Mechanical Measurements

Description

This book focuses both on the basics and more complex topics in mechanical measurements such as measurement errors & statistical analysis of data, regression analysis, heat flux, measurement of pressure, and radiation properties of surfaces. End of chapter problems, solved illustrations, and exercise problems are presented throughout the book to augment learning. It is a useful reference for students in both undergraduate and postgraduate programs. >^ Preface to the Second Edition Preface to the First Edition Acknowledgements Nomenclature Latin Alphabetical Symbols Acronyms Greek Symbols Contents About the Author Part I Measurements, Error Analysis and Design of Experiments 1 Measurements and Errors in Measurement 1.1 Introduction 1.1.1 Measurement Categories 1.1.2 General Measurement Scheme 1.1.3 Some Issues 1.2 Errors in Measurement 1.2.1 Systematic Errors (Bias) 1.2.2 Random Errors 1.3 Statistical Analysis of Experimental Data 1.3.1 Statistical Analysis and Best Estimate from Replicate Data 1.3.2 Error Distribution 1.3.3 Principle of Least Squares 1.3.4 Error Estimation - Single Sample 1.3.5 Student t Distribution 1.3.6 Test for Normality 1.3.7 Non Parametric Tests 1.3.8 Outliers and Their Rejection 1.4 Propagation of Errors 1.5 Specifications of Instruments and Their Performance 2 Regression Analysis 2.1 Introduction to Regression Analysis 2.2 Linear Regression 2.2.1 Linear Fit by Least Squares 2.2.2 Uncertainties in the Fit Parameters 2.2.3 Goodness of Fit and the Correlation Coefficient 2.3 Polynomial Regression 2.3.1 Method of Least Squares and Normal Equations 2.3.2 Goodness of Fit and the Index of Correlation or R2 2.3.3 Multiple Linear Regression 2.4 General Non-linear Fit 2.5 χ2 Test of Goodness of Fit 2.6 General Discussion on Regression Analysis Including Special Cases 2.6.1 Alternate Procedures of Obtaining Fit Parameters 2.6.2 Segmented or Piecewise Regression 3 Design of Experiments 3.1 Design of Experiments 3.1.1 Goal of Experiments 3.1.2 Full Factorial Design 3.1.3 2k Factorial Design 3.1.4 More on Full Factorial Design 3.1.5 One Half Factorial Design 3.1.6 Other Simple Design Part II Measurements of Temperature, Heat Flux, and Heat Transfer Coefficient 4 Measurements of Temperature 4.1 Introduction 4.2 Thermometry or the Science and Art of Temperature Measurement 4.2.1 Preliminaries 4.2.2 Practical Thermometry 4.3 Thermoelectric Thermometry 4.3.1 Thermoelectric Effects 4.3.2 On the Use of Thermocouple for Temperature Measurement 4.3.3 Use of Thermocouple Tables and Practical Aspects of Thermoelectric Thermometry 4.4 Resistance Thermometry 4.4.1 Basic Ideas 4.4.2 Platinum Resistance Thermometer and the Callendar Correction 4.4.3 RTD Measurement Circuits 4.4.4 Thermistors 4.5 Pyrometry 4.5.1 Radiation Fundamentals 4.5.2 Brightness Temperature and the Vanishing Filament Pyrometer 4.5.3 Total Radiation Pyrometer 4.5.4 Ratio Pyrometer and the Two-Color Pyrometer 4.5.5 Gas Temperature Measurement 4.6 Other Temperature Measurement Techniques 4.6.1 Liquid in Glass or Liquid in Metal Thermometers 4.6.2 Bimetallic Thermometer 4.6.3 Liquid Crystal Thermometers 4.6.4 IC Temperature Sensor 4.7 Measurement of Transient Temperature 4.7.1 Temperature Sensor as a First-Order System—Electrical Analogy 4.7.2 Response to Step Input 4.7.3 Response to a Ramp Input 4.7.4 Response to a Periodic Input 5 Systematic Errors in Temperature Measurement 5.1 Introduction 5.2 Examples of Temperature Measurement 5.2.1 Surface Temperature Measurement Using a Compensated Probe 5.2.2 Measurement of Temperature Inside a Solid 5.2.3 Measurement of Temperature of a Moving Fluid 5.2.4 Summary of Sources of Error in Temperature Measurement 5.3 Conduction Error in Thermocouple Temperature Measurement 5.3.1 Lead Wire Model 5.3.2 The Single Wire Model 5.3.3 Heat Loss Through Lead Wire 5.3.4 Typical Application and Thermometric Error 5.3.5 Measurement of Temperature Within a Solid 5.4 Measurement of Temperature of a Moving Fluid 5.4.1 Temperature Error Due to Radiation 5.4.2 Reduction of Radiation Error: Use of Radiation Shield 5.4.3 Analysis of Thermometer Well Problem 6 Heat Flux and Heat Transfer Coefficient 6.1 Measurement of Heat Flux 6.1.1 Foil-Type Heat Flux Gauge 6.1.2 Transient Analysis of Foil Gauge 6.1.3 Thin Film Sensors 6.1.4 Cooled Thin Wafer Heat Flux Gauge 6.1.5 Axial Conduction Guarded Probe 6.1.6 Slug Type Sensor 6.1.7 Slug Type Sensor Response Including Non-Uniformity in Temperature 6.1.8 Thin Film Heat Flux Gauge—Transient Operation 6.2 Measurement of Heat Transfer Coefficient 6.2.1 Film Coefficient Transducer 6.2.2 Cylindrical Heat Transfer Coefficient Probe Part III Measurement of Pressure, Fluid Velocity, Volume Flow Rate, Stagnation, and Bulk Mean Temperatures 7 Measurement of Pressure 7.1 Basics of Pressure Measurement 7.2 U-Tube Manometer 7.2.1 Well Type Manometer 7.2.2 Dynamic Response of a U Tube Manometer 7.3 Bourdon Gauge 7.3.1 Dead Weight Tester 7.4 Pressure Transducers 7.4.1 Pressure Tube with Bonded Strain Gauge 7.4.2 Bridge Circuits for Use with Strain Gauges 7.4.3 Diaphragm/Bellows Type Transducer 7.4.4 Capacitance Type Diaphragm Gauge 7.4.5 Piezoelectric Pressure Transducer 7.5 Measurement of Pressure Transients 7.5.1 Thermal System 7.5.2 Pressure Measurement in a Liquid System 7.5.3 Pressure Measurement in a Gas System 7.5.4 Transient Response of a Bellows Type Pressure Transducer 7.5.5 Transients in a Force Balancing Element for Measuring Pressure 7.6 Measurement of Vacuum 7.6.1 McLeod Gauge 7.6.2 Pirani Gauge 7.6.3 Ionization Gauge 7.6.4 Alphatron Gauge 8 Measurement of Fluid Velocity 8.1 Introduction 8.2 Pitot–Pitot Static and Impact Probes 8.2.1 Pitot and Pitot Static Tube 8.2.2 Effect of Compressibility 8.2.3 Supersonic Flow 8.2.4 Orientation Effects and Multi-hole Probes 8.3 Velocity Measurement Based on Thermal Effects 8.3.1 Hot Wire Anemometer 8.3.2 Constant Temperature or CT Anemometer 8.3.3 Useful Heat Transfer Correlation 8.3.4 Constant Current or CC Anemometer 8.3.5 Practical Aspects 8.3.6 Measurement of Transients (Velocity Fluctuations) 8.3.7 Directional Effects on Hot Wire Anemometer 8.4 Doppler Velocimeter 8.4.1 The Doppler Effect 8.4.2 Ultrasonic Doppler Velocity Meter 8.4.3 Laser Doppler Velocity Meter 8.5 Time of Flight Velocimeter 8.5.1 Simultaneous Measurement of Position and Velocity 8.5.2 Cross Correlation Type Velocity Meter 9 Volume Flow Rate 9.1 Measurement of Volume Flow Rate 9.2 Variable Area Type Flow Meters 9.2.1 Principle of Operation 9.2.2 Correction Factor 9.2.3 Types of Variable Area Flow Meters 9.2.4 Orifice Plate Meter 9.2.5 Flow Nozzle 9.2.6 Venturi Meter 9.2.7 Effect of Compressibility in Gas Flow Measurement 9.2.8 Sonic Orifice or the Sonic Nozzle 9.2.9 Selection of Variable Area Flow Meters 9.3 Rotameter or Drag Effect Flow Meter 9.3.1 Rotameter Analysis 9.4 Miscellaneous Types of Flow Meters 9.4.1 Positive Displacement Meters 9.4.2 Vortex Shedding Type Flow Meter 9.4.3 Turbine Flow Meter 9.5 Factors to Be Considered in the Selection of Flow Meters 9.6 Calibration of Flow Meters 9.6.1 Methods of Calibration 9.6.2 Soap Film Burette 9.6.3 Bell Prover System 9.6.4 Flying Start—Flying Finish Method with Static Weighing 10 Stagnation and Bulk Mean Temperature 10.1 Stagnation Temperature Measurement 10.1.1 Shielded Thermocouple Stagnation Temperature Probe 10.1.2 Dual Thin Film Enthalpy Probe 10.2 Bulk Mean Temperature 10.2.1 Flow in a Rectangular Duct Part IV Thermo-physical Properties, Radiation Properties of Surfaces, Gas Concentration, Force/Acceleration, torque, and Power 11 Measurement of Thermophysical Properties 11.1 Introduction 11.2 Thermal Conductivity 11.2.1 Basic Ideas 11.3 Steady State Methods 11.3.1 Guarded Hot Plate Apparatus: Solid Sample 11.3.2 Guarded Hot Plate Apparatus: Liquid Sample 11.3.3 Radial Heat Conduction Apparatus for Liquids and Gases 11.3.4 Thermal Conductivity Comparator 11.4 Transient Method 11.4.1 Laser Flash Method 11.5 Measurement of Heat Capacity 11.5.1 Heat Capacity of a Solid 11.5.2 Heat Capacity of Liquids 11.6 Measurement of Calorific Value of Fuels 11.6.1 Preliminaries 11.6.2 The Bomb Calorimeter 11.6.3 Continuous Flow Calorimeter 11.7 Measurement of Viscosity of Fluids 11.7.1 Laminar Flow in a Capillary 11.7.2 Saybolt Viscometer 11.7.3 Rotating Cylinder Viscometer 12 Radiation Properties of Surfaces 12.1 Introduction 12.1.1 Definitions 12.2 Features of Radiation Measuring Instruments 12.2.1 Components of a Reflectivity Measuring Instrument 12.3 Integrating Sphere 12.3.1 Hemispherical Emissivity 12.3.2 Hemispherical Directional Reflectivity 12.3.3 Directional Hemispherical Reflectivity 12.4 Measurement of Emissivity 12.4.1 Emissivity Measurement Using an Integrating Radiometer 12.4.2 Measurement of Emissivity by Transient Cooling in Vacuum 12.4.3 Calorimetric Method of Emissivity Measurement 12.4.4 Commercial Portable Ambient Temperature Emissometer 13 Gas Concentration 13.1 Introduction 13.1.1 Methods of Gas Concentration Measurement 13.2 Non-Separation Methods 13.2.1 Non-Dispersive Infrared Analyzer (NDIR) 13.2.2 Differential Absorption LIDAR (DIAL) 13.2.3 Chemiluminescence NOx Detection 13.3 Separation Methods 13.3.1 Gas Chromatography 13.3.2 Orsat Gas Analyzer 13.3.3 Particulate Matter—Soot (or Smoke) 14 Force/Acceleration, Torque, and Power 14.1 Introduction 14.2 Force Measurement 14.2.1 Platform Balance 14.2.2 Force to Displacement Conversion 14.2.3 Proving Ring 14.2.4 Conversion of Force to Hydraulic Pressure 14.2.5 Piezoelectric Force Transducer 14.3 Measurement of Acceleration 14.3.1 Preliminary Ideas 14.3.2 Characteristics of a Spring–Mass–Damper System 14.3.3 Piezoelectric Accelerometer 14.3.4 Laser Doppler Vibrometer 14.3.5 Fiber Optic Accelerometer 14.4 Measurement of Torque and Power 14.4.1 Mechanical Brake Arrangement—Prony Brake 14.4.2 Electric Generator as a Dynamometer 14.4.3 Measure Shear Stress on the Shaft 14.4.4 Tachometer—Mechanical Device 14.4.5 Non-Contact Optical RPM Meter Part V Data Manipulation and Examples from Laboratory Practice 15 Data Manipulation 15.1 Introduction 15.2 Mechanical Signal Conditioning 15.2.1 Betz Manometer 15.2.2 Optical Measurement of Twist Angle in a Wire 15.3 Electrical/Electronic Signal Conditioning 15.3.1 Signal Conditioning 15.3.2 Signal Amplification and Manipulation 15.3.3 Digital Panel Meter or Digital Voltmeter 15.3.4 Current Loop 16 Examples from Laboratory Practice 16.1 Introduction 16.2 Thermocouple Calibration Using a Data Logger 16.3 Calibration of a Digital Differential Pressure Gauge 16.4 Signal Conditioning for Torque Measurement Using Strain Gauges 16.5 Software Appendix A Bibliographic Notes and References A.1 Bibliographic Notes A.2 References Appendix B Useful Tables Index