C, IN THE INCOMPRESSIBLE FLUID EQUATION
29	3-8 DISCHARGE COEFFICIENT, C, AND THE EXPANSION FACTOR, ε, FOR GASES 3-9 CALCULATION OF EXPANSION FACTOR, ε 3-10 DETERMINING DISCHARGE COEFFICIENT FOR DIFFERENTIAL PRESSURE CLASS METERS
30	3-11 THERMAL EXPANSION/CONTRACTION OF INLET SECTION AND PRIMARY ELEMENT 3-12 SELECTION AND RECOMMENDED USE OF DIFFERENTIAL PRESSURE CLASS METERS 3-12.1 Beta, Pipe Size, and Reynolds Number 3-12.2 Uncertainty
31	Table 3-12.2-1 Uncertainty of Discharge Coefficient, C, (Uncalibrated) and Expansion Factor, ε
32	3-12.3 Unrecoverable Pressure Loss 3-12.4 Specified Installations 3-13 RESTRICTIONS OF USE 3-14 PROCEDURE FOR SIZING A DIFFERENTIAL PRESSURE CLASS METER
33	Figure 3-12.3-1 Unrecoverable Pressure Loss Versus Beta Ratio
34	3-15 FLOW CALCULATION PROCEDURE 3-16 SAMPLE CALCULATION Table 3-16-1 Natural Gas Analysis
38	3-17 REFERENCES
40	Section 4 Orifice Meters 4-1 NOMENCLATURE 4-2 INTRODUCTION 4-3 TYPES OF THIN-PLATE, SQUARE-EDGED ORIFICES 4-4 CODE COMPLIANCE REQUIREMENTS 4-5 MULTIPLE SETS OF DIFFERENTIAL PRESSURE TAPS
41	4-6 MACHINING TOLERANCES, DIMENSIONS, AND MARKINGS FOR ORIFICE PLATE 4-6.1 Deflection and the Required Thickness, E, of Orifice Plate Figure 4-6-1 Standard Orifice Plate
42	4-6.2 Upstream Face, A Figure 4-6.1-1 Deflection of an Orifice Plate by Differential Pressure Table 4-6.1-1 Recommended Plate Thickness, E, for Stainless Steel Orifice Plate
43	4-6.3 Downstream Face, B 4-6.4 Thickness, e, of the Orifice 4-6.5 Plate Thickness, E, and Bevel 4-6.6 Edges G, H, and I 4-6.7 Orifice Diameter, d 4-6.8 Eccentricity and Alignment of Orifice in Metering Section 4-6.9 Orifice Drain Hole
44	4-7 MACHINING TOLERANCES AND DIMENSIONS FOR DIFFERENTIAL PRESSURE TAPS 4-7.1 Flange Taps — Shape, Diameter, and Angular Position 4-7.2 Flange Taps Orifice Metering Runs — Spacing of Taps 4-7.3 Corner Tap Orifice Metering Runs
45	Figure 4-7-1 Location of Pressure Taps for Orifices With Flange Taps
46	Figure 4-7-2 Location of Pressure Taps for Orifices With Corner Taps
47	4-8 LOCATION OF TEMPERATURE AND STATIC PRESSURE MEASUREMENTS 4-9 EMPIRICAL FORMULATIONS FOR DISCHARGE COEFFICIENT, C
48	4-10 LIMITATIONS AND UNCERTAINTY OF EQ. (4-9-1) FOR DISCHARGE COEFFICIENT, C 4-10.1 Limits of Use 4-10.2 Uncertainties of the Discharge Coefficient of Uncalibrated Orifice Sections
49	4-11 UNCERTAINTY OF EXPANSION FACTOR, ε Figure 4-10.1-1 Minimum Reynolds Number for Flange Taps
50	4-12 UNRECOVERABLE PRESSURE LOSS 4-13 CALCULATIONS OF DIFFERENTIAL PRESSURE CLASS FLOW MEASUREMENT SYSTEMATIC UNCERTAINTY 4-13.1 Derivation 4-13.2 Uncertainty Calculation — General
51	Table 4-13.1-1 Sensitivity Coefficients in the General Equation for Differential Pressure Meters
52	Table 4-13.2.1-1 Example 1 — Systematic Uncertainty Analysis for Given Steam Flow Orifice Metering Run Table 4-13.2.2-1 Example 2 — Systematic Uncertainty Analysis for Given Steam Flow Orifice Metering Run
53	4-13.3 Random Uncertainty Due to Data Fluctuations 4-13.4 Instrumentation Uncertainties for the Determination of Flow Measurement Systematic Uncertainties Table 4-13.2.3-1 Example 3 — Systematic Uncertainty Analysis for Given Gas Flow and Meter Tube
54	4-13.5 Uncertainty of Typical Gas Fuel Flow Measurement for a Laboratory-Calibrated Orifice Metering Section 4-14 PROCEDURE FOR FITTING A CALIBRATION CURVE AND EXTRAPOLATION TECHNIQUE
55	Table 4-13.4.1-1 Systematic Uncertainty, 0.075% Accuracy Class Differential Pressure Transmitter Table 4-13.4.2-1 Systematic Uncertainty, 0.075% Accuracy Class Static Pressure Transmitter Table 4-13.5-1 Systematic Uncertainty Analysis for Given Gas flowmetering Run With Laboratory Calibration
56	4-15 REFERENCES
57	Section 5 Nozzles and Venturis 5-1 NOMENCLATURE 5-2 INTRODUCTION 5-3 REQUIRED PROPORTIONS OF ASME NOZZLES 5-3.1 Entrance Section 5-3.2 Throat Section
58	5-3.3 Exit End Section 5-3.4 General Requirements for ASME Flow Nozzles Figure 5-3-1 High β Nozzle
59	Figure 5-3-2 Low β Nozzle Figure 5-3-3 Throat Tap Nozzle for β > 0.44
60	Figure 5-3-4 Throat Tap Nozzle for β ≤ 0.44 Figure 5-3-5 Throat Tap Nozzle End Detail
61	Figure 5-3-6 Example Throat Tap Nozzle Flow Section
62	Figure 5-3.4-1 ASME Nozzle Required Surface Finish to Produce a Hydraulically Smooth Surface
63	5-4 NOZZLE PRESSURE TAP REQUIREMENTS 5-4.1 Wall Tap Nozzles Figure 5-3.4-2 Boring in Flow Section Upstream of Nozzle
64	5-4.2 Throat Tap Nozzles 5-5 NOZZLE INSTALLATION REQUIREMENTS 5-5.1 Flanged Installation 5-5.2 Installation Without Flanges 5-5.3 Centering 5-5.4 Straight Lengths 5-5.5 Flow Conditioners 5-5.6 Diffusers 5-5.7 Assembly
65	5-6 DISCHARGE COEFFICIENT FOR ASME NOZZLES 5-6.1 High β and Low β Nozzles Figure 5-5.6-1 Nozzle With Diffusing Cone
66	5-6.2 Throat Tap Nozzles 5-7 THE ASME VENTURI TUBE Figure 5-6.2.1-1 Reference Curve for Throat Tap Nozzles
67	Figure 5-7-1 Profile of the ASME Venturi
68	5-8 VENTURI DESIGN AND DESIGN VARIATIONS 5-8.1 Entrance Section 5-8.2 Convergent Section 5-8.3 Throat 5-8.4 Divergent Section
69	5-8.5 Roughness 5-8.6 Materials 5-8.7 Manufacture 5-8.8 Characteristics of a Machined Convergent Section 5-8.9 Characteristics of a Fabricated Convergent Section 5-9 VENTURI PRESSURE TAPS 5-9.1 Number of Taps 5-9.2 Tap Location 5-9.3 Tap Hole Edge 5-9.4 Tap Length
70	5-9.5 Tap Size 5-9.6 Pressure Taps With Annular Chambers. 5-10 DISCHARGE COEFFICIENT OF THE ASME VENTURI 5-10.1 Equation for the Discharge Coefficient 5-10.2 Uncertainty of Discharge Coefficient for Uncalibrated Flow Sections 5-11 INSTALLATION REQUIREMENTS FOR THE ASME VENTURI 5-11.1 Installation Requirements 5-12 LABORATORY CALIBRATIONS 5-13 UNCERTAINTY OF EXPANSION FACTOR, ε
71	5-14 UNRECOVERABLE PRESSURE LOSS 5-14.1 ASME Nozzles Without a Diffusing Section 5-14.2 ASME Nozzles With a Diffusing Section 5-14.3 ASME Venturis 5-15 REFERENCES
72	Section 6 Differential Pressure Class Meter Installation and Flow Conditioning Requirements 6-1 NOMENCLATURE 6-2 INTRODUCTION 6-2.1 Recommended Practice 6-3 METERING SECTION REQUIREMENTS
73	6-3.1 Fabrication of the Metering Section Pipe 6-4 METER INSTALLATION IN THE METERING SECTION 6-4.1 Alignment 6-4.2 Centering
74	6-5 ADDITIONAL PIPE LENGTH REQUIREMENTS 6-5.1 Pipe Length 6-5.2 Cases Not Covered 6-5.3 Pipe Diameter Requirements
75	Table 6-5.1-1 Straight Lengths for Orifice Meters
76	Table 6-5.1-2 Straight Lengths for Nozzles
77	Table 6-5.1-3 Straight Lengths for Classical Venturi
78	Figure 6-5.3.1-1 Allowable Diameter Steps for 0.2% Additional Uncertainty
79	6-6 FLOW CONDITIONERS AND INSTALLATION 6-6.1 Flow Conditioner Design 6-6.2 Flow Conditioner Loss 6-7 INSTALLATION OF TEMPERATURE SENSORS
80	Figure 6-6.1-1 Flow Conditioner Designs
81	6-8 REFERENCES Table 6-6.1.1-1 Hole Coordinates for Perforated Plate Table 6-6.2-1 Loss Coefficients for Flow Conditioners
82	Section 7 Sonic Flow Nozzles and Venturis — Critical Flow, Choked Flow Conditions 7-1 NOMENCLATURE 7-2 INTRODUCTION 7-2.1 Advantages and Disadvantages of Sonic Flowmeters
83	Table 7-1-1 Symbols Specifically Applied in Section 7 (in Addition to Symbols in Table 2-3-1)
84	Figure 7-2-1 Ideal Mach Number Distribution Along Venturi Length at Typical Subcritical and Sonic Flow Conditions
85	7-2.2 Historical Development of Concepts
86	7-2.3 General Considerations Figure 7-2.2-1 Definition of Sonic Flow as the Maximum of the Flow [See Eq. (7-2-1)]
87	7-3 DEFINITIONS AND DESCRIPTION OF TERMS 7-3.1 Definitions 7-3.2 General
88	Figure 7-3.2-1 Schematic Representation of Flow Defects at Venturi Throat
89	7-4 GUIDING PRINCIPLES 7-5 INSTRUMENTS AND METHODS OF MEASUREMENT 7-5.1 General Figure 7-3.2-2 Schematic Diagram of Sonic Surfaces at the Throat of an Axially Symmetric Sonic Flow Venturi Nozzle
90	Figure 7-4-1 Requirements for Maintaining Sonic Flow in Venturi Nozzles Figure 7-4-2 Mass Flow Versus Back-Pressure Ratio for a Flow Nozzle Without a Diffuser and a Venturi Nozzle With a Diffuser
91	7-5.2 Design Criteria 7-5.3 Standardized Flow Nozzle and Venturi Designs
92	Figure 7-5.3.1-1 Standardized Toroidal Throat Sonic Flow Venturi Nozzle
93	7-6 INSTALLATION 7-6.1 General Figure 7-5.3.3-1 Standardized Cylindrical Throat Sonic Flow Venturi
94	7-6.2 Standardized Inlet Flow Conditioner 7-6.3 Inlet Configurations for Sonic Venturi Nozzles 7-7 PRESSURE AND TEMPERATURE MEASUREMENTS 7-7.1 Pressure Measurements Figure 7-5.3.4-1 ASME Long-Radius Flow Nozzles
95	Figure 7-6.2-1 Standardized Inlet Flow Conditioner and Locations for Pressure and Temperature Measurements Figure 7-6.3-1 Comparison of the “Continuous Curvature” Inlet With the “Sharp-Lip, Free-Standing” Inlet
96	Figure 7-7.1.1-1 Static and Total (Stagnation) Pressure Measurements on a Pipe
97	Figure 7-7.1.2-1 Standardized Pressure Tap Geometry Installation
98	7-8 COMPUTATION OF RESULTS 7-8.1 Basic Theoretical Relationships 7-8.2 Classifications for Theoretical Mass Flow
99	7-8.3 Method for Determining the Deviation from Ideal Gas State 7-8.4 Ideal Gas Relationships
100	Figure 7-8.3-1 Generalized Compressibility Chart
101	7-8.5 Real Gas Relationships 7-8.6 Real Gases, Using Complex Property Equations
102	Figure 7-8.6.1-1 Calculation Processes for the Isentropic Path From Inlet to Sonic Throat for a Real Gas Using the Method of Johnson
103	7-9 FLOW UNCERTAINTY 7-9.1 Uncertainty in Sonic Flow Function Calculations 7-9.2 Calibration Methods and Uncertainty Estimates for Discharge Coefficients
104	7-10 DISCHARGE COEFFICIENTS 7-10.1 Method of Correlation of Discharge Coefficients 7-10.2 Discharge Coefficients for Toroidal Throat
105	Table 7-10.2-1 Summary of Points Plotted in Figure 7-10.2-1 and Coefficients for Eq. (7-10-2)
106	Figure 7-10.2-1 Composite Results for Toroidal-Throat Venturi Nozzles
107	7-10.3 Discharge Coefficients for Cylindrical Throat Venturi Nozzles 7-10.4 Discharge Coefficients for ASME Low-β Throat Tap Flow Nozzles (Arnberg and Ishibashi, 2001b) Figure 7-10.2-2 Mean Line Discharge Coefficient Curves for Toroidal-Throat Venturi Nozzles
108	7-10.5 Boundary Layers and Discharge Coefficients 7-11 OTHER METHODS AND EXAMPLES 7-11.1 Traditional and Useful Methods for the Computation of Flow 7-11.1.1 Method 3: Real Gas Approximation Using the Ideal Gas Sonic Flow Function Corrected by the Compressibility Factor. Table 7-10.3-1 Discharge Coefficients for Cylindrical-Throat Venturi Nozzles
109	Figure 7-11.1.1-1 Error in Method 3 for Air Based on Sonic Flow Functions When Using Air Property Data Table 7-11.1.1-1 Percent Error in Method 3 Based on Sonic Flow Functions and Air Property Data
110	7-11.1.2 Method 4: Real Gases and Vapors, Thermodynamic Property Tables.
111	7-11.1.3 Method 5: Ideal Gas, Ratio of Specific Heats Assumed Constant. Table 7-11.1.2.1-1 Sonic Flow Function, C*i, and Critical Property Ratios [Ideal Gases and Isentropic Relationships, Eqs. (7-2-7) Through (7-2-9)] Versus Type of Ideal Gas
112	7-11.1.4 Method 6: Ideal Gas, Ratio of Specific Heats at Inlet Stagnation State. Figure 7-11.1.4-1 Error in Sonic Flow Function, C*i, for Air Using Method 6 Based on Ideal Gas Theory With Ratio of Specific Heats Corresponding to the Inlet Stagnation State
113	7-11.1.5 Method 7: Ideal Gas, Gas Tables.
114	7-12 SPECIAL APPLICATIONS 7-12.1 Special Applications of Sonic Flow Nozzles and Venturis
115	7-13 REFERENCES
118	Section 8 Flow Measurement by Velocity Traverse 8-1 NOMENCLATURE 8-2 INTRODUCTION 8-2.1 Flow Computation
119	Table 8-1-1 Symbols Specifically Applied in Section 8 (in Addition to Symbols in Table 2-3-1)
120	8-3 TRAVERSE MEASUREMENT LOCATIONS
121	8-3.1 Pipes Figure 8-3.1-1 Pipe Velocity Measurement Loci
122	Table 8-3.1-1 Locations and Weighting Factors for Gaussian Method in Pipes Table 8-3.1-2 Locations and Weighting Factors for Chebychev Method in Pipes
123	Table 8-3.1-3 Locations and Weighting Factors for the Log-Linear Method in Pipes Table 8-3.1-4 Locations and Weighting Factors for the Equal-Area Method in Pipes
124	8-3.2 Rectangular Ducts Table 8-3.2-1 Locations and Weighting Factors for the Gaussian Method in Rectangular Ducts
125	Table 8-3.2-2 Locations and Weighting Factors for Chebychev Method in Rectangular Ducts
126	Figure 8-3.2-1 Duct Velocity Measurement Loci for Gaussian Distribution Table 8-3.2-3 Locations and Weighting Factors for the Equal-Area Velocity Method in Rectangular Ducts
127	8-4 RECOMMENDED OR REQUIRED LOCATIONS OF MEASUREMENT SECTIONS Figure 8-3.2-2 Recommended Number of Measurement Loci for the Equal-Area Method
128	8-5 USE AND CALIBRATION REQUIREMENTS FOR SENSORS 8-5.1 Pitot Tubes
129	Figure 8-5.1-1 Pitot Tubes Not Requiring Calibration
130	Figure 8-5.1-2 Pitot Tubes Needing Calibration But Acceptable
131	Figure 8-5.1.2-1 Wedge-Type Five-Hole Probe Installation Schematic
132	Figure 8-5.1.2-2 Five-Hole Probe Designs
133	Figure 8-5.1.2-3 The Fechheimer Probe Installation
134	8-5.2 Calibration of Current and Propeller Meters 8-6 FLOW MEASUREMENT BY PITOT RAKE
135	Figure 8-6-1 Insertion Type Pitot Rake
136	Figure 8-6-2 Pitot Rake
137	8-7 GENERAL REQUIREMENTS 8-7.1 Pressure-Sensing Lines 8-7.2 Required Pressure Measurement Uncertainty 8-7.3 Velocity Traverse — Moveable Sensor 8-8 FLOW COMPUTATION CORRECTIONS Figure 8-6-3 Impact Pressure Tube Rake
138	8-8.1 Blockage Correction for Static Taps Upstream of Pitot Tubes 8-8.2 Blockage Correction for Current and Propeller Meters 8-9 UNCERTAINTY ANALYSIS
139	8-10 REFERENCES Table 8-9-1 Sample Uncertainty Estimate
140	Section 9 Ultrasonic Flowmeters 9-1 SCOPE 9-2 PURPOSE 9-3 DEFINITIONS AND SYMBOLS 9-3.1 Terminology
141	9-3.2 Symbols 9-4 APPLICATIONS Table 9-3.2-1 Symbols Specifically Applied in Section 9 (in Addition to Symbols in Table 2-3-1)
142	9-4.1 Liquid Flow Measurement 9-4.2 Gas Flow Measurement 9-5 FLOWMETER DESCRIPTION 9-5.1 Primary Device (Sensor)
143	9-5.2 Secondary Device (Electronics) 9-5.3 Operating Principles Figure 9-5.1.3-1 Common Acoustic Path Configurations
144	Figure 9-5.3.2-1 Wetted Recessed Transducer Configuration
146	9-5.4 Acoustic Signal 9-5.5 Measurement Circuitry 9-6 PERFORMANCE-AFFECTING CHARACTERISTICS 9-6.1 Meter Characteristics
147	Figure 9-5.5-1 Acoustic Flow Measuring System Block Diagram
148	Figure 9-6.1.1.3-1 Reflective Path Transducer Configuration
150	Figure 9-6.1.2.5-1 Recessed Transducer Configuration Figure 9-6.1.2.6-1 Protruding Transducer Configuration
151	Figure 9-6.1.2.7-1 Flush Transducer Configuration
152	9-6.2 Flow Characteristics Figure 9-6.1.2.9-1 Waveguide Transducer Configuration
153	Figure 9-6.2.2-1 Cross-Beam Transducer Configuration
155	9-6.3 Installation Considerations
156	9-7 CALIBRATION 9-7.1 Purpose 9-7.2 Factory Calibration 9-7.3 Laboratory Calibration
157	9-7.4 Field Calibration 9-7.5 Dry Calibration 9-7.6 Calibration Considerations 9-7.7 Measurement Uncertainty
158	9-8 ERROR SOURCES AND THEIR REDUCTION 9-8.1 Axial Velocity Measurement Uncertainty
159	9-8.2 Signal Detection 9-8.3 Computation and Integration 9-8.4 Velocity Profile Uncertainties
160	9-8.5 Cross Section Dimensional Errors Figure 9-8.4-1 Laminar (Blue) and Turbulent (Red) Flow Velocity Profiles and 1-, 2-, 3-, and 5-Beam Acoustic Patch Diagrams
161	9-8.6 Acoustic Path Location 9-8.7 Upstream and Downstream Flow Disturbances 9-8.8 Proximity to Other Meters 9-8.9 Equipment Degradation
162	Section 10 Tracer Method for Measuring Water Flow 10-1 NOMENCLATURE 10-2 INTRODUCTION 10-2.1 Applicability 10-3 CONSTANT RATE INJECTION METHOD
163	10-4 TRACER SELECTION 10-5 MIXING LENGTH AND MIXING DISTANCE 10-5.1 Experimental Derivation of Mixing Length Table 10-1-1 Symbols Specifically Applied in Section 10 (in Addition to Symbols in Table 2-3-1)
164	Figure 10-5-1 Schematic Control Volume Figure 10-5.1-1 Experimental Results
165	10-5.2 Methods of Reducing the Mixing Distance 10-5.3 Experimental Checking 10-6 PROCEDURE 10-6.1 Preparation of the Injection Solution 10-6.2 Injection of the Concentrated Solution
166	10-6.3 Measurement of Injected Flow 10-6.4 Samples 10-7 FLUOROMETRIC METHOD OF ANALYSIS 10-7.1 Fluorometer Description 10-7.2 Factors Affecting Fluorescence Table 10-7.2-1 Temperature Exponents for Tracer Dyes
167	10-7.3 Fluorometer Calibration 10-8 FLOW TEST SETUP 10-8.1 Tracer Injection Setup
168	Figure 10-7.3-1 Example Calibration Curves
169	Figure 10-8.1-1 Tracer Injection Schematic
170	10-8.2 Sampling Methods 10-8.3 Flow-Through Tracer Flow Signal Figure 10-8.2-1 Sampling System Figure 10-8.3-1 Fluorometer Signal Versus Time
171	10-9 UNCERTAINTY 10-9.1 Systematic Errors 10-9.2 Example of Uncertainty Analysis — Fluorescent Tracer Table 10-9.2-1 Typical Uncertainties Using a Fluorescent Tracer
172	10-10 REFERENCE
173	Section 11 Vortex Shedding Meters 11-1 NOMENCLATURE 11-2 PRINCIPLE OF MEASUREMENT Table 11-1-1 Symbols Specifically Applied in Section 11 (in Addition to Symbols in Table 2-3-1)
174	11-3 FLOWMETER DESCRIPTIONS 11-3.1 Physical Components 11-3.2 Flow Tube 11-3.3 Transmitter Figure 11-2-1 Vortex Formation
175	11-3.4 Equipment Markings 11-4 APPLICATION CONSIDERATIONS 11-4.1 Sizing 11-4.2 Process Influences
176	11-4.3 Safety
177	11-5 INSTALLATION 11-5.1 Adjacent Piping 11-5.2 Flowmeter Orientation 11-5.3 Flowmeter Location
178	11-5.4 New Installations 11-5.5 Complementary Measurements 11-6 OPERATION 11-7 CALIBRATION AND UNCERTAINTY 11-7.1 Calibration Methods Figure 11-5.5-1 Locations of Pressure and Temperature Measurements
179	11-7.2 Mean K-Factor Calculation and Uncertainty 11-7.3 Installation Influence on Uncertainty Figure 11-7.1-1 Illustration of a K-Factor Curve
180	11-7.4 Measurement Uncertainty Examples Table 11-7.3-1 Recommended Distance From Disturbance for Less Than 0.5% Increase in Uncertainty Table 11-7.4-1 Vortex Measurement Uncertainty Example
181	11-8 REFERENCES Table 11-7.4-2 Vortex Measurement Uncertainty Example With Installation Uncertainty Table 11-7.4-3 Vortex Measurement Uncertainty Example With Vortex Meter, Pressure Sensor, and Temperature Sensor Uncertainties
182	Section 12 Mechanical Meters 12-1 NOMENCLATURE 12-2 INTRODUCTION Table 12-1-1 Symbols Specifically Applied in Section 12 (in Addition to Symbols in Table 2-3-1)
183	12-3 TURBINE METERS 12-3.1 Meter Design Data and Construction Details 12-4 TURBINE METER SIGNAL TRANSDUCERS AND INDICATORS 12-5 CALIBRATION
184	12-5.1 Meter Factor
185	12-5.2 Temperature Range 12-5.3 Pressure Loss 12-5.4 Installation Conditions 12-5.5 Mechanically Driven External Equipment 12-5.6 Temperature and Pressure Effects 12-6 RECOMMENDATIONS FOR USE 12-6.1 Start-up Recommendation
186	12-6.2 Over-Range Protection 12-6.3 Bypass 12-6.4 Maintenance and Inspection Frequency 12-6.5 Other Installation Considerations 12-6.6 Accessories Installation
187	12-7 PIPING INSTALLATION AND DISTURBANCES 12-7.1 Swirl Effect 12-7.2 Velocity Profile Effect 12-8 EXAMPLE OF FLOW MEASUREMENT BY TURBINE METER WITH NATURAL GAS 12-8.1 Meter Flow
188	12-8.2 Normalizing Meter Flows 12-8.3 Systematic Uncertainty Calculation of Flow in Units of Normalized Flow 12-8.4 Specific Range of Flow 12-9 RANDOM UNCERTAINTY DUE TO TIME VARIANCE OF DATA
189	12-10 FIELD CHECKS 12-11 POSITIVE DISPLACEMENT METERS
190	Figure 12-11-1 Positive Displacement Volumeters
191	12-11.1 Positive Displacement Meter Performance 12-11.2 Calibration Requirements 12-11.3 Interpolation of Calibration Data
192	12-12 REFERENCES Figure 12-11.3-1 Method of Interpolation of Positive Displacement Meter Performance From Calibration Data to Other Fluid Viscosity and Operating Conditions
194	Section 13 Coriolis Mass Flowmeters 13-1 DEFINITIONS AND NOMENCLATURE 13-1.1 Definitions 13-1.2 Nomenclature 13-2 INTRODUCTION 13-2.1 Sensor Physical Properties
195	Table 13-1.2-1 Symbols Specifically Applied in Section 13 (in Addition to Symbols in Table 2-3-1)
196	13-3 METER CONSTRUCTION 13-3.1 Primary Device Figure 13-3.1-1 Typical Mechanical Arrangement
197	13-3.2 Secondary Device Figure 13-3.1-2 Oscillating Flow Tubes
198	13-4 CALIBRATION AND UNCERTAINTY 13-4.1 Calibration 13-4.2 Lab Calibration and Testing Considerations Figure 13-3.2-1 Electronic Transmitter
200	Table 13-4.2.1.3.2-1 Measurement Recommendations for Different Gas Test Pressures Table 13-4.2.2.4-1 Best Practices for Liquid and Gas Testing Data Collection Time
202	13-4.3 Fluid Properties Affecting Meter Performance Figure 13-4.2.3-1 Typical Calibration Curve With Uncertainty Bands (2σ Limits Shown)
203	Figure 13-4.3.2.1-1 Temperature Effect on Zero (2σ Limits Shown)
204	Figure 13-4.3.2.2-1 Pressure Effect on Span (2σ Limits Shown)
205	13-5 APPLICATION CONSIDERATIONS 13-5.1 Materials of Construction 13-5.2 Installation
206	Figure 13-5.1.2-1 Pressure Drop Versus Mass Flow
207	13-6 FIELD UNCERTAINTY EXAMPLES 13-6.1 Example 1 13-6.2 Example 2
208	Table 13-6.1-1 Example 1 — Analysis of Unheated Natural Gas Applications at Maximum Flow Rate
209	Table 13-6.1-2 Example 1 — Analysis of Unheated Natural Gas Application at Minimum Flow Rate
210	Table 13-6.2-1 Example 2 — Analysis of Heated Natural Gas Applications at Maximum Flow Rate
211	13-6.3 Example 3 Table 13-6.2-2 Example 2 — Analysis of Heated Natural Gas Applications at Minimum Flow Rate
212	13-6.4 Example 4 Table 13-6.3-1 Example 3 — Analysis of Liquid Condensate Application With Flowmeter Zeroed
213	Table 13-6.4-1 Example 4 — Analysis of Liquid Condensate Application With Flowmeter Not Zeroed
214	Table I-1-1 Symbols Used in Mandatory Appendix I (in Addition to Symbols in Table 2-3-1) MANDATORY APPENDIX I LABORATORY CALIBRATION EVALUATION AND EXTRAPOLATION I-1 NOMENCLATURE I-2 GENERAL REQUIREMENTS
215	I-3 CALIBRATION CONDITIONS I-4 DATA EVALUATION
218	Table I-6-1 Calibration Data, Test Data, and Predicted Value for an ASME Throat Tap Nozzle I-5 EXTRAPOLATION TO HIGHER REYNOLDS NUMBERS OR FLOW I-6 EXAMPLE CALCULATION
219	Figure I-6.3-1 Regression of Calibration Data With 95% Confidence Limits
221	NONMANDATORY APPENDICES NONMANDATORY APPENDIX A PULSATING FLOW MEASUREMENT A-1 NOMENCLATURE A-2 INTRODUCTION A-3 ORIFICES, NOZZLES, AND VENTURIS
222	Figure A-3.1-1 Measured Errors Versus Oscillating Differential Pressure Amplitude Relative to the Steady State Mean
223	Table A-3.1-1 Error Threshold Versus Relative Amplitude of ΔP
224	Figure A-3.2-1 Fluid-Metering System Block Diagram
227	Figure A-3.6-1 Experimental and Theoretical Pulsation Error A-4 TURBINE METERS IN PULSATING FLOW
228	Figure A-4.1-1 Semi-Log Plot of Theoretical Meter Pulsation Error Versus Rotor Response Parameter for Sine Wave Flow Fluctuation, D2 = 0.1, and Pulsation Index, I = 0.1 and 0.2
231	A-5 REFERENCES
234	Figure B-1-1 Graph of Critical Flow Functions for Air NONMANDATORY APPENDIX B CRITICAL FLOW FUNCTIONS FOR AIR BY R. C. JOHNSON B-1 GENERAL B-2 REFERENCES
235	Figure C-1-1 Graph of Deviation of Critical Flow Functions for Air (Shown in Figure B-1-1) NONMANDATORY APPENDIX C DEVIATION OF JOHNSON C* VALUES C-1 GENERAL C-2 REFERENCES
236	NONMANDATORY APPENDIX D REAL GAS CORRECTION FACTORS D-1-1 GENERAL D-2 REFERENCES
237	Figure D-1-1 Graph of Correction Factors for Air to Real Gas From Ideal Gas, up to 30 atm
238	Figure D-1-2 Graph of Correction Factors for Air to Real Gas From Ideal Gas, up to 100 atm
239	Figure D-1-3 Graph of Correction Factors for Air to Real Gas From Ideal Gas, up to 300 atm
240	NONMANDATORY APPENDIX E CONVERSION FACTORS E-1 GENERAL
241	Table E-1-1 Conversions to SI (Metric) Units
243	Table E-1-2 Conversion Factors for Pressure (Force/Area)
244	Table E-1-3 Conversion Factors for Specific Volume (Volume/Mass)
245	Table E-1-4 Conversion Factors for Specific Enthalpy and Specific Energy (Energy/Mass)
247	Table E-1-5 Conversion Factors for Specific Entropy, Specific Heat, and Gas Constant [Energy/(Mass × Temperature)]
248	Table E-1-6 Conversion Factors for Viscosity (Force × Time/Area ~ Mass/Length × Time)
249	Table E-1-7 Conversion Factors for Kinematic Viscosity (Area/Time)
250	NONMANDATORY APPENDIX F THERMAL EXPANSION TABLES F-1 GENERAL
256	Table F-1-2 Thermal Expansion Data (U.S. Customary)
259	NONMANDATORY APPENDIX G HISTORICAL DEFINITIONS OF UNITS OF MEASUREMENT G-1 DEFINITIONS
260	G-2 REFERENCES