Gupta - Comprehensive Volume Capacity Measurements

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New Delhi Bangalore Chennai Cochin Guwahati HyderabadJalandhar Kolkata Lucknow Mumbai RanchiVisit us at www.newagepublishers.comPUBLISHING FOR ONE WORLD

NEW AGE INTERNATIONAL (P) LIMITED, PUBLISHERS

Copyright 2006 New Age International (P) Ltd., PublishersPublished by New Age International (P) Ltd., Publishers

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ISBN : 978-81-224-2437-9

PUBLISHING FOR ONE WORLD

NEW AGE INTERNATIONAL (P) LIMITED, PUBLISHERS4835/24, Ansari Road, Daryaganj, New Delhi - 110002Visit us at www.newagepublishers.com

Dedicated to my wife Mrs Prem Gupta

and

to my children

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PREFACENo teaching institute or University teaches measurement of basic parameters like volume.

At school only preliminaries are dealt with about volume measurement. A new entrant, to acalibration laboratory dealing in calibration and testing of volumetric glassware does not findhimself/ herself a comfortable starter. The reason is there is no book dedicated to such asubject. If someone refers to him the Dictionary of Applied Physics volume IV, which datesback to very early part of 20th century or to Notes on Applied Sciences of 1950 published byNational Physical Laboratory, U.K. it certainly gives him an impression that he has come to aprimitive field and has been trapped. Even a better experience scientist gives him direction tocarry out his work in the prescribed manner without furnishing him the reasons to do so. Basicreason is no efforts have been made to consolidate the research work carried out during thelast century and to make it assessable to a normal user.

No body talks about the solid artefacts which serve as primary standard of volume. Wateris normally used as a medium for calibrating volumetric measures. But the corrections applicableare still based on old data of water density and temperature scale. Recent work on densitymeasurement of water, taking in to account of isotopic composition of water and solubility forair, is not often used.

Efforts therefore have been made to use latest water and mercury density data to preparecorrection tables. The coefficients of expansion, density of standard weights, air density andreference temperature are the variable, which comes in the equation in preparing the correctionstables. Therefore, a large variety of coefficients of expansions have been taken in preparingeasy to use tables. The coefficient chosen are such that practically all material used in fabricatingvolumetric measures are covered. A separate table of corrections for unit difference in thecoefficients of expansion has been constructed which will make it possible to find the correctionsfor any coefficients of expansion. There are two internationally accepted values for the densityof mass standards. Similarly there are two reference temperatures to which the capacity ofmeasures are referred to, so separate set of tables have been made for each possible combinationsof density values of mass standard and reference temperatures. The corrections have beencalculated to 4th decimal place instead of 3rd decimal place.

Solid based primary standards of volume have been discussed. Inter-comparison atinternational level and collating the results of measurements by various laboratories has beendiscussed. The principle of measurement has remained the same it is the technology whichhas changed. The establishment of solid base volume standards and their international inter-comparison has considerably improved reproducibility in volume measurements.

The chapter on the surface tension effect on the meniscus volume gives an insight storyof physics and measurements. It is for the first time that analytical formula for meniscusvolumes in tubes of different diameters has been worked out. It will go a long way in understandingthe purpose of calibration and limitations associated with it. To measure volume of any liquidthrough a volumetric measure is meaningful if proper corrections are applied due to change insurface tension and density of the liquid. Meniscus volume and corrections applicable due to

change in capillarity constant for tubes of diameter from 0.2 mm to 120 mm have been given inthe form of tables at the end of the chapter 7. The subject matter is treated in a way, which caninterest an undergraduate physics student.

The hierarchy in volume measurement and method of its realisation has been taken up.Design, fabrication and material requirements of standard capacity measures have beenexplained. Range of capacity of these measures is from a few cm3 to several thousand dm3.Secondary standard capacity measures in glass from 50 litres to 5 cm3 have been discussed inrespect of their design, calibration and use.

The methods of measurement and calibration of capacity of vertical, horizontal andspherical storage tanks, together with road tankers, vehicle tanks, ships and barges have beendescribed for the first time in a consolidated way.

It is my pleasant duty to thank quite a number of people, who have encouraged me ateach step to complete the book. I am grateful to Professor A.R. Verma, Dr. A.P. Mitra FRS, andProf S.K. Joshi, all former Directors of National Physical Laboratory, New Delhi, who havebeen a constant source of encouragement to me during the preparation of the manuscript. Iwish to thank Mrs Reeta Gupta and other colleagues at the National Physical Laboratory, NewDelhi, who have been helpful in procuring material for the book. The work carried out at theNational Physical Laboratory, New Delhi and mentioned in the book was teamwork, so everycolleague of mine at that time, alive or dead, deserves my appreciation and thanks.

S. V. Gupta

viii Preface

CONTENTS

Chapter 1 Units and Primary Standard of Volume1.1 Introduction ................................................................................................... 11.2 Volume and Capacity ..................................................................................... 11.3 Reference Temperature ................................................................................. 1

1.3.1 Reference or Standard Temperature for Capacity Measurement ..... 21.3.2 Reference or Standard Temperature for Volume Measurement ....... 2

1.4 Unit of Volume or Capacity ........................................................................... 21.5 Primary Standard of Volume ........................................................................ 3

1.5.1 Solid Artefact as Primary Standard of Volume................................... 31.5.2 Maintenance ......................................................................................... 31.5.3 Material ................................................................................................ 31.5.4 Primary Volume Standards Maintained by National Laboratories ... 4

1.6 Measurement of Volume of Solid Artefacts .................................................. 41.6.1 Dimensional Method ............................................................................ 51.6.2 Volume of Solid Body by Hydrostatic Method .................................... 5

1.7 Water as a Standard ...................................................................................... 61.7.1 SMOW................................................................................................... 71.7.2 International Temperature Scale of 1990 (ITS90) .............................. 8

1.8 International Inter-Comparison of Volume Standards ................................ 91.8.1 Principle ............................................................................................... 91.8.2 Participation ......................................................................................... 91.8.3 Aims and Objectives of the Project ..................................................... 91.8.4 Preparation or Procurement of the Artefact .................................... 101.8.5 Method to be Used in Determination of the Parameter(s) of the

Artefact ................................................................................................ 10

Preface .......................................................................................................................... vii

x Contents

1.8.6 Time Schedule in Consultation with the ParticipatingLaboratories ...................................................................................... 10

1.8.7 Method of Reporting the Results with Detailed Analysis ofUncertainty ....................................................................................... 10

1.8.8 Monitoring the Progress of the Measurements at DifferentLaboratories and the Influence Parameters LikeTemperature ...................................................................................... 10

1.8.9 Monitoring the Required Parameter(s) of the Artefact .................... 111.8.10 Collating and Correlating the Results of Determination by

Participating Laboratories .............................................................. 111.8.11 Evaluation of Results from Participating Laboratories .................. 11

1.9 Example of International Inter-Comparison of Volume Standards ........... 141.9.1 Participation and Pilot Laboratory ................................................... 141.9.2 Objective ............................................................................................. 151.9.3 Artefacts ............................................................................................. 151.9.4 Method of Measurement .................................................................... 171.9.5 Time Schedule .................................................................................... 181.9.6 Equipment and Standard used by Participating Laboratories ......... 181.9.7 Results of Measurement by Participating Laboratories .................. 19

1.10 Methods of Calculating Most Likely Value with Example ......................... 201.10.1 Median and Arithmetic Mean of Volume of CS 85 .......................... 201.10.2 Weighted Mean of Volume of CS 85 ................................................ 20

1.11 Realisation of Volume and Capacity ............................................................ 211.11.1 International Inter-Comparison of Capacity Measures .................. 21

Chapter 2 Standards of Volume/Capacity2.1 Realisation and Hierarchy of Standards ..................................................... 252.2 Classification of Volumetric Measures ........................................................ 27

2.2.1 Content Type ...................................................................................... 272.2.2 Delivery Type ..................................................................................... 28

2.3 Principle of Maintenance of Hierarchy for Capacity Measures ................. 282.4 First Level Capacity Measures ................................................................... 29

2.4.1 25 dm3 Capacity Measure at NPL India ............................................ 292.4.2 50 dm3 Capacity Measure ................................................................... 322.4.3 Pipe Provers (Standard of Dynamic Volume Measurement) ........... 332.4.4 A Typical Pipe Prover ........................................................................ 332.4.5 Principle of Working .......................................................................... 342.4.6 Movement of Sphere During Proving Cycle ..................................... 35

2.5 Secondary Standards Capacity Measures/Level II Standards ................... 372.5.1 Single Capacity Content Type Measures .......................................... 372.5.2 Volume of the Fillet ........................................................................... 392.5.3 Multiple Capacity Content Measures ................................................ 39

Contents xi

2.6 Delivery Type Measures .............................................................................. 402.6.1 Measures having Cylindrical Body with Semi-spherical Ends ......... 412.6.2 Measures having Cylindrical Body with no Discontinuity ............... 422.6.3 Volume of the Portion Bounded by Two Quadrants ......................... 432.6.4 Measures having Cylindrical Body with Conical Ends ..................... 45

2.7 Secondary Standards Automatic Pipettes in Glass .................................... 472.7.1 Automatic Pipettes ............................................................................. 472.7.2 Three-way Stopcock ........................................................................... 482.7.3 Old Pipettes ........................................................................................ 482.7.4 Maximum Permissible Errors for Secondary Standard

Capacity Measure .............................................................................. 502.8 Working Standard and Commercial Capacity Measures ........................... 51

2.8.1 Working Standard Capacity Measures used in India ....................... 512.8.2 Commercial Measures ....................................................................... 51

2.9 Calibration of Standard Measures ............................................................... 522.9.1 Secondary Standard Capacity Measures ........................................... 522.9.2 Working Standard Measures ............................................................. 52

Chapter 3 Gravimetric Method3.1 Methods of Determining Capacity ............................................................... 543.2 Principle of Gravimetric Method ................................................................ 543.3 Determination of Capacity of Measures Maintained at Level I or II ........ 54

3.3.1 Determination of the Capacity of a Delivery Measure..................... 553.3.2 Determination of the Capacity of a Content Measure ..................... 56

3.4 Corrections to be Applied ............................................................................ 583.4.1 Temperature Correction .................................................................... 583.4.2 Correction Due to Variation of Air Density ...................................... 603.4.3 Correction Due to a Unit Difference in Coefficients of Expansion .. 60

3.5 Use of Mercury in Gravimetric Method ..................................................... 613.5.1 Temperature Correction .................................................................... 61

3.6 Description of Tables ................................................................................... 623.6.1 Correction Tables using Water as Medium ...................................... 633.6.2 Correction Tables using Mercury as Medium .................................. 63

3.7 Recording and calculations of capacity ........................................................ 643.7.1 Example .............................................................................................. 64

Chapter 4 Volumetric Method4.1 Applicability of Volumetric Method ........................................................... 1144.2 Multiple and one to one Transfer Methods .............................................. 1144.3 Corrections Applicable in Volumetric Method.......................................... 115

4.3.1 Temperature Correction in Volumetric Method ............................ 115

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4.4 Use of a Volumetric Measure at a Temperature other than itsStandard Temperature .............................................................................. 116

4.5 Volumetric Method .................................................................................... 1174.5.1 From a Delivery Measure to a Content Measure ........................... 1174.5.2 Calibration of Content to Content Measure (working standard

capacity measures) .......................................................................... 1184.6 Error due to Evaporation and Spillage ..................................................... 119

4.6.1 Collected Formulae .......................................................................... 1204.6.2 Miscellaneous Statements ............................................................... 1204.6.3 Spillage ............................................................................................. 120

Chapter 5 Volumetric Glassware5.1 Introduction ............................................................................................... 132

5.1.1 Facilities at NPL for Calibration of Volumetric Glassware ........... 1325.1.2 Special Volumetric Equal-arm Balances ......................................... 133

5.2 Volumetric Glassware ................................................................................ 1335.3 Cleaning of Volumetric Glassware ............................................................ 133

5.3.1 Precautions in use of Cleaning Agents ........................................... 1345.3.2 Cleaning of Small Volumetric Glassware ....................................... 1345.3.3 Delivery Measure kept filled with Distilled Water ........................ 1355.3.4 Drying of a Content Measure .......................................................... 1355.3.5 Test of Cleanliness ........................................................................... 135

5.4 Reading and Setting the Level of Meniscus ............................................. 1355.4.1 Convention for Reading ................................................................... 1355.4.2 Method of Reading............................................................................ 1365.4.3 Error due to Meniscus Setting ........................................................ 137

5.5 Factors Influencing the Capacity of a Measure ........................................ 1375.5.1 Temperature .................................................................................... 1375.5.2 Delivery Time and Drainage Time .................................................. 1375.5.3 Delivery Time and Drainage Volume for a Burette ....................... 1385.5.4 Volume Delivered and Delivery Time of Pipettes .......................... 1415.5.5 Relation between Vw and Parameters of a Delivery Measure ....... 143

5.6 Factors Influencing the Determination of Capacity ................................. 1445.6.1 Meniscus Setting .............................................................................. 1445.6.2 Surface Tension ................................................................................ 1445.6.3 Effect of Change in Surface Tension ............................................... 1455.6.4 The Error in Meniscus Volume when Surface Tension is

Reduced to Half ............................................................................... 1455.6.5 Use of Liquids other than Water ..................................................... 1455.6.6 Correction in Volume in mm3 (0.001 cm3) against Capillary

Constants and Tube Diameters ........................................................ 1465.6.7 Non-uniformity of Temperature ...................................................... 146

Contents xiii

5.7 Influence Parameters and their Contribution to FractionalUncertainty ................................................................................................ 146

5.8 Filling a Measure ....................................................................................... 1475.8.1 Filling the Content Measure ........................................................... 1475.8.2 Filling of a Delivery Measure .......................................................... 147

5.9 Determination of the Capacity with Mercury as Medium ....................... 1485.10 Criterion for Fixing Maximum Permissible Errors ................................. 148

Chapter 6 Calibration of Glass ware6.1 Burette ....................................................................................................... 151

6.1.1 Jets for Stopcock of Burettes ........................................................... 1516.1.2 Burette-key ....................................................................................... 1536.1.3 Graduations on a Burette ................................................................. 1536.1.4 Setting up a Burette ......................................................................... 1536.1.5 Leakage Test .................................................................................... 1546.1.6 Delivery Time................................................................................... 1556.1.7 Calibration of Burette ...................................................................... 1556.1.8 Delivery Time of Burettes in SecondsA Comparison ................... 1566.1.9 MPE (Tolerance) / Basic Dimensions of Burettes ........................... 156

6.2 Graduated Measuring Cylinders ............................................................... 1576.2.1 Types of Measuring Cylinders ......................................................... 1576.2.2 Inscriptions ....................................................................................... 160

6.3 Flasks ....................................................................................................... 1606.3.1 One-mark Volumetric Flasks .......................................................... 1606.3.2 Graduated Neck Flask ..................................................................... 1646.3.3 Micro Volumetric Flasks ................................................................. 165

6.4 Pipettes ....................................................................................................... 1676.4.1 One Mark Bulb Pipette .................................................................... 1676.4.2 Graduated Pipettes........................................................................... 171

6.5 Micro-pipettes ............................................................................................ 1736.5.1 Capacity and Colour Code ................................................................ 1736.5.2 Nomenclature of Micropipettes ....................................................... 1736.5.3 Measuring Micropipettes ................................................................. 1746.5.4 Folins Type Micropipettes .............................................................. 1756.5.5 Micro Washout Pipettes .................................................................. 1766.5.6 Micro Pipettes Weighing Type ........................................................ 1766.5.7 Micro-litre Pipettes of Content Type .............................................. 1786.5.8 Micro-litre Pipettes .......................................................................... 178

6.6 Special Purpose Glass Pipettes ................................................................. 1806.6.1 Disposable Serological Pipettes ....................................................... 1806.6.2 Piston Operated Volumetric Instrument ........................................ 1816.6.3 Special Purpose Micro-pipette (44.7 ml capacity) ........................... 184

xiv Contents

6.7 Automatic Pipette ...................................................................................... 1856.7.1 Automatic Pipettes in Micro-litre Range ........................................ 1856.7.2 Automatic Pipettes (5 cm3 to 5 dm3) ................................................ 187

6.8 Centrifuge Tubes ....................................................................................... 1886.8.1 Non-graduated Conical Bottom Centrifuge Tube ........................... 1886.8.2 Non-graduated Conical Bottom Centrifuge Tube with Stopper ..... 1896.8.3 Graduated Conical Centrifuge Tube with Stopper ......................... 1896.8.4 Non-graduated Cylindrical Bottom Centrifuge Tube

without Stopper ................................................................................ 1906.9 Use of a Volumetric Measure at a Temperature other than its

Standard Temperature .............................................................................. 1916.10 Effective Volume of Reagents used in Volumetric Analysis .................... 1916.11 Examples of Calibration ............................................................................. 191

6.11.1 Calibration of a Burette ................................................................. 1916.11.2 Calibration of a Micropipette ......................................................... 195

Chapter 7 Effect of Surface Tension on Meniscus Volume7.1 Introduction ............................................................................................... 1967.2 Excess of Pressure on Concave Side of Air-liquid Interface .................... 1977.3 Differential Equation of the Interface Surface ......................................... 1997.4 Basis of Bashforth and Adams Tables ....................................................... 2007.5 Equilibrium Equation of a Liquid Column Raised due to

Capillarity ................................................................................................... 2017.6 Rise of Liquid in Narrow Circular Tube ................................................... 203

7.6.1 Case I u = 0 ....................................................................................... 2057.6.2 Case II u 0 but du/dx is small ..................................................... 205

7.7 Rise of Liquid in Wider Tube .................................................................... 2087.7.1 Rayleigh Formula ............................................................................. 2087.7.2 Laplace Formula ............................................................................... 210

7.8 Authors Approach ..................................................................................... 2127.8.1 Air-liquid Interface is Never Spherical ........................................... 2127.8.2 Air-Liquid Interface is Ellipsoidal ................................................... 2137.8.3 Equilibrium of the Volume of the Liquid Column .......................... 2147.8.4 Lord Kelvins Approach.................................................................... 2167.8.5 Discussion of Results ....................................................................... 216

7.9 Volume of Water Meniscus in Right Circular Tubes ............................... 2207.10 Dependence of Meniscus Volume on Capillary Constant ......................... 2207.11 For Liquid Systems having Finite Contact Angles .................................. 221

7.11.1 Authors Approach for Liquids having any Contact Angle .......... 221

Chapter 8 Storage Tanks8.1 Introduction ............................................................................................... 231

Contents xv

8.2 Definitions .................................................................................................. 2328.3 Storage Tanks ............................................................................................ 234

8.3.1 Shape ................................................................................................ 2348.3.2 Position of the Tank with Respect to Ground ................................ 2348.3.3 Number of Compartments ............................................................... 2358.3.4 Conditions of Maintenance (Influence Quantities) ......................... 2358.3.5 Accuracy Requirement ..................................................................... 235

8.4 Capacity of the Tanks ................................................................................ 2368.5 Maximum Permissible Errors of Tanks of Different Shapes................... 2368.6 Vertical Storage Tank with Fixed Roof ..................................................... 2368.7 Horizontal Tank ......................................................................................... 2388.8 General Features of Storage Tank ........................................................... 2388.9 Methods of Calibration of Storage Tanks ................................................. 239

8.9.1 Dimensional Method ........................................................................ 2398.9.2 Volumetric Method........................................................................... 246

8.10 Descriptive Data ........................................................................................ 2468.11 Strapping Method....................................................................................... 247

8.11.1 Precautions ..................................................................................... 2478.11.2 Equipment used in Strapping ........................................................ 2488.11.3 Strapping Procedure ...................................................................... 2528.11.4 Maximum Permissible Errors in Circumference Measurement . 253

8.12 Corrections Applicable to Measured Values ............................................. 2538.12.1 Step Over Correction ..................................................................... 2538.12.2 Temperature Correction ................................................................ 2548.12.3 Correction due to Sag .................................................................... 254

8.13 Volumetric Method (Liquid Calibration) ................................................... 2558.13.1 Portable Tank ................................................................................. 2558.13.2 Positive Displacement Meter ......................................................... 2558.13.3 Fixed Service Tank ........................................................................ 2558.13.4 Weighing Liquid ............................................................................. 256

8.14 Liquid Calibration Process ........................................................................ 2568.14.1 Priming ........................................................................................... 2568.14.2 Material Required........................................................................... 2568.14.3 Considerations to be Kept in Mind ................................................ 256

8.15 Temperature Correction in Liquid Transfer Method............................... 258

Chapter 9 Calibration of Vertical Storage Tank9.1 Measurement of Circumference................................................................ 262

9.1.1 Strapping Levels (Locations) for Vertical Storage Tanks .............. 2629.2 Measurement of Thickness of the Shell Plate ......................................... 2639.3 Vertical Measurements ............................................................................. 2649.4 Deadwood ................................................................................................... 265

xvi Contents

9.5 Bottom of Tank .......................................................................................... 2659.5.1 Flat Bottom ...................................................................................... 2659.5.2 Bottom with Conical, Hemispherical, Semi-ellipsoidal or

having Spherical Segment .............................................................. 2669.6 Measurement of Tilt of the Tank .............................................................. 2669.7 Floating Roof Tanks ................................................................................... 267

9.7.1 Liquid Calibration for Displacement by the Floating-roof ............. 2679.7.2 Variable Volume Roofs ..................................................................... 268

9.8 Calibration by Internal Measurements ..................................................... 2689.8.1 Outline of the Method ...................................................................... 2689.8.2 Equipment ........................................................................................ 269

9.9 Computation of Capacity of a Tank and Preparing Gauge Tablefor Vertical Storage Tank .......................................................................... 2709.9.1 Principle of Preparing Gauge Table (Calibration Table) ................ 270

9.10 Calculations ................................................................................................ 2739.11 Deadwood ................................................................................................... 2749.12 Tank Bottom .............................................................................................. 2749.13 Floating Roof Tanks................................................................................... 2749.14 Computation of Gauge Tables in Case of Tanks Inclined

with the Vertical ........................................................................................ 2759.14.1 Correction for Tilt ........................................................................... 2759.14.2 Example of Strapping Method ....................................................... 276

9.15 Example of Internal Measurement Method.............................................. 2799.15.1 Data Obtained by Internal Measurement ..................................... 2799.15.2 Gauge Table Volume Versus Height ............................................. 280

9.16 Deformation of Tanks ................................................................................ 281

Chapter 10 Horizontal Storage Tanks10.1 Introduction ............................................................................................... 28310.2 Equipment Required .................................................................................. 28310.3 Strapping Locations for Horizontal Tanks ............................................... 283

10.3.1 Butt-welded Tank ........................................................................... 28410.3.2 Lap-welded Tank ............................................................................ 28410.3.3 Riveted Over Lap Tank .................................................................. 28510.3.4 Locations ........................................................................................ 28510.3.5 Precautions ..................................................................................... 285

10.4 Partial Volume in Main Cylindrical Tanks ............................................... 28510.4.1 Area of Segment ............................................................................. 286

10.5 Partial Volumes in the two Heads ............................................................ 28710.5.1 Partial Volumes for Knuckle Heads .............................................. 28710.5.2 Ellipsoidal or Spherical Heads ....................................................... 288

Contents xvii

10.5.3 Bumped (Dished Heads) ................................................................. 28910.5.4 Volume in the Tank ....................................................................... 28910.5.5 Values of K for H/D > 0.5 .............................................................. 289

10.6 Applicable Corrections ............................................................................... 29010.6.1 Tape Rise Corrections .................................................................... 29010.6.2 Expansion/Contraction of Shell Due to Liquid Pressure ............. 29010.6.3 Flat Heads Due to Liquid Pressure .............................................. 29010.6.4 Effects of Internal Temperature on Tank Volume ....................... 29010.6.5 Effects on Volume of Off Level Tanks ........................................... 290

Chapter 11 Calibration of Spheres, Spheroids and Casks11.1 Spherical Tank ........................................................................................... 30611.2 Calibration.................................................................................................. 307

11.2.1 Strapping Method ........................................................................... 30711.2.2 Liquid Calibration .......................................................................... 308

11.3 Computations ............................................................................................. 30811.3.1 Direct from Formula and Tables ................................................... 30811.3.2 Alternative Method (Reduction Formula) ..................................... 30811.3.3 Example of Calculation for Sphere ................................................ 310

11.4 Spheroid ...................................................................................................... 31111.5 Calibration.................................................................................................. 312

11.5.1 Strapping ........................................................................................ 31211.5.2 Step-wise Calculations ................................................................... 31211.5.3 Example for Partial Volumes of a Spheroid .................................. 313

11.6 Temperature Correction ............................................................................ 31511.6.1 Coefficients of Volume Expansion for Steel and Aluminium ....... 315

11.7 Storage Tanks for Special Purposes ......................................................... 31511.7.1 Casks and Barrels........................................................................... 315

11.8 Geometric Shapes and Volumes of Casks ................................................. 31711.8.1 Cask Composed of two Frusta of Cone.......................................... 31711.8.2 Cask-volume of Revolution of an Ellipse ....................................... 31711.8.3 Cask Composed of two Frusta of Revolution of a Branch of

a Parabola....................................................................................... 31811.9 Calibration/ Verification of Casks .............................................................. 319

11.9.1 Reporting/Marking the Values Rounded Upto ............................... 31911.9.2 Uncertainty in Measurement ......................................................... 31911.9.3 Calibration Procedures ................................................................... 320

11.10 Vats ....................................................................................................... 32111.10.1 Shape ............................................................................................. 32111.10.2 Material ......................................................................................... 32111.10.3 Calibration .................................................................................... 321

11.11 Re-calibration of any Storage Tank when due .......................................... 322

xviii Contents

Chapter 12 Large Capacity Measures12.1 Introduction ................................................................................................ 32912.2 Essential Parts of a Measure ..................................................................... 329

12.2.1 Graduated Scale of the Measure .................................................... 32912.3 Design Considerations for Main Body ....................................................... 332

12.3.1 Measure Inscribed within a Sphere ............................................... 33212.3.2 General Case................................................................................... 334

12.4 Delivery Pipe .............................................................................................. 33612.4.1 Slant Cone at the Bottom ............................................................... 33612.4.2 Measures with Cylindrical Delivery Pipe ...................................... 338

12.5 Small Arithmetical Calculation Errors ...................................................... 33812.5.1 Adjusting Device ............................................................................. 338

12.6 Designing of Capacity Measures ................................................................ 33912.6.1 Symmetrical Content Measures ..................................................... 33912.6.2 Asymmetrical Content Measure (with a Conical Outlet) .............. 34012.6.3 Measures with Cylindrical Delivery Pipe ...................................... 34012.6.4 Dimensions of Symmetrical Measures .......................................... 34012.6.5 Delivery Measures with Slant Cone as Delivery Pipe................... 342

12.7 Material ...................................................................................................... 34412.7.1 Thickness of Sheet used ................................................................. 344

12.8 Construction of Measures .......................................................................... 34512.8.1 Steps for Construction .................................................................... 34512.8.2 Requirements of Construction ....................................................... 34512.8.3 Stationary Measure ........................................................................ 34512.8.4 Portable Measure ........................................................................... 346

12.9 Dimensions of Measures of Specific Designs............................................. 34612.9.1 Design and Dimensions of Measures with Asymmetric

Delivery Cone ................................................................................ 34712.9.2 Measures Designed at NPL, India ................................................. 349

Chapter 13 Vehicle Tanks and Rail Tankers13.1 Introduction ............................................................................................... 351

13.1.1 Definitions ...................................................................................... 35113.1.2 Basic Construction ......................................................................... 35313.1.3 Pumping and Metering .................................................................. 35313.1.4 Other Devices ................................................................................. 353

13.2 Classification of Vehicle Tanks ................................................................. 35313.2.1 Pressure Tanks .............................................................................. 35413.2.2 Pressure Testing ............................................................................ 35413.2.3 Temperature Controlled Tanks ..................................................... 355

Contents xix

13.3 Requirements ............................................................................................. 35513.3.1 National Requirements .................................................................. 35513.3.2 Material Requirements .................................................................. 35513.3.3 Change in Reference Height .......................................................... 35613.3.4 Change in Capacity ........................................................................ 35613.3.5 Air Trapping ................................................................................... 35613.3.6 For Better Emptying ...................................................................... 35613.3.7 Deadwood Positioning .................................................................... 35613.3.8 Dome and Level Gauging Device .................................................. 35613.3.9 Shape of the Shell .......................................................................... 35713.3.10 Maximum Filling Level for Vehicle Tanks ................................. 357

13.4 Discharge Device ....................................................................................... 35713.4.1 Single Drain Pipe and Stop Valve .................................................. 358

13.5 Maximum Permissible Errors ................................................................... 35813.6 Level Measuring Devices........................................................................... 358

13.6.1 Dipstick ........................................................................................... 35813.6.2 Level Measuring Device ................................................................ 359

13.7 Volume/Capacity Determination ............................................................... 36013.7.1 Water Gauge Plant ......................................................................... 36113.7.2 Level Track .................................................................................... 362

13.8 Calibrating a Single Compartment Vehicle Tank .................................... 36213.8.1 General Precautions ...................................................................... 36213.8.2 Filling of the Vehicle Tank ............................................................ 36313.8.3 Calibration of a Vehicle Tank ........................................................ 36313.8.4 Verification of the Vehicle Tank .................................................... 36413.8.5 Temperature Corrections .............................................................. 364

13.9 Intermediate Measure ............................................................................... 36413.9.1 Construction and Shape ................................................................. 364

13.10 Increase in Capacity of Vehicle Tanks due to Pressure ........................... 36613.10.1 Example ......................................................................................... 367

13.11 Water-weighing Method for Verification of Tanks .................................. 36813.12 Strapping Method for Calibration of the Vehicle ...................................... 37013.13 Suspended Water ....................................................................................... 370

Chapter 14 Barges and Ship Tanks14.1 Introduction ............................................................................................... 372

14.1.1 Some Definitions ............................................................................ 37214.2 Brief Description ........................................................................................ 373

14.2.1 Sketch of a Tanker ......................................................................... 37414.3 Measurement and Calibration .................................................................. 375

xx Contents

14.4 Strapping Method ....................................................................................... 37514.4.1 Equipment ...................................................................................... 37514.4.2 Location of Measurements ............................................................ 37514.4.3 Linear Measurement Procedure ................................................... 37614.4.4 Temperature Correction and Deadwood Distribution .................. 38014.4.5 Format of Calibration Certificate .................................................. 38114.4.6 Numerical Example ........................................................................ 381

14.5 Liquid Calibration Method ........................................................................ 38714.5.1 Shore Tanks and Meters................................................................ 38714.5.2 Filling Locations of the Tank ........................................................ 38714.5.3 Filling Procedure ............................................................................ 38814.5.4 Net and Total Capacities of the Barge .......................................... 388

14.6 Calculating from the Detailed Drawings of the Tanks and the Barge .. 389

Index ....................................................................................................... 391

UNITS AND PRIMARY STANDARD OF VOLUME

1.1 INTRODUCTION

The accurate knowledge of volume of solids, liquids and gases is required in all walks of lifeincluding that of trade and commerce. In addition, the volume of a solid or liquid must beknown to calculate its density. The frequency of the need of volume measurement is as muchas that of measurement of mass. In this book, however, we will be restricting to measurementof volume of solids and liquids. Precise volumetric measurements are required in breweries,petroleum and dairy industry and in water management. More precise measurements arerequired in scientific research and chemical analysis. Liquids have to be contained in physicalartefacts, which are called measures. So finding the capacity of these measures is also a part ofvolume measurement.

1.2 VOLUME AND CAPACITY

There are two terms, which are often used in volume measurements. One is capacity and theother is volume. Both terms represent the same quantity. The capacity is the property of avessel or container and is characterised by how much liquid, it is able to hold or deliver. Thesevessels or containers are generally termed as volumetric measures. So capacity is the propertyof volumetric measures. While volume is the basic property of matter in relation to its occupationof space, so it applies to every material body.

1.3 REFERENCE TEMPERATURE

Both volume of a body and capacity of a volumetric measure depend upon temperature. Hencestatement about the capacity of a volumetric measure or volume of a body should necessarilycontain a statement of temperature. Saying only, the volume of a body is so many units ofvolume, does not carry much weight unless we specify temperature to which it is referring.Now if every body gives the results of a volume measurement at its temperature of measurementthan it will be difficult to compare the results given by two persons for the same body but at

1CHAPTER

2 Comprehensive Volume and Capacity Measurements

different temperatures. To obviate this difficulty, one solution is that all measurements ofvolume are carried out at one temperature, which is again not possible. As in this case, alllaboratories and work places, at which volume measurements are carried out, have to bemaintained at the same temperature. So better viable solution is that measurements are carriedout at different temperatures but all results are adjusted to a common agreed temperature.This agreed temperature is called as reference/standard temperature, which is kept same for acountry or region. However reference temperature may be kept different for differentcommodities and regions of globe. Depending upon general climate of a country or region, itmay be 27 C, 20 C or 15 C. For all European countries including U.K. it is 20 C for generalpurpose, and 15.5 C for petroleum products. However, India due to its tropical climate, hasadopted 27 C for general purpose and 15.5 C for petroleum industry. Other tropical countrieshave, similarly, adopted 27 C for general purpose and 15.5 C for petroleum industry.

1.3.1 Reference or Standard Temperature for Capacity MeasurementThe capacity of a volumetric measure is defined by the volume of liquid, which it contains ordelivers under specified conditions and at the standard temperature. The capacity of eachmeasure, in India, is referred to 27 C. However temperatures of 20 C and 15 C are alsopermitted for specific purposes.

1.3.2 Reference or Standard Temperature for Volume MeasurementThe results of volume measurements of all solids generally refer to 27 C, in India. Howevertemperatures of 20 C and 15 C are also permitted for specific purposes.

1.4 UNIT OF VOLUME OR CAPACITY

In earlier days the unit of volume and capacity used to be different. The unit of volume wastaken as the cube of the unit of length. The unit of capacity was defined as the space occupiedby one kilogram of water at the temperature of its maximum density.

The Kilogram de Archives of 1799, the unit of mass was defined equal to the mass of waterat its maximum density and occupying the space of one decimetre cube. But later on it wasrealised that there was some error in realising the decimetre cube. So in 1879 the unit of mass-the kilogram was de-linked with water and its volume. The kilogram was defined as the massof the International Prototype Kilogram. The mass of the International Prototype Kilogramwas itself made, as far as possible, equal to the mass of the Kilogram de Archives. The volumeof one kilogram of water at its maximum density was found to be 1.000 028 dm3. So in 1901,third General Conference for Weights and Measures (CGPM) decided a new unit of volume andnamed it as litre. The litre was defined as the volume occupied by one kilogram of water at itstemperature of maximum density and at standard atmospheric pressure. The unit was termedas the unit of capacity. For finding the capacity of a measure, the unit litre was used and forvolume, the unit decimetre cube continued to be used. The symbol l was assigned to the litre in1948 by the 9th CGPM. However the controversy of having two units for essentially the samequantity remained and finally in 1964 the CGPM in its 11th conference abrogated the definitionof the litre altogether but allowed the name litre to be used as another name of one decimetrecube. Keeping in view the fact that the letter l, the symbol of litre as adopted in 1948, may be

Units and Primary Standard of Volume 3

confused with numeral one, the 16th CGPM, in 1979, sanctioned the use of the letter L also assymbol of litre.

So presently, in International System of Units (SI), the unit of volume as well as that ofcapacity is cubic metre with symbol m3. The cubic metre is equal to the volume of a cubehaving an edge equal to one metre. But sub-multiples of cubic metre, like cubic decimetre(symbol dm3), cubic centimetre (symbol cm3) and cubic millimetre (symbol mm3) may also beused. Litre (1), millilitre (ml) and micro-litre (l) may be used as special names for dm3, cm3 andmm3 respectively. L may also be used as symbol of litre.

1.5 PRIMARY STANDARD OF VOLUME

Volume of a solid is determined either by dimensional measurements or by hydrostatic weighing.Dimensional method gives the volume of the solid in base unit of length i.e. metre. Hydrostaticweighing method requires a medium of known density and gives the volume of the body interms of mass and density of liquid displaced. The primary standard of volume, therefore, is asolid artefact of known geometry. Its volume is calculated from the measurements of itsdimensions.

1.5.1 Solid Artefact as Primary Standard of VolumeSolids of known geometry are maintained as artefact standards of volume. Two simplergeometrical shapes are those of cube and sphere. Both these shapes are used for making solidartefacts as standard of volume.

1.5.1.1 Shape Solid Artefacts of Spherical in ShapeThe spherical shape is obtained by rolling mill process. Spheres of diameters around 85 mmhave been made. Peak to peak difference between the diameters of the sphere, so far made,vary from 220 nm to 28 nm.

1.5.1.2 Shape Solid Artefacts in the Shape of a CubeThe cubical shape is achieved by using the method of optical grinding, lapping and finalpolishing. The plainness of its faces is examined by using interference method or an auto-collimator.

1.5.2 MaintenanceSpherical shape is attainable and maintainable far more easily than the cubical shape. In cubicalshape, the edges cannot be made perfect straight lines, or the corners as points. Further, thereis always a danger of chipping of edges and corners causing change in volume if the artefact isin the shape of a cube.

1.5.3 MaterialThe material requirements for the two shapes are different. The material for cubical shapemust be such that can be worked out using optical grinding, lapping techniques and is able toacquire high degree of polish. The material should not be brittle, otherwise edges will not bemaintained but should have low coefficient of expansion. Quartz fulfils all the requirements.Other materials are silicon, low expansion glass and zerodur. For spherical shape steel is good


except its rusting property. Silicon crystals are being used to determine the Avogadros numberso its physical constants like coefficient of expansion are well measured, hence Silicon is nowpreferred over any other materials. Avogadros number is the number of molecules, atoms orentities in one gram molecule of substance.

1.5.4 Primary Volume Standards Maintained by National LaboratoriesThe shape, material, value of volume along with uncertainty of solid artefacts maintained asprimary standard of density/volume are given in table 1.1

Table 1.1 Solid Artefacts as Primary Standards of Density/Volume

Country Laboratory Shape Material Volume cm3 Uncertainty

USA NIST Sphere Steel 134.067 062 0.2 ppm

Disc Silicon 86.049 788 0.3 ppm

Australia NML Sphere ULE glass 228.519 022 0.25 ppm

Japan NRLM Sphere Quartz 319.996 801 0.36 ppm

Italy IMGC Sphere Silicon 429.647 784 0.13 ppm

Sphere Zerodur 386.675 59 0.18 ppm

Germany PTB Cube Zerodur 394/542 60 0.8 ppm

India NPL Sphere Quartz 268.225 1 1.0 ppm

One such standard is shown below

Photo of a silicon sphere from NRLM, Japan

1.6 MEASUREMENT OF VOLUME OF SOLID ARTEFACTS

As seen above practically every national measurement laboratory maintains its volume/ densitystandard in the form of an artefact. Some determine its volume by dimensional method others


derive the volume of their primary standard through hydrostatic weighing using water asdensity standard. In the latter case, the primary standard of mass is used as reference standardin hydrostatic weighing.

1.6.1 Dimensional Method1.6.1.1 SphereDiameter of a solid artefact in the shape of sphere is measured by the use of Saunders typeinterferometer [1] with a parallel plates etalon or by Spherical Fizeaus type interferometer [2].

For measurement of various diameters, a great circle is marked on the sphere. Thediameter of this great circle is measured with the help of an interferometer. The circle isusually named as equator. N sets of equiangular points are chosen on this circle. Each setconsists of two diametrically opposite points. M equiangular points divide each of the n greatcircles passing through these 2N points. The diameters of these M great circles are inter-compared to see the roundness of the sphere. Further details may be obtained from the bookby the author [3].

1.6.1.2 CubeDimensions of a cube are determined by using commercially available interferometers and theerrors due to roundness of edges and corners, out of plainness of faces are estimated andproper corrections are applied [4,5].

1.6.2 Volume of Solid Body by Hydrostatic MethodHydrostatic method is based on the Archimedes Principle. The principle states that if a solid isimmersed in a fluid, it loses its weight, and loss in weight is equal to the weight of the fluiddisplaced. If a solid body has a perfectly smooth surface and fluid wets the surface, then volumeof the fluid displaced is equal to that of the body. If the density of the fluid is known thenvolume of fluid displaced i.e. volume of solid may be calculated by dividing the loss in mass ofthe solid by density of the fluid. Generally water is used as fluid for this purpose. The body isfirst weighed in air and then in water.

Let M1, M2 be respectively the apparent masses of the body when weighed against theweights of density D first in air and then in water. Let 1 and 2 be density of air at the time oftwo weighing while be density of water at the temperature of measurement. Then

M1 (1 1 /D) = M V1 gdT1

, and

M2 (1 2/D) = M V gdT2

Where T1 and T2 are values of surface tension of water at the time of two weighing and dis the diameter of the suspension wire and V is the volume of the body.

Subtracting the two equations we getV ( 1) = M1 (1 1/D) M2 (1 2/D) + d T1/g d T2/g, giving

V = [M1 (1 1/D) M2 (1 2/D) + (d/g){T1 T2}]/( 1)A good care is required to ensure that the length of the portion of wire submerged in

water and surface tension of the liquid at its intersection remains unchanged in each of twoweighing steps. The real problem comes in wetting the surface of the solid completely. If the


solid is not wetted properly then the calculated value of volume of solid will be more than theactual. The problem may be greatly reduced by :

Removing of air bubbles sticking to surface of the solid by mechanical means. Removing dissolved air by creating a partial vacuum through a water pump or any

other vacuum pump. Boiling the water with solid inside it to remove air and then cooling after cutting off

the air contact by suitable plugging the system containing water and the solid. Thismethod is time consuming and it is difficult to ensure the temperature equilibriuminside the solid especially when it is made of ceramic like material.

Thorough cleaning of the surface of the solid body. Having the solid with highly polished and smooth surface.

1.6.2.1 Effect of Surface Tension in Hydrostatic WeighingLet the diameter of the wire from which the solid body is suspended be d mm, then an upwardforce equal to dT will be acting on it at the air liquid intersection. So the loss in apparent massof the body in water will be dT/g.

For water, surface tension T = 72 mN/m, the error could be 23.08 mg for a wire of diameter1 mm. However, the apparent mass of the body in water is determined by two weighing, namely(1) when the hanger alone is in water and (2) when body is placed in hanger. Apparent mass ofthe body will be the difference of two readings. There will be no error in apparent mass of thebody in water if surface tension does not change during these two weighing. But surface tensionof water changes drastically with contamination, so even with 10 percent change in surfacetension, the error in volume measurement will be equal to the volume of water of mass 2.3 mg,which is roughly equivalent 2.3 mm3. If the true volume of the body is 10 cm3 then relativeerror will be 2.3 parts in 10000.

1.6.2.2 Effect of Different Immersion Length of the Suspended WireIf the change in water level, in the two weighing, is 1 mm, then change in immersed volume ofthe wire of diameter 1 mm will be 0.7854 mm3, which will amount to an error of 0.8 parts in10000 in a body of true volume 10 cm3. Normally much thinner wires of platinum are used forthis purpose so error due to wire immersing at different length is further reduced.

The hydrostatic weighing method is quite often used for determining the purity of gold inornaments. Let us assume a bangle of 15 g whose purity of gold is to be determined. If thebangle is of pure gold with density 17.31 gcm3, then its volume should be 15/17.31 = 0.86655 cm3.An error of 0.000 8 cm3 as calculated above will make the measured volume as 0.86575 cm3 andgiving the density of the bangle as 17.29 gcm3.

1.7 WATER AS A STANDARD

Water is being used as a liquid of known density from very long time. So measurement of itsdensity has remained a concern to all metrologists. In the last decade of 19th century, Chappuisof BIPM, International Bureau of Weights & Measures, Paris and Thiesen of PTR PhysikalischTechnische Reichsanstalt, Germany, measured the density of water at different temperatures.They expressed their results in terms of two totally different formulae. The two formulae givedensity of water at different temperatures which differed by 6 parts per million around 25 oCbut by 9 parts per million at 40 oC. At that time, the idea of isotopic composition of water and itseffect on the density was not clear. Hence isotopic composition of water was not taken in to


account. Similarly air dissolves in water and lowers its density, but the extent to which dissolutionof air affects the density of water was not known. With the development of new technology inmeasurement and the growing demand of accuracy in knowing the density of water, severalnational laboratories took up the job of measurement of water density with a precision betterthan one parts per million. Last 25 years of twentieth century were spent to measure thedensity of well defined and air free water. Each laboratory expressed its results in differentforms. BIPM set up an international Committee for harmonising the results of variouslaboratories. Simultaneously the Author also took up the job of expressing the density of waterat different temperatures using the recent results of measurement of water density by variouslaboratories. The author reported latest expression and values of density of water in the SecondInternational Conference on Metrology in New Millennium and Global Trade, held at NPL,New Delhi, in February 2001 [6, 7]. Most recently the international Committee set by BIPMhas also come to a conclusion and expressed density of water as a function of temperature [8].But the values of water density obtained by the author and the Committee differ only by a fewparts per ten million. The density table in terms of international temperature scale ITS 90 ofSMOW has been given in table 1.1. Henceforth the table 1.1 should be used for gravimetricdetermination of capacity of all the capacity measures and volumetric glassware, when water isused as standard of known density.

1.7.1 SMOWStandard Mean Ocean Water with acronym SMOW means pure water having different isotopesof water satisfying the following relations

RD = (155.76 0.05) 106

and R18 = (2005.2 0.05) 106

The international community has agreed to the aforesaid values after determining theisotope abundance ratios of samples of water taken from different sources and locations in thesea. It may be mentioned that due to different isotopic composition of water, the density ofwater may differ only by a few parts in one million.

Pure water molecules are formed when one oxygen atom combines with two atoms ofhydrogen. However oxygen as well as hydrogen is found to have different isotopes. Atoms ofisotopes of an element have same number of electrons and protons but different number ofneutrons in the nucleus. In other words, isotopes will have same chemical properties butdifferent physical properties; especially the relative mass values of its atoms will be different.Atomic mass number is the ratio the mass of an atom to the mass of one hydrogen atom and issimply called as mass number. For example most of the atoms of oxygen have mass number 16but there are some atoms having mass number 17 and 18. Similarly most of atoms of hydrogenhave mass number 1 but there are some atoms with mass number 2. So in water we have mostof the molecules having one atom of oxygen of mass number 16 and two hydrogen atoms ofmass number 1. But there could be some molecules having one oxygen atom of mass number17 or 18 combining with two hydrogen atoms of mass number 1. Similarly there will be somemolecules of water having one oxygen atom of mass number 16 combined with two hydrogenatoms of mass number 2.

The abundance ratio is the ratio of the number of isotopic atoms of specific mass number,present in a given volume, to the number of atoms of the normal mass number. For example:oxygen has isotopes of mass number 18 and 17, while its normal mass number is 16. Then theabundance ratio denoted as R18 is the ratio of number of atoms of mass number 18 to those of


mass number 16, present in a given volume. Similarly the abundance ratio of isotopes of waterwith oxygen of mass number 18 or hydrogen mass number 2 will respectively be

R18 = n(18O)/n(16O) and

RD = n(D)/n(H)Density values given in table 1.1 are of air-free SMOW.Corrections, if accuracy so demands, are applied for isotopic composition by the following

relation (V-SMOW) = 0.233 18O + 0.0166 D

Similarly for the water having dissolved air, additional correction is applied to the densityvalues given in the table 1.1 by the following relation:

/ kgm3 = ( 0.004612 + 0.000 106t)Where = degree of saturation.t = temperature in oC. = density of sample water in kgm3.

RD = ratio of number deuterium atoms to the number of hydrogen atoms.R18 = ratio of oxygen atoms of mass number 18 to the number of oxygen atoms of mass

number 16. = deviation from unity of the ratio of abundance ratio of the sample to the abundance

ratio of the SMOW.

For example 18O = [R18(sample)/R18(SMOW)1] and D = [RD(sample)/RD (SMOW)1]

1.7.2 International Temperature Scale of 1990 (ITS90)We know that elements and compounds change its phase (solid to liquid or liquid to gaseousstate) at specified conditions only at a fixed temperature. International temperature scale is aset of such accurately determined temperatures at which phase transition takes place of certainpure elements and compounds water. The set covers the range of temperatures likely to bemet in day to day life. We can measure thermodynamic temperature only through thethermometers whose equation of state can be written down explicitly without having to introduceunknown temperature dependent constants. These thermometers are called as primarystandards which are only a few world-wide and also the reproducibility of measurements throughsuch instrument are not quite satisfactory.

The use of such thermometers to high accuracy is difficult and time-consuming. Howeverthere exist secondary thermometers, such as the platinum resistance thermometer, whosereproducibility can be better by a factor of ten than that of any primary thermometer. So phasechange temperatures are measured of several elements. The elements are such that these areavailable in the pure form. Such measurements are taken at national measurement laboratoriesworld-wide. International Community then accepts a set of such temperatures. Such a set oftemperatures is known as practical temperatures scale. In order to allow the maximumadvantage to be taken of these secondary thermometers the General Conference of Weightsand Measures (CGPM) has, in the course of time, adopted successive versions of an internationaltemperature scale. The first of these was in 1927 as ITS 127. Subsequently depending uponnew experiments carried out with better available technology, various temperature scale suchas IPTS 48 in 1948 and IPTS68 in 11968 have been adopted. Finally in January, 1990, CGPMadopted a new set of temperatures, which is known as ITS 90.


Primary thermometers that have been used to provide accurate values of thermodynamictemperature include the constant-volume gas thermometer, the acoustic gas thermometer,the spectral and total radiation thermometers and the electronic noise thermometer.

1.8 INTERNATIONAL INTER-COMPARISON OF VOLUME STANDARDS1.8.1 PrincipleLike all other International inter-comparisons of standards of other quantities, standards ofvolume/ capacity are also inter-compared keeping a certain objective(s) in view. In these inter-comparisons, several national measurement laboratories participate. So participants list andidentification of the pilot laboratory is the first thing to start such a project. The pilot laboratorytakes upon it the responsibility of co-ordinating with other laboratories. Its job is to outline inclear-cut terms the following:

The aims and objective(s) of the project. Preparation or procurement of the artefact. Method to be used in determination of the attribute of the artefact under investigation.

In the present case it is volume of the artefact. Time schedule in consultation with the participating laboratories. Method of reporting the results with detailed analysis of uncertainty. Monitoring the progress of the measurements at different laboratories and the

influence parameters like temperature. Quite often, the Pilot laboratory determines the attribute of the artefact before and

after the determination of the attribute by each participating laboratory. Collating and correlating the results of determination by participating laboratories.

1.8.2 ParticipationA preliminary meeting is held to prepare a list of likely participating laboratories and to assignthe job of the pilot laboratory to one of the willing participating laboratories. The Pilot laboratorymay contact the other laboratories whose participation is considered necessary. The laboratorywill prepare the list of participating laboratories, address with communication facilities availableat each laboratory and name of contact person in each laboratory.

1.8.3 Aims and Objectives of the ProjectThe aims and objective of the project may be any one, some or all the following points mentionedbelow:

1. To establish mutual recognition for the available measurement facilities with knownand stated uncertainty of measurements.

2. To build up confidence in measurement capability for specific quantity (volume inthis case) with the known uncertainty.

3. To ascertain and quantify the change in measured quantity due to specific influenceparameter.

4. To ensure the user or user industry for the measurements carried out by the laboratorywith specified uncertainty.

5. To ensure the maintenance of other standards for other quantities with the requireduncertainty. For example calibration of standards of mass requires determination ofits volume. So each laboratory requires the capability for measurement of volume ofmass standard with the required uncertainty.


1.8.4 Preparation or Procurement of the ArtefactBefore proceeding further, let us defines the word attribute as the property of the artefact,under investigation; for example, in the present case, volume of the artefact is measured. Theartefact of stable volume and having a highly smooth and polished surface, whose volume canpreferably be determined through dimensional method, is used as travelling standard; everyparticipating laboratory assigns the value of the volume to the same artefact. For this purpose,a suitable artefact is prepared or procured by the pilot laboratory. The artefact should be suchthat the attribute under investigation., (volume in this case) does not change during its transportto different laboratories. Its carrying case along with its handling equipment should be properlydesigned and instruction for its use including cleaning etc. should be detailed out. Material ofthe travelling standard should be such that the attribute under investigation does not changewith time, if it is not possible then a well-defined relation between the changes in the attributewith respect to time should be clearly stated and every participating laboratory should berequested to use the given relation only. Other parameters, which affect the value of theattribute, should be well documented and each laboratory should use the same document.

1.8.5 Method to be Used in Determination of the Parameter(s) of the ArtefactThe method for determination of the required attribute should be clearly detailed out, unlessthe object is to study the compatibility of the different methods of measurements for the sameattribute. Say in case of measurement of volume of a travelling standard, it should be specifiedas to which method is used, the dimensional or hydrostatic. Every measurement should betraceable to the national standards maintained in the country and it should be clearly specifiedin the report.

1.8.6 Time Schedule in Consultation with the Participating LaboratoriesFor the success of a project of this nature, a well-defined, optimum time schedule should beworked out in advance. Each laboratory should follow the time schedule and the Pilot laboratoryshould monitor it. One problem, which is commonly faced by the developing countries, is thecustom clearance and handling of artefact at that stage. Each participating Laboratory shouldtake special pains to sort out the custom clearance problem well in advance. The Pilot Laboratoryshould provide a set of clear instructions for handling the artefact especially by the custompeople.

1.8.7 Method of Reporting the Results with Detailed Analysis of UncertaintyA detailed procedure for calculating the uncertainty should be laid out. The influence parametersshould be clearly defined and the associated uncertainty should be grouped in appropriate class(Type A or B) [9]. Each participating laboratory should be asked to report the uncertaintyassociated with the defined parameters, even if it is insignificant according to the participatinglaboratory. Uncertainty in base standards or national standards is to be stated and taken intoaccount and should be grouped as Type B uncertainty.

1.8.8 Monitoring the Progress of the Measurements at Different Laboratories and theInfluence Parameters Like Temperature

There are certain influence factors, which affect the value of the measured value of the parameterunder investigation in a very complicated and unknown way. In this case the parameter should


be monitored by each laboratory and reported to the pilot laboratory. Pilot laboratory shouldmake arrangement for monitoring of such parameter during transport of the artefact.

1.8.9 Monitoring the Required Parameter(s) of the ArtefactIn some cases, the Pilot Laboratory measures the parameter under investigation before andafter a participating laboratory, so as to see for any change in the parameter and to assess anydamage during transportation. For example, in case of mass standards, there may be a changein mass value of the travelling standard due to a scratch caused by rough handling.

1.8.10 Collating and Correlating the Results of Determination by ParticipatingLaboratories

Finally all the results are statistically evaluated and assessed for their correctness within thestated uncertainty by the laboratory. Any bias component in a particular laboratory or anartefact is identified and accounted for. Great care should be taken that the sentiments of nolaboratory are hurt. Adverse comments about a laboratory, if any, should be avoided.

1.8.11 Evaluation of Results from Participating LaboratoriesBasic problem in collating the results of international inter-comparisons is the variation ofresults, though each laboratory may claim a reasonable uncertainty. If all the results reportedare arranged in ascending order of their magnitudes, then results on either end may becomesusceptible and one starts wondering if those results should be considered or not in compilingthe final value. One simple criterion is the Dixons test, which may be used for ignoring or notignoring the results on either end. As a policy one should not ignore or at least appear to ignoreany result. It is, therefore, advisable to apply a method so that none of the result is ignored.Some laboratories have better equipment and manpower so will report the results with smalleruncertainty values, which are likely to be more reliable. One has to give some more respect toresults obtained with smaller values of uncertainty. So do not ignore any results, but give moreweight factor to results with smaller uncertainty, keeping in mind that outliers do not affectthe result too much. Outliers can be identified by the Dixon outlier test as given below. Forcollating and analysing the results from different laboratories host of other statistical methodsare available in the literature.

1.8.11.1 Outlier Dixon TestBasic assumption of this test is that all reported results follow normal distribution. Forapplication of the test, all observations are arranged in either ascending or descending order. Ifthe lower value result is under suspicion, the results are arranged in descending order. Theresults are arranged in ascending order if the higher value result is to be tested for outlier. Sothat suspected result is the last i.e. nth result is under scrutiny, n being the total number ofresults. Depending upon the value of n, the test parameter is taken as one of the followingratios:

(Xn Xn1)/ (Xn X1 ) for 3 < n < 7

(Xn Xn1)/ (Xn X2 ) for 8 < n < 10

(Xn Xn2)/ (Xn X2 ) for 11 < n < 13

(Xn Xn2)/ (Xn X3 ) for 14 < n < 24For given n, the value of test parameter should not exceed the corresponding critical

value given in the table 1.2.


If nth - the last result happens to be an outlier then test is applied to the n-1st results. Theprocess should continue till the test parameter is less than the critical values given in thetable.

Table 1.2 Critical Values for Dixon Outlier Test

n Test parameter Critical Value4 0.7655 (XnXn1)/(XnX1) 0.6206 0.5607 0.507

8 0.5549 (XnXn1)/ (Xn X2) 0.512

10 0.477

11 0.57612 (XnXn2)/ (Xn X2) 0.54613 0.521

14 0.54615 0.52516 0.50717 0.49018 0.47519 (XnXn2)/ (Xn X3) 0.46220 0.45021 0.44022 0.43023 0.42124 0.41325 0.406

The result under test is Xn.Generally speaking, to collate the results from participating laboratories, we may adopt

any of the three methods as described below. The methods are: Arithmetic mean method, Median method, and Weighted mean method.

1.8.11.2 Arithmetic Mean Method Simple mean or the arithmetic mean Xm is defined as

Xm = Xi /n, where i takes all values from 1 to n andestimated standard deviation s of the single observation is given by

s = [(Xi Xm)2/(n 1)]1/2

While standard uncertainty of the mean U(Xm) is given as

U(Xm) = [(Xi Xm)2/{n(n 1)}]1/2

Though taking arithmetic mean appears to be more reasonable in the first instance, buthere extreme values of the results effect more than the ones, which are closer to mean values.


Standard deviation s and U(Xm) is rather more sensitive to inclusion of reported extreme values.This point will be further clarified, when we discuss the results of the example later.

1.8.11.3 Median MethodIn this method, all results are arranged in ascending order and the result, which comes exactlyin midway is taken as median for the odd number of results. If the number of results is even,then the arithmetic mean of the two middle ones is taken as the median. In this method onlyone or two of the reported results are taken into consideration. The notations used are

Xmed = med{Xi}The uncertainty attributable, according to Muller [22], to median is based on the Median

of the Absolute Deviations, which is abbreviated as MAD and defined as

MAD = med {'Xi Xmed'}The standard uncertainty in this case is given by

U(Xmed ) = 1.9 MAD/(n1)1/2

It may be noted that median is unaffected by outliers as long they exist, while arithmeticmean is greatly affected by an outlier. However median method does not distinguish betweengood and bad values. Equal importance is given to every result irrespective of uncertainty.Mean is affected equally by the result having very large uncertainty as by the one with verysmall uncertainty. To overcome this defect weighted mean method may be used.

1.8.11.4 Weighted MeanThough it is natural that the results obtained with smaller uncertainty are more reliable thanthose with larger uncertainty, but no such distinction has been made while taking the arithmeticmean, which appears to be not fair. So to give due importance to the results obtained bysmaller uncertainty, we may assign a weight equal to inverse of the square of the uncertaintyto each result; i.e. a result Xi with uncertainty U(Xi ) will have the weight equal to U

2(Xi ).So weighted mean Xwm, is given by

Xwm = { U2(Xi). Xi}/{ U2(Xi)}While uncertainty of weighted means U(Xwm) is given by

U(Xwm) = { U2(Xi)}1/2

1.8.11.5 Derivation of Standard Uncertainty in Case of Weighted MeanWeighted uncertainty = weight factor wi times uncertainty

Weighted variance = Square of weighted uncertaintyMean variance of inter-comparison = Sum of weighted variances from all laboratories

divided by the sum of the weight factors uncertainty is the square root of the varianceIf Ui is uncertainty with weight factor Ui

2,so weighted uncertainty = Ui Ui

2 = Ui1

Weighted variance = Ui2,

Total variance = Ui2Total uncertainty = (Ui2 )1/2,Mean uncertainty = uncertainty/sum of weight factors

= (Ui2 )1/2/(Ui2 )= (Ui2 ) 1/2.


1.8.11.6 Outlier Test for EnTo look for the outlier if any, find En the normalised deviation for each laboratory by theformula given below.

En = 0.5 [{Xi Xwm}/{U2(Xi ) + U

2(Xwm)}1/2]

A result having En value larger than 1.5 is excluded for the purpose of taking weightedmean. But as soon as a result is excluded, the value of U(Xwm) will change, so iterative processis applied, starting from the largest until all results contributing to the mean have |En| valuessmaller than 1.5. Taking into account the individual uncertainties yields an objective criterionfor outliers to be excluded. The limit value of |En| =1.5 corresponds to a confidence level of99.7% or to a limit of three times standard deviation.

The method assumes that the individual uncertainty has been estimated by following acommon approach and taking same influence factors and sources of uncertainty in to account.So all parameters and influenced factors should be identified and classified either in Type A orin Type B should be sent along with other instructions. For estimating the uncertainty, everybody should be told to follow the ISO Guide [9]. Otherwise a single wrong result with a wronglyunderestimated (too small) standard uncertainty would strongly influence or even fully determinethe weighted mean. On the other hand, a high quality measurement with overestimated (toolarge) standard uncertainty would only weakly contribute to the mean value so calculated.

1.9 EXAMPLE OF INTERNATIONAL INTER-COMPARISON OF VOLUMESTANDARDS

Practically every national laboratory while calibrating their mass standards measures volumeof the standard mass pieces by using hydrostatic method. The volume of the standard gives itstrue mass after applying the proper buoyancy correction. As the uncertainty available incomparison of two 1 kg mass pieces is as high as 1in 109, so the volume measurements shouldalso be carried with a standard uncertainty of 1 in 106. It was, therefore, felt necessary to carryout round robin test between national laboratories for determination of volume of solid artefactshaving volume corresponding to stainless steel weights of mass values between 2 kg and 500 g.So a project of inter-laboratory comparison of volume standards to access the volumemeasurement capability of various Laboratories was discussed in 7th Conference of EurometMass Contact Persons Meeting in 1995 at DFM, Lygby, Denmark. The project Inter-laboratorycomparison of measurement standards in field of density (Volume of solids) was proposed byMr. J G Ulrich and was agreed to as the EUROMET Project No. 339. The final report on theproject was published by EUROMET in August 2000, some portions of this project report [10]are discussed below.

1.9.1 Participation and Pilot LaboratoryThe Laboratories of European countries, which took part in the inter-comparison [10] were:.

1. Swiss Federal Office of Metrology, (OFMET), Switzerland2. Swedish National Testing and Research Institute (SP), Sweden3. Physikalisch Technische Budesanstalt (PTB), Germany4. Bundesamt fur Eich-und Vermessungswesen

Gupta - Comprehensive Volume Capacity Measurements

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