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About the Book Mechanical Measurements is a core subject in the Mechanical Engineering curriculum. The course prepares the undergraduate (may skip some advanced topics and analyses) student for understanding and appreciating the practical aspects of Mechanical Engineering. The topics covered in the ...

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About the Book Mechanical Measurements is a core subject in the Mechanical Engineering curriculum. The course prepares the undergraduate (may skip some advanced topics and analyses) student for understanding and appreciating the practical aspects of Mechanical Engineering. The topics covered in the book will be very useful for post graduate students. The book presents a sound foundation on the basics of measurement science as applied to measurement of quantities that are critical to a mechanical engineer. Measurement involves both an Art part pertaining to the skills to be developed for performing “good” measurements and a Science part that prepares the engineer to innovate new measurement techniques. The role of this text is to prepare the engineering student to do both. The book contains sixteen chapters and is divided in to five modules. The first module contains 3 Chapters that deal with measurement errors and statistical analysis of data, regression analysis and design of experiments. The second module comprises of 3 Chapters that deal with the measurement of very important quantities that are central to thermal measurements viz., temperature, systematic errors in temperature measurements and heat flux. The third module comprises of 4 Chapters and deals with the measurement of Pressure, Velocity, Volume flow rate and Bulk mean temperature. The fourth module comprises of 4 Chapters and deals with the measurement of Thermophysical properties, Radiation properties of surfaces, Gas concentration, Force/Acceleration, torque and power. The fifth module consists of Chapters 15 and 16 and deals with computer assisted data acquisition-data manipulation and examples from laboratory practice. Worked examples are presented throughout the book. Exercises for the student are arranged at the end of each module. Useful Tables are provided in Appendix. Glossary, nomenclature and subject index are arranged to help the reader navigate through the book with ease.

S.P. Venkateshan

About the Author The author is presently Professor Emeritus in the Department of Mechanical Engineering of Indian Institute of Technology, Madras. The author was involved in instrumentation and building of experimental facilities since he started his career in research and teaching in 1970. Earliest work of the author was in building solid state lasers while working on a project for the Aeronautics Research and Development Board at Indian Institute of Science, Bangalore. Subsequently he worked on design of experimental rig for measurement of energy transfer in molecular beams at Yale University, USA. After joining IIT Madras he has been guiding research in the general area of Heat Transfer and has seen many experimental facilities developed over the past thirty five years. He also worked with NASA at JPL, USA in design of facilities for the National Archives during 1993-94. Impetus for the book came from his experience in design and building of research facilities as well as from his teaching of a subject called Measurements in Thermal Science for the past twenty five years at IIT Madras.

S.P. Venkateshan

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MECHANICAL MEASUREMENTS (2nd Edition)

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MECHANICAL MEASUREMENTS (2nd Edition)

S.P. Venkateshan

Professor Emeritus Department of Mechanical Engineering Indian Institute of Technology Madras Chennai, INDIA

John Wiley & Sons Ltd.

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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)1243 779777 Fax : +44 (0)1243 775878 e-mail : [email protected] Web : www.wiley.com

For distribution in rest of the world other than the Indian sub-continent Under licence from:

Athena Academic Ltd. Suit LP24700, Lower Ground Floor 145-157 St. John Street, London, ECIV 4PW. United Kingdom Email: [email protected] Web: athenaacademic.com ISBN : 978-11-1911-556-4 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.

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Dedicated to the Shakkottai Family

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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

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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

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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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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. S.P. Venkateshan xi

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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

A c

C

Cd CD Cp CV D d

E

Eb

Acceleration, m/s2 or Speed of sound, m/s or Any parameter, appropriate unit Area, m2 Callendar correction, ◦ C or Linear damping coefficient, N · s/m or Gas concentration, m−3 or Speed of light, 3 × 108 m/s Specific heat, J/k g◦ C or Capacitance of a liquid system, m2 or Capacitance of a gas system, m · s2 or Electrical capacitance, F Coefficient of discharge, no unit Drag coefficient, no unit Specific heat of a gas at constant pressure, J/k g◦ C Specific heat of a gas at constant volume, J/k g◦ C Diameter, m Diameter, m or Degrees of freedom or Piezoelectric constant, Coul/N Electromotive force (emf), V or Emissive power, W/m2 or Young’s modulus, Pa Total emissive power of a black body, W/m2

xiii

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xiv E bλ Es E˙ f fD F FA g G

Gr h

h¯ HV HHV LHV I

Iλ J k ¯ kA K L m

˙ m M

n ni N NSt

Spectral emissive power of a black body, W/m2 μ m Shear modulus, Pa Enthalpy flux, W/m2 Frequency, s−1 or H z or Friction factor, no unit Doppler shift, H z Force, N Fuel air ratio, k g( f uel)/k g(air) Acceleration due to gravity, standard value 9.804m/s2 Gain, Numerical factor or in dB or Gauge constant, appropriate units or Bulk modulus, Pa Grashof number, no unit Heat transfer coefficient, W/m2◦ C or Head, m or Enthalpy, J/k g Overall heat transfer coefficient, W/m2◦ C Heating value, J/k g Higher Heating Value, J/k g Lower Heating Value, J/k g Electrical current, A or Influence coefficient, appropriate unit or Moment of inertia, m4 Spectral radiation intensity, W/m2 · μ m · ste Polar moment of inertia, m4 Boltzmann constant, 1.39 × 10−23 ,J/K Number of factors in an experiment, no unit or Thermal conductivity, W/m◦ C Thermal conductivity area product, W · m/◦ C Flow coefficient, no unit or Spring constant, N/m Length, m Fin parameter, m−1 or Mass, k g or Mean of a set of data, appropriate unit Mass flow rate, k g/s Mach number, no unit or Molecular weight, g/mol or Moment, N · m or Velocity of approach factor, no unit Index in a polytropic process, no unit or Number of data in a sample, no unit Number of levels for the i th factor, no unit Number of data in the population, no unit or Number count in analog to digital conversion, no unit Strouhal number, no unit

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xv Nu p p pm V P

PD p0 Pe Pr q Q

Q˙ P Q˙ T R

Rg ℜ Re s S Stk Se St t

tP t t 90 T T TB Tc T st Tt T tp T90

Nusselt number, no unit Pressure, Pa or Probability, no unit Gas concentration based on volume, m−3 Pressure, Pa Perimeter, m Power, W Dissipation constant, W/m Stagnation pressure, Pa Peclet number = R e · P r, no unit Prandtl number, ν/α, no unit Electrical charge (Coulomb), Coul or Heat flux, W/m2 Any derived quantity, appropriate unit or Heat transfer rate, W or Volume flow rate, m3 /s etc. Peltier heat (power), W Thomson heat (power), W Electrical resistance, Ω or Fluid friction resistance, 1/m · s or radius, m or Thermal resistance, m2◦ C/W Gas constant, J/k g · K Universal gas constant, J/mol · K Reynolds number Entropy, J/K or Entropy rate, W/K or Spacing, m Surface area, m2 Stoke number, no unit Electrical sensitivity, appropriate unit Thermal sensitivity, appropriate unit Time, s or Temperature, ◦ C or K or t - distribution or Thickness, m Platinum resistance temperature, ◦ C Temperature according to ITS90, ◦ C Period of a wave, s or Temperature, K or Torque, N · m Brightness temperature, K Color temperature, K Steam point temperature, K Total or Stagnation temperature, K or ◦ C Triple point temperature, K Temperature according to ITS90, K

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xvi u V

VP VS VT W

x X¯ XC XL Y Z

Uncertainty in a measured quantity, Appropriate units or ratio or percentage Potential difference(Volts) or Volume, m3 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

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xvii PRT or PT RTD SRM USB

Platinum Resistance Thermometer Resistance Temperature Detector Standard Reference Material Universal Serial Bus

Greek symbols α

β

γ δ

Δ ǫ ε ελh εh η φ κ λ μ

ν π ρ

σ

Area (fractional) of the tail of the χ2 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 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 ◦ Ratio of specific heats of a gas, C p /C V Thickness, mm or μ m or Displacement, m Change or difference or error in the quantity that follows Δ Strain, m/m or more usually μ m/m Emissivity, no unit Spectral Hemispherical emissivity, no unit Total Hemispherica...