Mechanical Measurements S

Mechanical Measurements S. P. Venkateshan

Mechanical Measurements

Second Edition S. P. Venkateshan Department of Mechanical Engineering Indian Institute of Technology Madras Chennai, Tamil Nadu, India

ISBN 978-3-030-73619-4 ISBN 978-3-030-73620-0 (eBook) https://doi.org/10.1007/978-3-030-73620-0

Jointly published with ANE Books India. The printed edition, there is a local printed edition of this work available via Ane Books in South Asia (India, Pakistan, Sri Lanka, Bangladesh, Nepal and Bhutan) and Africa (all countries in the African subcontinent). ISBN of the Co-Publisher’s edition: 978-9-383-65691-2

1st edition: © Ane Books Pvt. Ltd 2008 2nd edition: © The Author(s) 2022 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publishers, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publishers nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publishers remain neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland Dedicated to the Shakkottai Family Preface to the Second Edition

The second edition of the book has been thoroughly revised and all errors that have come to my notice have been corrected. Additions have been made at various places in the book. Notable additions are in the statistical analysis of measured data in Module I. Important questions regarding normality of deviations and identiﬁcation of outliers have been discussed in great detail. These should interest the advanced reader who is looking for an understanding of these issues. Thermistors have been described in greater detail in Chap. 4. Also, the line reversal technique of measuring gas temperature has been described in greater detail. Theory of the integrating sphere has been discussed in detail in Chap. 12. Module V has been augmented with more examples from laboratory practice. Exercises are now positioned at the end of each module. Many new exercise problems have been added in this edition. The modules have been rearranged with the number of chapters going up by one to a total of sixteen chapters in this edition. Many references are indicated as footnotes in the text apart from the bibliography and the list of references given in the Appendix. All illustrations have been redrawn for this edition using “tikz”—a program environment compatible with “latex”. All graphs have been replotted for this edition using QtiPlot. In general, these were done to improve the quality of the illustrations and also to bring uniformity in the format. It is hoped that the second edition will be received with the same enthusiasm as the original edition by the student community.

Chennai, India S. P. Venkateshan

vii Preface to the First Edition

In recent times there have been rapid changes in the way we perceive measurements because new technologies have become accessible to any one who cares to use them. Many of the instruments that one takes for granted now were actually not there when I started my engineering studies in the 1960s. The training that we received those days, in Mechanical Engineering, did not include a study of “Mechanical Measurements”. Whatever was learnt was purely by doing experiments in various laboratory classes! Electrical Engineers were better off because they studied “Electrical Measurement” for a year. The semester system was to be introduced far in the future. Even when “Mechanical Measurements” was introduced as a subject of study, the principles of measurements were never discussed fully, the emphasis being the descriptive study of instruments! In those days, an average mechanical engineer did not have any background in measurement errors and their analysis. Certainly he did not know much about regression, design of experiments, and related concepts. At that time the integrated chip was to appear in the future and the digital computer was in its infancy. We have seen revolutionary changes in both these areas. These developments have changed the way we look at experiments and the art and science of measurements. The study of measurements became divorced from the study of instruments and the attention shifted to the study of the measurement process. The emphasis is more on knowing how to make a measurement rather than with what. One chooses the best option available with reasonable expense and concentrates on doing the measurement well. I have been teaching a course that was known as “Measurements in Thermal Science” for almost 20 years. Then the title changed to “Measurements in Thermal Engineering”! The emphasis of the course, however, has not changed. The course is one semester long and the student learns about the measurement process for almost third of this duration. After he understands the principles he is ready to learn about measurement of quantities that are of interest to a mechanical engineer. The course stresses the problem-solving aspect rather than the mundane descriptive aspects. The student is asked to use library and web resources to learn about instruments on her/his own. In the meanwhile, I have produced a video series (40 lectures each of 55 mins duration on “Measurements in Thermal Science”) that has been widely circulated. ix x Preface to the First Edition

Thanks to the NPTEL project (National Program for Technology Enhanced Learning) I had an opportunity to bring out another video lecture series (50 lectures of 55 mins duration each, this time called “Mechanical Measurements”). This is being broadcast over the ‘Technology Channel’. Also I have prepared a five module web course with the same title. Interested reader can access the web course through the IIT Madras web site. This effort has encouraged me to write a more detailed book version of “Mechanical Measurements” that is now in your hands. I have arranged this book in five parts, each part being referred to as a module. Details of what is contained in each module is given in an abstract form at the beginning of each module. It has taken me close to three years to produce this book. Over this period I have improved the readability of the text and weeded out unnecessary material and have tried to give to the reader what I believe is important. I have tried to give a balanced treatment of the subject, trying hard to keep my bias for thermal measurements! The text contains many worked examples that will help the reader understand the basic principles involved. I have provided a large number of problems, at the end of the book, arranged module wise. These problems have appeared in the examination papers that I have set for students in my classes over the years. The problems highlight the kind of numerics that are involved in practical situations. Even though the text is intended to be an undergraduate text book it should interest practicing engineers or any one who may need to perform measurements as a part of his professional activity! I place the book in the hands of the interested reader in the hope that he will find it interesting and worth his while. The reader should not be contented with a study of the book that contains a large number of line drawings that represent instruments. He should spend time in the laboratory and learn how to make measurements in the real world full of hard ware!

Chennai, India S. P. Venkateshan Acknowledgements

The writing of the book has involved support from several people. My research scholars have extended cooperation during the recording of the video lectures. The feedback received from them—Dr. Rameche Candane, Mr. M. Deiveegan, Mr. T. V. V. Sudhakar, and Mr. G. Venugopal—helped in correcting many errors. Their feedback also helped me in improving the material while transforming it into the book form. The photographs used in the book have been taken by Mr. M. Deiveegan with assistance from G. Venugopal in the Heat Transfer and Thermal Power, Internal Combustion Engines and the Thermal Turbo machines Laboratories, Department of Mechanical Engineering, IIT Madras. I am grateful to Prof. B. V. S. S. S. Prasad for permitting me to take pictures of the heat flux gages. Mr. T. V. V. Sudhakar and Mr. G. Venugopal have also helped me by sitting through the classes in “Measurements in Thermal Engineering” and also by helping with the smooth running of the course. The atmosphere in the Heat Transfer and Thermal Power Laboratory has been highly conducive for the book writing activity. The interest shown by my colleagues has been highly encouraging. Many corrections were brought to my notice by Mr. Renju Kurian and Mr. O. S. Durgam, who went through the first edition very carefully. I thank both of them for this help. I thank Dr. Eng. Mostafa Abdel-Mohimen, Benha University, Egypt, for pointing out mistakes in the figure and correspondingly the description of diaphragm type pressure gauge. Corrections have been made in the revised second edition. I acknowledge the input, to this book, of Dr. Prasanna Swaminathan, who designed a class file called “bookspv.cls” which has made it possible to improve the aesthetic quality of the book.

S. P. Venkateshan

xi Nomenclature

Note: (1) Symbols having more than one meaning are context speciﬁc. (2) Sparingly used symbols are not included in the Nomenclature.

Latin Alphabetical Symbols a Acceleration, m/s2 or Speed of sound, m/s or Any parameter, appropriate unit A Area, m2 c Callendar correction, ◦C or Linear damping coefficient, N · s/m or Gas concentration, m−3 or Speed of light, 3 × 108 m/s C Specific heat, J/kg◦C or Capacitance of a liquid system, m2 or Capacitance of a gas system, m · s2 or Electrical capacitance, F Cd Coefficient of discharge, no unit CD Drag coefficient, no unit ◦ C p Specific heat of a gas at constant pressure, J/kg C ◦ CV Specific heat of a gas at constant volume, J/kg C D Diameter, m d Diameter, m or Degrees of freedom or Piezoelectric constant, Coul/N E Electromotive force (emf), V or Emissive power, W/m2 or Young’s modulus, Pa 2 Eb Total emissive power of a black body, W/m 2 Ebλ Spectral emissive power of a black body, W/m μm Es Shear modulus, Pa E˙ Enthalpy flux, W/m2 f Frequency, s−1 or Hz or Friction factor, no unit f D Doppler shift, Hz F Force, N FA Fuel air ratio, kg( fuel)/kg(air) g Acceleration due to gravity, standard value 9.804 m/s2

xiii xiv Nomenclature

G Gain, Numerical factor or in dB or Gauge constant, appropriate units or Bulk modulus, Pa Gr Grashof number, no unit h Heat transfer coefficient, W/m2◦C or Head, m or Enthalpy, J/kg − h Overall heat transfer coefficient, W/m2◦C HV Heating value, J/kg HHV Higher Heating Value, J/kg LHV Lower Heating Value, J/kg I Electrical current, A or Influence coefficient, appropriate unit or Moment of inertia, m4 2 Iλ Spectral radiation intensity, W/m · μm · ste J Polar moment of inertia, m4 k Boltzmann constant, 1.39 × 10−23, J/K Number of factors in an experiment, no unit or Thermal conductivity, W/m◦C − k A Thermal conductivity area product, W · m/◦C K Flow coefficient, no unit or Spring constant, N/m L Length, m m Fin parameter, m−1 or Mass, kg or Mean of a set of data, appropriate unit m˙ Mass flow rate, kg/s M Mach number, no unit or Molecular weight, g/mol or Moment, N · m or Velocity of approach factor, no unit n Index in a polytropic process, no unit or Number of data in a sample, no unit ni Number of levels for the ith factor, no unit N Number of data in the population, no unit or Number count in analog to digital conversion, no unit NSt Strouhal number, no unit Nu Nusselt number, no unit p Pressure, Pa or Probability, no unit −3 ppmV Gas concentration based on volume, m P Pressure, Pa Perimeter, m Power, W PD Dissipation constant, W/m p0 Stagnation pressure, Pa Pe Peclet number = Re · Pr, no unit Pr Prandtl number, ν/α, no unit q Electrical charge (Coulomb), Coul or Heat flux, W/m2 Q Any derived quantity, appropriate unit or Heat transfer rate, W or Volume flow rate, m3/s etc. ˙ Q P Peltier heat (power), W ˙ QT Thomson heat (power), W R Electrical resistance, or Fluid friction resistance, 1/m · s or radius, m or Thermal resistance, m2◦C/W Rg Gas constant, J/kg · K R Universal gas constant, J/mol · K Nomenclature xv

Re Reynolds number s Entropy, J/K or Entropy rate, W/K or Spacing, m S Surface area, m2 Stk Stoke number, no unit Se Electrical sensitivity, appropriate unit St Thermal sensitivity, appropriate unit t Time, s or Temperature, ◦C or K or t - distribution or Thickness, m ◦ tPt Platinum resistance temperature, C ◦ t90 Temperature according to ITS90, C T Period of a wave, s T or Temperature, K or Torque, N · m TB Brightness temperature, K Tc Color temperature, K Tst Steam point temperature, K ◦ Tt Total or Stagnation temperature, K or C Ttp Triple point temperature, K T90 Temperature according to ITS90, K u Uncertainty in a measured quantity, Appropriate units or ratio or percentage V Potential difference (Volts) or Volume, m3 or Velocity, m/s VP Peltier voltage, μV VS Seebeck voltage, μV VT Thomson voltage, μV W Mass speciﬁc heat product, J/◦C or Weight of an object, N x Displacement, m − X Indicated mean or average value of any quantity X XC Capacitive reactance, X L Inductive reactance, Y Expansion factor, no unit Z Electrical impedance,

Acronyms ac Alternating current ADC Analog to Digital Converter APD Avalnche Photo Diode BSN Bosch Smoke Number DAC Digital to Analog Converter DAQ Data Acquisition DAS Data Acquisition System dc Direct current DIAL Differential Absorption LIDAR DOE Design Of Experiment xvi Nomenclature

DPM Digital panel meter FID Flame Ionization Detector GC Gas Chromatography GC IR GC with Infrared spectrometer GC MS GC with Mass spectrometer HC Hydro Carbon IR Infra Red ISA Instrument Society of America LASER Light Ampliﬁcation by Stimulated Emission of Radiation LDV Laser Doppler Anemometer LIDAR Light Detection and Ranging LVDT Linear Voltage Differential Transformer MS Mass Spectrometer NDIR Non Dispersive Infrared Analyzer NOx Mixture of oxides of nitrogen Op Amp Operational Ampliﬁer PC Personal Computer PRT or PT Platinum Resistance Thermometer RTD Resistance Temperature Detector SRM Standard Reference Material USB Universal Serial Bus

Greek Symbols

α Area (fractional) of the tail of the χ 2 distribution or Coefficient of linear expansion, /◦C or Pitch angle in a multi-hole probe, rad or ◦ or Seebeck coefficient, μV/◦C or Shock angle in wedge flow, rad or ◦ or Temperature coefficient of resistance of RTD, ◦C−1 β Constant in the temperature response of a thermistor, K or Diameter ratio in a variable area meter, no unit or Extinction coefficient, m−1 or Isobaric coefficient of cubical expansion, 1/K or Yaw angle in a multi-hole probe, rad or ◦ γ Ratio of specific heats of a gas, C p/CV δ Thickness, mm or μm or Displacement, m Change or difference or error in the quantity that follows ε Strain, m/m or more usually μm/m ε Emissivity, no unit ελh Spectral Hemispherical emissivity, no unit εh Total Hemispherical emissivity, no unit η Similarity variable in one-dimensional transient conduction φ Non-dimensional temperature or Phase angle, rad or ◦ κ Dielectric constant, F/m λ Wavelength, μm Nomenclature xvii

μ Dynamic viscosity, kg/m · s or Mean of data or Micro (10−6) ν Kinematic viscosity, m2/s or Poisson ratio, no unit π Mathematical constant, 3.14159... or Peltier emf, μV ρ Density, kg/m3 or Correlation coefficient (linear fit) or the index of correlation (non-linear fit) or Reflectivity, no unit σ Stress, Pa (more commonly Mpa or Gpa) or Stefan Boltzmann constant, 5.67 × 10−8 W/m2 K 4 or Thomson coefficient, μV/◦C or Standard deviation, appropriate unit σe Estimated standard distribution, appropriate unit 2 σa Absorption cross section, m 2 σs Scattering cross section, m 2 σt Total cross section, m σx Standard deviation of the x’s σy Standard deviation of the y’s σxy Covariance θ Temperature difference, ◦C τ Shear stress, Pa or Time constant, s or Transmittance, no unit ω Circular frequency, rad/s ωn Natural circular frequency, rad/s Electrical resistance (Ohms) χ 2 Chi squared distribution, appropriate unit ζ Damping ratio for a second order system, no unit Contents

Part I Measurements, Error Analysis and Design of Experiments 1 Measurements and Errors in Measurement ...... 3 1.1 Introduction ...... 3 1.1.1 MeasurementCategories...... 4 1.1.2 General Measurement Scheme ...... 5 1.1.3 SomeIssues...... 5 1.2 ErrorsinMeasurement ...... 6 1.2.1 Systematic Errors (Bias) ...... 6 1.2.2 Random Errors ...... 6 1.3 Statistical Analysis of Experimental Data ...... 8 1.3.1 Statistical Analysis and Best Estimate fromReplicateData...... 8 1.3.2 ErrorDistribution...... 9 1.3.3 Principle of Least Squares ...... 12 1.3.4 Error Estimation - Single Sample ...... 14 1.3.5 Student t Distribution ...... 19 1.3.6 Test for Normality ...... 22 1.3.7 NonParametricTests...... 30 1.3.8 Outliers and Their Rejection ...... 33 1.4 Propagation of Errors ...... 43 1.5 Speciﬁcations of Instruments and Their Performance ...... 46 2 Regression Analysis ...... 49 2.1 Introduction to Regression Analysis ...... 49 2.2 Linear Regression ...... 51 2.2.1 Linear Fit by Least Squares ...... 51 2.2.2 Uncertainties in the Fit Parameters ...... 53 2.2.3 Goodness of Fit and the Correlation Coefﬁcient ...... 56 2.3 Polynomial Regression ...... 57 2.3.1 Method of Least Squares and Normal Equations ...... 57 2.3.2 Goodness of Fit and the Index of Correlation or R2 .... 58 2.3.3 Multiple Linear Regression ...... 60 xix xx Contents

2.4 General Non-linear Fit ...... 63 2.5 χ 2 Test of Goodness of Fit ...... 66 2.6 General Discussion on Regression Analysis Including Special Cases ...... 70 2.6.1 Alternate Procedures of Obtaining Fit Parameters . . . . . 70 2.6.2 Segmented or Piecewise Regression ...... 73 3 Design of Experiments ...... 79 3.1 Design of Experiments ...... 79 3.1.1 Goal of Experiments ...... 79 3.1.2 FullFactorialDesign ...... 80 3.1.3 2k FactorialDesign ...... 81 3.1.4 MoreonFullFactorialDesign ...... 84 3.1.5 OneHalfFactorialDesign ...... 85 3.1.6 OtherSimpleDesign ...... 88 ExerciseI ...... 94

Part II Measurements of Temperature, Heat Flux, and Heat Transfer Coefﬁcient 4 Measurements of Temperature ...... 109 4.1 Introduction ...... 109 4.2 Thermometry or the Science and Art of Temperature Measurement ...... 109 4.2.1 Preliminaries...... 109 4.2.2 PracticalThermometry ...... 114 4.3 ThermoelectricThermometry ...... 116 4.3.1 ThermoelectricEffects ...... 116 4.3.2 On the Use of Thermocouple for Temperature Measurement ...... 123 4.3.3 Use of Thermocouple Tables and Practical Aspects of Thermoelectric Thermometry ...... 127 4.4 Resistance Thermometry ...... 138 4.4.1 Basic Ideas ...... 138 4.4.2 Platinum Resistance Thermometer and the Callendar Correction ...... 139 4.4.3 RTDMeasurementCircuits ...... 142 4.4.4 Thermistors ...... 148 4.5 Pyrometry...... 158 4.5.1 Radiation Fundamentals ...... 159 4.5.2 Brightness Temperature and the Vanishing FilamentPyrometer ...... 162 4.5.3 TotalRadiationPyrometer ...... 168 4.5.4 Ratio Pyrometer and the Two-Color Pyrometer ...... 169 4.5.5 Gas Temperature Measurement ...... 172 4.6 Other Temperature Measurement Techniques ...... 173 Contents xxi

4.6.1 Liquid in Glass or Liquid in Metal Thermometers . . . . . 174 4.6.2 Bimetallic Thermometer ...... 177 4.6.3 LiquidCrystalThermometers...... 182 4.6.4 IC Temperature Sensor ...... 183 4.7 Measurement of Transient Temperature ...... 184 4.7.1 Temperature Sensor as a First-Order System—ElectricalAnalogy ...... 184 4.7.2 Response to Step Input ...... 186 4.7.3 Response to a Ramp Input ...... 191 4.7.4 Response to a Periodic Input ...... 194 5 Systematic Errors in Temperature Measurement ...... 197 5.1 Introduction ...... 197 5.2 Examples of Temperature Measurement ...... 197 5.2.1 Surface Temperature Measurement Using a Compensated Probe ...... 197 5.2.2 Measurement of Temperature Inside a Solid ...... 198 5.2.3 Measurement of Temperature of a Moving Fluid ...... 199 5.2.4 Summary of Sources of Error in Temperature Measurement ...... 200 5.3 Conduction Error in Thermocouple Temperature Measurement ...... 201 5.3.1 Lead Wire Model ...... 201 5.3.2 The Single Wire Model ...... 201 5.3.3 Heat Loss Through Lead Wire ...... 203 5.3.4 Typical Application and Thermometric Error ...... 204 5.3.5 Measurement of Temperature Within a Solid ...... 206 5.4 Measurement of Temperature of a Moving Fluid ...... 210 5.4.1 Temperature Error Due to Radiation ...... 211 5.4.2 Reduction of Radiation Error: Use of Radiation Shield...... 213 5.4.3 Analysis of Thermometer Well Problem ...... 215 6 Heat Flux and Heat Transfer Coefficient ...... 221 6.1 MeasurementofHeatFlux...... 221 6.1.1 Foil-Type Heat Flux Gauge ...... 221 6.1.2 Transient Analysis of Foil Gauge ...... 226 6.1.3 Thin Film Sensors ...... 229 6.1.4 Cooled Thin Wafer Heat Flux Gauge ...... 230 6.1.5 Axial Conduction Guarded Probe ...... 231 6.1.6 Slug Type Sensor ...... 232 6.1.7 Slug Type Sensor Response Including Non-UniformityinTemperature ...... 235 6.1.8 Thin Film Heat Flux Gauge—Transient Operation . . . . . 238 6.2 Measurement of Heat Transfer Coefficient ...... 242 6.2.1 Film Coefficient Transducer ...... 242 xxii Contents

6.2.2 Cylindrical Heat Transfer Coefﬁcient Probe ...... 243 ExerciseII ...... 246

Part III Measurement of Pressure, Fluid Velocity, Volume Flow Rate, Stagnation, and Bulk Mean Temperatures 7 Measurement of Pressure ...... 261 7.1 BasicsofPressureMeasurement...... 261 7.2 U-Tube Manometer ...... 262 7.2.1 Well Type Manometer ...... 265 7.2.2 Dynamic Response of a U Tube Manometer ...... 268 7.3 Bourdon Gauge ...... 273 7.3.1 DeadWeightTester ...... 274 7.4 Pressure Transducers ...... 274 7.4.1 Pressure Tube with Bonded Strain Gauge ...... 275 7.4.2 Bridge Circuits for Use with Strain Gauges ...... 279 7.4.3 Diaphragm/Bellows Type Transducer ...... 283 7.4.4 Capacitance Type Diaphragm Gauge ...... 288 7.4.5 Piezoelectric Pressure Transducer ...... 290 7.5 Measurement of Pressure Transients ...... 291 7.5.1 ThermalSystem ...... 291 7.5.2 Pressure Measurement in a Liquid System ...... 292 7.5.3 Pressure Measurement in a Gas System ...... 292 7.5.4 Transient Response of a Bellows Type Pressure Transducer ...... 293 7.5.5 Transients in a Force Balancing Element forMeasuringPressure ...... 295 7.6 Measurement of Vacuum ...... 297 7.6.1 McLeod Gauge ...... 298 7.6.2 Pirani Gauge ...... 300 7.6.3 Ionization Gauge ...... 300 7.6.4 Alphatron Gauge ...... 302 8 Measurement of Fluid Velocity ...... 303 8.1 Introduction ...... 303 8.2 Pitot–Pitot Static and Impact Probes ...... 304 8.2.1 PitotandPitotStaticTube...... 304 8.2.2 Effect of Compressibility ...... 308 8.2.3 Supersonic Flow ...... 311 8.2.4 Orientation Effects and Multi-hole Probes ...... 314 8.3 Velocity Measurement Based on Thermal Effects ...... 317 8.3.1 HotWireAnemometer ...... 317 8.3.2 Constant Temperature or CT Anemometer ...... 319 8.3.3 UsefulHeatTransferCorrelation...... 320 8.3.4 Constant Current or CC Anemometer ...... 321 8.3.5 Practical Aspects ...... 323 Contents xxiii

8.3.6 Measurement of Transients (Velocity Fluctuations) . . . . 325 8.3.7 Directional Effects on Hot Wire Anemometer ...... 326 8.4 Doppler Velocimeter ...... 328 8.4.1 The Doppler Effect ...... 328 8.4.2 Ultrasonic Doppler Velocity Meter ...... 330 8.4.3 Laser Doppler Velocity Meter ...... 332 8.5 TimeofFlightVelocimeter ...... 335 8.5.1 Simultaneous Measurement of Position andVelocity ...... 339 8.5.2 Cross Correlation Type Velocity Meter ...... 340 9 Volume Flow Rate ...... 343 9.1 MeasurementofVolumeFlowRate ...... 343 9.2 VariableAreaTypeFlowMeters...... 344 9.2.1 PrincipleofOperation ...... 344 9.2.2 CorrectionFactor ...... 346 9.2.3 Types of Variable Area Flow Meters ...... 347 9.2.4 OriﬁcePlateMeter...... 347 9.2.5 Flow Nozzle ...... 352 9.2.6 VenturiMeter ...... 354 9.2.7 Effect of Compressibility in Gas Flow Measurement ...... 356 9.2.8 Sonic Oriﬁce or the Sonic Nozzle ...... 358 9.2.9 Selection of Variable Area Flow Meters ...... 361 9.3 RotameterorDragEffectFlowMeter ...... 361 9.3.1 RotameterAnalysis ...... 362 9.4 Miscellaneous Types of Flow Meters ...... 366 9.4.1 Positive Displacement Meters ...... 366 9.4.2 Vortex Shedding Type Flow Meter ...... 367 9.4.3 TurbineFlowMeter ...... 367 9.5 Factors to Be Considered in the Selection of Flow Meters ...... 369 9.6 CalibrationofFlowMeters ...... 369 9.6.1 Methods of Calibration ...... 369 9.6.2 Soap Film Burette ...... 370 9.6.3 BellProverSystem...... 372 9.6.4 Flying Start—Flying Finish Method with Static Weighing ...... 373 10 Stagnation and Bulk Mean Temperature ...... 375 10.1 Stagnation Temperature Measurement ...... 375 10.1.1 Shielded Thermocouple Stagnation Temperature Probe ...... 376 10.1.2 DualThinFilmEnthalpyProbe ...... 377 10.2 BulkMeanTemperature...... 378 10.2.1 Flow in a Rectangular Duct ...... 380 ExerciseIII...... 382 xxiv Contents

Part IV Thermo-physical Properties, Radiation Properties of Surfaces, Gas Concentration, Force/Acceleration, torque, and Power 11 Measurement of Thermophysical Properties ...... 391 11.1 Introduction ...... 391 11.2 Thermal Conductivity ...... 392 11.2.1 Basic Ideas ...... 392 11.3 Steady State Methods ...... 393 11.3.1 Guarded Hot Plate Apparatus: Solid Sample ...... 393 11.3.2 Guarded Hot Plate Apparatus: Liquid Sample ...... 396 11.3.3 Radial Heat Conduction Apparatus for Liquids andGases ...... 397 11.3.4 Thermal Conductivity Comparator ...... 400 11.4 TransientMethod ...... 402 11.4.1 LaserFlashMethod ...... 402 11.5 Measurement of Heat Capacity ...... 404 11.5.1 Heat Capacity of a Solid ...... 404 11.5.2 Heat Capacity of Liquids ...... 407 11.6 Measurement of Calorific Value of Fuels ...... 407 11.6.1 Preliminaries...... 408 11.6.2 TheBombCalorimeter ...... 410 11.6.3 Continuous Flow Calorimeter ...... 413 11.7 Measurement of Viscosity of Fluids ...... 414 11.7.1 Laminar Flow in a Capillary ...... 415 11.7.2 Saybolt Viscometer ...... 418 11.7.3 Rotating Cylinder Viscometer ...... 419 12 Radiation Properties of Surfaces ...... 423 12.1 Introduction ...... 423 12.1.1 Definitions...... 424 12.2 Features of Radiation Measuring Instruments ...... 427 12.2.1 Components of a Reflectivity Measuring Instrument ...... 428 12.3 Integrating Sphere ...... 429 12.3.1 Hemispherical Emissivity ...... 430 12.3.2 Hemispherical Directional Reflectivity ...... 433 12.3.3 Directional Hemispherical Reflectivity ...... 434 12.4 MeasurementofEmissivity ...... 435 12.4.1 Emissivity Measurement Using an Integrating Radiometer ...... 436 12.4.2 Measurement of Emissivity by Transient Cooling in Vacuum ...... 436 12.4.3 Calorimetric Method of Emissivity Measurement ...... 439 12.4.4 Commercial Portable Ambient Temperature Emissometer ...... 442 Contents xxv

13 Gas Concentration ...... 445 13.1 Introduction ...... 445 13.1.1 Methods of Gas Concentration Measurement ...... 448 13.2 Non-Separation Methods ...... 449 13.2.1 Non-Dispersive Infrared Analyzer (NDIR) ...... 449 13.2.2 Differential Absorption LIDAR (DIAL) ...... 451 13.2.3 Chemiluminescence NOx Detection ...... 454 13.3 Separation Methods ...... 456 13.3.1 GasChromatography...... 456 13.3.2 Orsat Gas Analyzer ...... 459 13.3.3 Particulate Matter—Soot (or Smoke) ...... 460 14 Force/Acceleration, Torque, and Power ...... 467 14.1 Introduction ...... 467 14.2 ForceMeasurement...... 468 14.2.1 Platform Balance ...... 468 14.2.2 Force to Displacement Conversion ...... 469 14.2.3 ProvingRing...... 473 14.2.4 Conversion of Force to Hydraulic Pressure ...... 473 14.2.5 Piezoelectric Force Transducer ...... 474 14.3 Measurement of Acceleration ...... 474 14.3.1 Preliminary Ideas ...... 475 14.3.2 Characteristics of a Spring–Mass–Damper System . . . . . 476 14.3.3 Piezoelectric Accelerometer ...... 485 14.3.4 Laser Doppler Vibrometer ...... 486 14.3.5 Fiber Optic Accelerometer ...... 489 14.4 Measurement of Torque and Power ...... 490 14.4.1 Mechanical Brake Arrangement—Prony Brake ...... 490 14.4.2 Electric Generator as a Dynamometer ...... 491 14.4.3 Measure Shear Stress on the Shaft ...... 492 14.4.4 Tachometer—Mechanical Device ...... 495 14.4.5 Non-Contact Optical RPM Meter...... 495 ExerciseIV ...... 498

Part V Data Manipulation and Examples from Laboratory Practice 15 Data Manipulation ...... 505 15.1 Introduction ...... 505 15.2 Mechanical Signal Conditioning ...... 506 15.2.1 Betz Manometer ...... 506 15.2.2 Optical Measurement of Twist Angle in a Wire ...... 508 15.3 Electrical/Electronic Signal Conditioning ...... 508 15.3.1 Signal Conditioning ...... 509 15.3.2 Signal Ampliﬁcation and Manipulation ...... 509 15.3.3 Digital Panel Meter or Digital Voltmeter ...... 522 xxvi Contents

15.3.4 CurrentLoop...... 524 16 Examples from Laboratory Practice ...... 529 16.1 Introduction ...... 529 16.2 Thermocouple Calibration Using a Data Logger ...... 530 16.3 Calibration of a Digital Differential Pressure Gauge ...... 533 16.4 Signal Conditioning for Torque Measurement Using Strain Gauges ...... 534 16.5 Software ...... 536 ExerciseV ...... 538

Appendix A: Bibliographic Notes and References ...... 539 Appendix B: Useful Tables ...... 545 Index ...... 555 About the Author

Prof. S. P. Venkateshan obtained his Ph.D. from the Indian Institute of Science, Bangalore, in 1977. After spending three years at Yale University, he joined the Indian Institute of Technology (IIT) Madras in 1982. He retired as Professor and Head, Department of Mechanical Engineering in 2012. Subsequently, he served IIT Madras as Professor Emeritus till November 2016. He has taught subjects related to heat transfer, thermodynamics, measurements, and computational methods. His research interests include radiation heat transfer, conjugate heat transfer—experimental and numerical, measurement of thermophysical properties by inverse heat transfer methods, and instrumentation. He has graduated 30 doctoral candidates and 25 master’s candidates. He was also Head of Regional Sophisticated Instrumentation Centre (RSIC) at IIT Madras. In addition to more than 200 published research papers to his credit, Prof. Venkateshan has also authored several books.

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