About the Book The first module The second module The third module The fourth module The fifth module About the Author S.P .

Transcription

1 S.P. Venkateshan

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3 MECHANICAL MEASUREMENTS (2nd Edition)

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5 MECHANICAL MEASUREMENTS (2nd Edition) S.P. Venkateshan Professor Emeritus Department of Mechanical Engineering Indian Institute of Technology Madras Chennai, INDIA John Wiley & Sons Ltd.

6 Mechanical Measurements (2nd Edition) 2015 S.P. Venkateshan First Edition: 2008 Reprint: 2009, 2010, 2013 Second Edition: 2015 This Edition Published by John Wiley & Sons Ltd The Atrium, Southern Gate Chichester, West Sussex PO19 8SQ United Kingdom Tel : +44 (0) Fax : +44 (0) customer@wiley.com Web : For distribution in rest of the world other than the Indian sub-continent Under licence from: Athena Academic Ltd. Suit LP24700, Lower Ground Floor St. John Street, London, ECIV 4PW. United Kingdom athenaacademic@gmail.com Web: athenaacademic.com ISBN : All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, except as permitted by the UK Copyright, Designs and Patents Act 1988, without the prior permission of the publisher. Designations used by companies to distinguish their products are often claimed as trademarks. All brand names and product names used in this book are trade names, service marks, trademarks or registered trademarks of their respective owners. The publisher is not associated with any product or vendor mentioned in this book. Library Congress Cataloging-in-Publication Data A catalogue record for this book is available from the British Library.

7 Dedicated to the Shakkottai Family

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9 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 Chpater 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 Chapter 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 as 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. S.P. Venkateshan vii

10 viii 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 1960 s. Training we received in 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 Measurements 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 mean while I have produced a video series (40 lectures each of 55 minutes duration on Measurements in Thermal Science ) that has been widely circulated. 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 minutes duration each, this time called Mechanical Measurements ). This is being broadcast over the Technology

11 ix 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 content 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! S.P. Venkateshan

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13 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 feed back also helped me in improving the material while transforming it to 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 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 qulaity of the book. I particularly thank Athena Academic Ltd and Wiley, UK for bringing out this text in an expeditious manner. I thank my wife for all support during my book writing activity. xi S.P. Venkateshan

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15 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/s 2 or Speed of sound, m/s or Any parameter, appropriate unit A Area, m 2 c Callendar correction, C or Linear damping coefficient, N s/m or Gas concentration, m 3 or Speed of light, m/s C Specific heat, J/kg C or Capacitance of a liquid system, m 2 or Capacitance of a gas system, m s 2 or Electrical capacitance, F C d Coefficient of discharge, no unit C D Drag coefficient, no unit C p Specific heat of a gas at constant pressure, J/kg C C V 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/m 2 or Young s modulus, Pa E b Total emissive power of a black body, W/m 2 xiii

16 xiv E bλ Spectral emissive power of a black body, W/m 2 μm E s Shear modulus, Pa Ė Enthalpy flux, W/m 2 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 9.804m/s 2 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/m 2 C or Head, m or Enthalpy, J/kg h Overall heat transfer coefficient, W/m 2 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, m 4 I λ Spectral radiation intensity, W/m 2 μm ste J Polar moment of inertia, m 4 k Boltzmann constant, ,J/K Number of factors in an experiment, no unit or Thermal conductivity, W/m C ka 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 ṁ 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 n i Number of levels for the i th factor, no unit N Number of data in the population, no unit or Number count in analog to digital conversion, no unit Strouhal number, no unit N St

17 xv Nu Nusselt number, no unit p Pressure, Pa or Probability, no unit ppm V Gas concentration based on volume, m 3 P Pressure, Pa Perimeter, m Power, W P D Dissipation constant, W/m p 0 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/m 2 Q Any derived quantity, appropriate unit or Heat transfer rate, W or Volume flow rate, m 3 /s etc. Q P Peltier heat (power), W Q T Thomson heat (power), W R Electrical resistance, Ω or Fluid friction resistance, 1/m s or radius, m or Thermal resistance, m 2 C/W R g Gas constant, J/kg K R Universal gas constant, J/mol K Re Reynolds number s Entropy, J/K or Entropy rate, W/K or Spacing, m S Surface area, m 2 Stk Stoke number, no unit S e Electrical sensitivity, appropriate unit S t Thermal sensitivity, appropriate unit t Time, s or Temperature, C or K or t - distribution or Thickness, m t Pt Platinum resistance temperature, C t 90 Temperature according to ITS90, C T Period of a wave, s T or Temperature, K or Torque, N m T B Brightness temperature, K T c Color temperature, K T st Steam point temperature, K T t Total or Stagnation temperature, K or C T tp Triple point temperature, K Temperature according to ITS90, K T 90

18 xvi u V V P V S V T W x X X C X L Y Z Uncertainty in a measured quantity, Appropriate units or ratio or percentage Potential difference(volts) or Volume, m 3 or Velocity, m/s Peltier voltage, μv Seebeck voltage, μv Thomson voltage, μv Mass specific heat product, J/ C or Weight of an object, N Displacement, m Indicated mean or average value of any quantity X Capacitive reactance, Ω Inductive reactance, Ω Expansion factor, no unit Electrical impedance, Ω Acronyms ac dc ADC APD BSN DAC DAQ DAS DIAL DOE DPM FID GC GC IR GC MS HC ISA IR LASER LDV LIDAR LVDT MS NDIR NO x Op Amp PC Alternating current Direct currebt Analog to Digital Converter Avalnche Photo Diode Bosch Smoke Number Digital to Analog Converter Data Acquisition Data Acquisition System Differential Absorption LIDAR Design Of Experiment Digital panel meter Flame Ionization Detector Gas Chromatography GC with Infrared spectrometer GC with Mass spectrometer Hydro Carbon Instrument Society of America Infra Red Light Amplification by Stimulated Emission of Radiation Laser Doppler Anemometer Light Detection and Ranging Linear Voltage Differential Transformer Mass Spectrometer Non Dispersive Infrared Analyzer Mixture of oxides of nitrogen Operational Amplifier Personal Computer

19 xvii PRT or PT RTD SRM USB Platinum Resistance Thermometer Resistance Temperature Detector Standard Reference Material 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 /C V δ Thickness, mm or μm or Displacement, m Δ Change or difference or error in the quantity that follows Δ ɛ Strain, m/m or more usually μm/m ε Emissivity, no unit ε λh Spectral Hemispherical emissivity, no unit ε h 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 μ Dynamic viscosity, kg/m s or Mean of data or Micro (10 6 ) ν Kinematic viscosity, m 2 /s or Poisson ratio, no unit π Mathematical constant, or Peltier emf, μv ρ Density, kg/m 3 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, W/m 2 K 4 or Thomson coefficient, μv / C or Standard deviation, appropriate unit

20 xviii σ e Estimated standard distribution, appropriate unit σ a Absorption cross section, m 2 σ s Scattering cross section, m 2 σ t Total cross section, m 2 σ x Standard deviation of the x s σ y Standard deviation of the y s σ xy Covariance θ Temperature difference, C τ Shear stress, Pa or Time constant, s or Transmittance, no unit ω Circular frequency, rad/s ω n Natural circular frequency, rad/s Ω Electrical resistance (Ohms) χ 2 Chi squared distribution, appropriate unit ζ Damping ratio for a second order system, no unit

21 Preface Acknowledgements Nomenclature Contents vii xi xiii xix I Measurements, Error Analysis and Design of Experiments 1 Measurements and Errors in measurement Introduction Measurement categories General measurement scheme Some issues Errors in measurement Systematic errors (Bias) Random errors Statistical analysis of experimental data Statistical analysis and best estimate from replicate data Error distribution Principle of Least Squares Error estimation - single sample Student t distribution Test for normality Nonparametric tests Outliers and their rejection Propagation of errors Specifications of instruments and their performance xix

22 xx CONTENTS 2 Regression analysis Introduction to regression analysis Linear regression Linear fit by least squares Uncertainties in the fit parameters Goodness of fit and the correlation coefficient Polynomial regression Method of least squares and normal equations Goodness of fit and the index of correlation or R Multiple linear regression General non-linear fit χ 2 test of goodness of fit General discussion on regression analysis including special cases Alternate procedures of obtaining fit parameters Segmented or piecewise regression Design of experiments Design of experiments Goal of experiments Full factorial design k factorial design More on full factorial design One half factorial design Other simple design Exercise I 89 I.1 Errors and error distributions I.2 Propagation of errors I.3 Regression analysis I.4 Design of experiments II Measurements of Temperature, Heat Flux and Heat Transfer Coefficient 4 Measurements of Temperature Introduction Thermometry or the science and art of temperature measurement Preliminaries Practical thermometry Thermoelectric thermometry Thermoelectric effects On the use of thermocouple for temperature measurement Use of thermocouple tables and Practical aspects of thermoelectric thermometry Resistance thermometry Basic ideas Platinum resistance thermometer and the Callendar correction RTD measurement circuits

23 CONTENTS xxi Thermistors Pyrometry Radiation fundamentals Brightness temperature and the vanishing filament pyrometer Total radiation pyrometer Ratio Pyrometry and the two color pyrometer Gas temperature measurement Other temperature measurement techniques Liquid in glass or liquid in metal thermometers Bimetallic thermometer Liquid crystal thermometers IC temperature sensor Measurement of transient temperature Temperature sensor as a first order system - Electrical analogy Response to step input Response to a ramp input Response to a periodic input Systematic errors in temperature measurement Introduction Examples of temperature measurement Surface temperature measurement using a compensated probe Measurement of temperature inside a solid Measurement of temperature of a moving fluid Summary of sources of error in temperature measurement Conduction error in thermocouple temperature measurement Lead wire model The single wire model Heat loss through lead wire Typical application and thermometric error Measurement of temperature within a solid Measurement of temperature of a moving fluid Temperature error due to radiation Reduction of radiation error: use of radiation shield Analysis of thermometer well problem Heat flux and Heat Transfer Coefficient Measurement of heat flux Foil type heat flux gauge Transient analysis of foil gauge Thin film sensors Cooled thin wafer heat flux gauge Axial conduction guarded probe Slug type sensor Slug type sensor response including non uniformity in temperature Thin film heat flux gauge - Transient operation Measurement of heat transfer coefficient Film coefficient transducer

24 xxii CONTENTS Cylindrical heat transfer coefficient probe Exercise II 229 II.1 Temperature measurement II.2 Transient temperature measurement II.3 Thermometric error II.4 Heat flux measurement III Measurement of Pressure, Fluid velocity, Volume flow rate, Stagnation and Bulk mean temperatures 7 Measurement of Pressure Basics of pressure measurement U - Tube manometer Well type manometer Dynamic response of a U tube manometer Bourdon gauge Dead weight tester Pressure transducers Pressure tube with bonded strain gauge Bridge circuits for use with strain gauges Diaphragm/Bellows type transducer Capacitance type diaphragm gauge Piezoelectric pressure transducer Measurement of pressure transients Transient response of a bellows type pressure transducer Transients in a force balancing element for measuring pressure Measurement of vacuum McLeod gauge Pirani gauge Ionization gauge Alphatron gauge Measurement of Fluid Velocity Introduction Pitot - Pitot static and impact probes Pitot and Pitot static tube Effect of compressibility Supersonic flow Orientation effects and multi-hole probes Velocity measurement based on thermal effects Hot wire anemometer Constant Temperature or CT anemometer Useful heat transfer correlation Constant Current or CC anemometer Practical aspects Measurement of transients (velocity fluctuations)

25 CONTENTS xxiii Directional effects on hot wire anemometer Doppler Velocimeter The Doppler effect Ultrasonic Doppler velocity meter Laser Doppler velocity meter Time of Flight Velocimeter Simultaneous measurement of position and velocity Cross correlation type velocity meter Volume flow rate Measurement of volume flow rate Variable area type flow meters Principle of operation Correction factor types of variable area flow meters Orifice plate meter Flow nozzle Venturi meter Effect of compressibility in gas flow measurement Sonic orifice or the sonic nozzle Selection of variable area flow meters Rotameter or Drag effect flow meter Rotameter analysis Miscellaneous types of flow meters Positive displacement meters Vortex shedding type flow meter Turbine flow meter Factors to be considered in the selection of flow meters Calibration of flow meters Methods of calibration Soap film burette Bell prover system Flying start - Flying finish method with static weighing Stagnation and Bulk mean temperature Stagnation temperature measurement Shielded thermocouple stagnation temperature probe Dual thin film enthalpy probe Bulk mean temperature Flow in a rectangular duct Exercise III 351 III.1 Pressure measurement III.2 Velocity measurement III.3 Volume flow rate

26 xxiv CONTENTS IV Thermo-physical properties, Radiation properties of surfaces, Gas concentration, Force/Acceleration,torque and power 11 Measurement of thermo-physical properties Introduction Thermal conductivity Basic ideas Steady state methods Guarded hot plate apparatus: solid sample Guarded hot plate apparatus: liquid sample Radial heat conduction apparatus for liquids and gases Thermal conductivity comparator Transient method Laser flash method Measurement of heat capacity Heat capacity of a solid Heat capacity of liquids Measurement of calorific value of fuels Preliminaries The Bomb calorimeter Continuous flow calorimeter Measurement of viscosity of fluids Laminar flow in a capillary Saybolt viscometer Rotating cylinder viscometer Radiation properties of surfaces Introduction Definitions Features of radiation measuring instruments Components of a reflectivity measuring instrument Integrating sphere Hemispherical emissivity Hemispherical directional reflectivity Directional hemispherical reflectivity Measurement of emissivity Emissivity measurement using an integrating radiometer Emissivity by transient cooling in vacuum Calorimetric method of emissivity measurement Commercial portable ambient temperature emissometer Gas concentration Introduction Methods of gas concentration measurement Non separation methods Non Dispersive Infrared Analyzer (NDIR) Differential Absorption LIDAR (DIAL) Chemiluminescence NO x detection

27 CONTENTS xxv 13.3 Separation methods Gas Chromatography Orsat gas analyzer Particulate matter - Soot (or smoke) Force/Acceleration, torque and power Introduction Force Measurement Platform balance Force to displacement conversion Proving ring Conversion of force to hydraulic pressure Piezoelectric force transducer Measurement of acceleration Preliminary ideas Characteristics of a spring - mass - damper system Piezoelectric accelerometer Laser Doppler Vibrometer Fiber Optic Accelerometer Measurement of torque and power Mechanical brake arrangement - Prony brake Electric generator as a dynamometer Measure shear stress on the shaft Tachometer - Mechanical Device Non contact optical RPM meter Exercise IV 457 IV.1 Thermo-physical properties IV.2 Radiation properties of surfaces IV.3 Gas concentration IV.4 Force, acceleration, Torque and Power V Data Manipulation and Examples from laboratory practice 15 Data Manipulation Introduction Mechanical signal conditioning Betz manometer Optical measurement of twist angle in a wire Electrical/Electronic signal conditioning Signal conditioning Signal Amplification and manipulation Digital panel meter or Digital voltmeter Current loop Examples from laboratory practice Introduction

28 xxvi CONTENTS 16.2 Thermocouple calibration using a data logger Calibration of a digital differential pressure gauge Signal conditioning for torque measurement using strain gauges Software Exercise V 497 A Bibliographic Notes and References 499 A.1 Bibliographic Notes A.2 References B Useful tables 505 Index 517

29 I Module I is a comprehensive introduction to any measurement including Mechanical Measurements - that are of interest to a mechanical engineer. This module consists of three chapters. Chapter 1 deals with basics of measurement along with the description of errors that almost always accompany any measurement. Chapter 2 considers a very important topic, viz. regression analysis. Regression helps in summarizing the measurements by evolving relationships between measured quantities that represent outcome of experiments. Chapter 3 discusses about design of experiments (DOE). Goal of DOE is to reduce the number of experiments that need to be performed and yet get the most amount of information about the outcome of the experiments.

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