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| موضوع: كتاب Mechanical Measurements السبت 01 يناير 2022, 12:47 am | |
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أخواني في الله أحضرت لكم كتاب Mechanical Measurements - 2nd Edition S.P. Venkateshan Professor Emeritus Department of Mechanical Engineering Indian Institute of Technology Madras Chennai, INDIA
و المحتوى كما يلي :
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, 3×108m/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 Eb Total emissive power of a black body, W/m2 xiiixiv Ebλ Spectral emissive power of a black body, W/m2μm Es Shear modulus, Pa E˙ Enthalpy flux, W/m2 f Frequency, s−1 or Hz or Friction factor, no unit fD Doppler shift, Hz F Force, N F A Fuel air ratio, kg(f uel)/kg(air) g Acceleration due to gravity, standard value 9.804m/s2 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 Iλ Spectral radiation intensity, W/m2 ·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 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 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 unitxv Nu Nusselt number, no unit p Pressure, Pa or Probability, no unit ppmV Gas concentration based on volume, m−3 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 Q˙ T Thomson heat (power), W R Electrical resistance, Ω or Fluid friction resistance, 1/m · s or radius, m or Thermal resistance, m2◦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, 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 T tp Triple point temperature, K T90 Temperature according to ITS90, Kxvi 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, Ω XL Inductive reactance, Ω Y Expansion factor, no unit Z Electrical impedance, Ω Acronyms ac Alternating current dc Direct currebt 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 DIAL Differential Absorption LIDAR DOE Design Of Experiment 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 ISA Instrument Society of America IR Infra Red 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 Computerxvii 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 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 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, Cp/CV δ Thickness, mm or μm or Displacement, m Δ Change or difference or error in the quantity that follows Δ 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 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, 5.67×10−8W/m2K4 or Thomson coefficient, μV/◦C or Standard deviation, appropriate unitxviii σe Estimated standard distribution, appropriate unit σa Absorption cross section, m2 σs Scattering cross section, m2 σt Total cross section, m2 σx 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 ωn Natural circular frequency, rad/s Ω Electrical resistance (Ohms) χ2 Chi squared distribution, appropriate unit ζ Damping ratio for a second order system, no unitPreface vii Acknowledgements xi Nomenclature xiii Contents xix I Measurements, Error Analysis and Design of Experiments 1 Measurements and Errors in measurement 3 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.1.1 Measurement categories . . . . . . . . . . . . . . . . . . . . . . . 4 1.1.2 General measurement scheme . . . . . . . . . . . . . . . . . . . 5 1.1.3 Some issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2 Errors in measurement . . . . . . . . . . . . . . . . . . . . . . . . . . 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 from replicate data . . 8 1.3.2 Error distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.3.3 Principle of Least Squares . . . . . . . . . . . . . . . . . . . . . 11 1.3.4 Error estimation - single sample . . . . . . . . . . . . . . . . . . 12 1.3.5 Student t distribution . . . . . . . . . . . . . . . . . . . . . . . . 17 1.3.6 Test for normality . . . . . . . . . . . . . . . . . . . . . . . . . . 19 1.3.7 Nonparametric tests . . . . . . . . . . . . . . . . . . . . . . . . . 28 1.3.8 Outliers and their rejection . . . . . . . . . . . . . . . . . . . . . 32 1.4 Propagation of errors . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 1.5 Specifications of instruments and their performance . . . . . . . . . 44 xixxx CONTENTS 2 Regression analysis 47 2.1 Introduction to regression analysis . . . . . . . . . . . . . . . . . . . 48 2.2 Linear regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 2.2.1 Linear fit by least squares . . . . . . . . . . . . . . . . . . . . . 49 2.2.2 Uncertainties in the fit parameters . . . . . . . . . . . . . . . . 51 2.2.3 Goodness of fit and the correlation coefficient . . . . . . . . . . 54 2.3 Polynomial regression . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 2.3.1 Method of least squares and normal equations . . . . . . . . . 54 2.3.2 Goodness of fit and the index of correlation or R2 . . . . . . . . 55 2.3.3 Multiple linear regression . . . . . . . . . . . . . . . . . . . . . . 57 2.4 General non-linear fit . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 2.5 χ2 test of goodness of fit . . . . . . . . . . . . . . . . . . . . . . . . . . 62 2.6 General discussion on regression analysis including special cases . 66 2.6.1 Alternate procedures of obtaining fit parameters . . . . . . . . 66 2.6.2 Segmented or piecewise regression . . . . . . . . . . . . . . . . 68 3 Design of experiments 73 3.1 Design of experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 3.1.1 Goal of experiments . . . . . . . . . . . . . . . . . . . . . . . . . 74 3.1.2 Full factorial design . . . . . . . . . . . . . . . . . . . . . . . . . 74 3.1.3 2k factorial design . . . . . . . . . . . . . . . . . . . . . . . . . . 75 3.1.4 More on full factorial design . . . . . . . . . . . . . . . . . . . . 78 3.1.5 One half factorial design . . . . . . . . . . . . . . . . . . . . . . 79 3.1.6 Other simple design . . . . . . . . . . . . . . . . . . . . . . . . . 82 Exercise I 89 I.1 Errors and error distributions . . . . . . . . . . . . . . . . . . . . . . 89 I.2 Propagation of errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 I.3 Regression analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 I.4 Design of experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 II Measurements of Temperature, Heat Flux and Heat Transfer Coefficient 4 Measurements of Temperature 103 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 4.2 Thermometry or the science and art of temperature measurement 104 4.2.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 4.2.2 Practical thermometry . . . . . . . . . . . . . . . . . . . . . . . . 108 4.3 Thermoelectric thermometry . . . . . . . . . . . . . . . . . . . . . . . 110 4.3.1 Thermoelectric effects . . . . . . . . . . . . . . . . . . . . . . . . 110 4.3.2 On the use of thermocouple for temperature measurement . . 117 4.3.3 Use of thermocouple tables and Practical aspects of thermoelectric thermometry . . . . . . . . . . . . . . . . . . . . . . . . . 120 4.4 Resistance thermometry . . . . . . . . . . . . . . . . . . . . . . . . . . 131 4.4.1 Basic ideas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 4.4.2 Platinum resistance thermometer and the Callendar correction132 4.4.3 RTD measurement circuits . . . . . . . . . . . . . . . . . . . . . 135CONTENTS xxi 4.4.4 Thermistors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 4.5 Pyrometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 4.5.1 Radiation fundamentals . . . . . . . . . . . . . . . . . . . . . . . 150 4.5.2 Brightness temperature and the vanishing filament pyrometer152 4.5.3 Total radiation pyrometer . . . . . . . . . . . . . . . . . . . . . . 157 4.5.4 Ratio Pyrometry and the two color pyrometer . . . . . . . . . . 159 4.5.5 Gas temperature measurement . . . . . . . . . . . . . . . . . . 161 4.6 Other temperature measurement techniques . . . . . . . . . . . . . 162 4.6.1 Liquid in glass or liquid in metal thermometers . . . . . . . . 163 4.6.2 Bimetallic thermometer . . . . . . . . . . . . . . . . . . . . . . 166 4.6.3 Liquid crystal thermometers . . . . . . . . . . . . . . . . . . . . 170 4.6.4 IC temperature sensor . . . . . . . . . . . . . . . . . . . . . . . 171 4.7 Measurement of transient temperature . . . . . . . . . . . . . . . . . 171 4.7.1 Temperature sensor as a first order system - Electrical analogy171 4.7.2 Response to step input . . . . . . . . . . . . . . . . . . . . . . . 173 4.7.3 Response to a ramp input . . . . . . . . . . . . . . . . . . . . . . 178 4.7.4 Response to a periodic input . . . . . . . . . . . . . . . . . . . . 179 5 Systematic errors in temperature measurement 183 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183 5.2 Examples of temperature measurement . . . . . . . . . . . . . . . . 183 5.2.1 Surface temperature measurement using a compensated probe183 5.2.2 Measurement of temperature inside a solid . . . . . . . . . . . 184 5.2.3 Measurement of temperature of a moving fluid . . . . . . . . . 185 5.2.4 Summary of sources of error in temperature measurement . . 186 5.3 Conduction error in thermocouple temperature measurement . . . 186 5.3.1 Lead wire model . . . . . . . . . . . . . . . . . . . . . . . . . . . 186 5.3.2 The single wire model . . . . . . . . . . . . . . . . . . . . . . . . 187 5.3.3 Heat loss through lead wire . . . . . . . . . . . . . . . . . . . . . 188 5.3.4 Typical application and thermometric error . . . . . . . . . . . 189 5.3.5 Measurement of temperature within a solid . . . . . . . . . . . 191 5.4 Measurement of temperature of a moving fluid . . . . . . . . . . . . 194 5.4.1 Temperature error due to radiation . . . . . . . . . . . . . . . . 194 5.4.2 Reduction of radiation error: use of radiation shield . . . . . . 196 5.4.3 Analysis of thermometer well problem . . . . . . . . . . . . . . 199 6 Heat flux and Heat Transfer Coefficient 205 6.1 Measurement of heat flux . . . . . . . . . . . . . . . . . . . . . . . . . 205 6.1.1 Foil type heat flux gauge . . . . . . . . . . . . . . . . . . . . . . 205 6.1.2 Transient analysis of foil gauge . . . . . . . . . . . . . . . . . . 210 6.1.3 Thin film sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . 212 6.1.4 Cooled thin wafer heat flux gauge . . . . . . . . . . . . . . . . . 213 6.1.5 Axial conduction guarded probe . . . . . . . . . . . . . . . . . . 214 6.1.6 Slug type sensor . . . . . . . . . . . . . . . . . . . . . . . . . . . 215 6.1.7 Slug type sensor response including non uniformity in temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218 6.1.8 Thin film heat flux gauge - Transient operation . . . . . . . . . 220 6.2 Measurement of heat transfer coefficient . . . . . . . . . . . . . . . . 223 6.2.1 Film coefficient transducer . . . . . . . . . . . . . . . . . . . . . 224xxii CONTENTS 6.2.2 Cylindrical heat transfer coefficient probe . . . . . . . . . . . . 225 Exercise II 229 II.1 Temperature measurement . . . . . . . . . . . . . . . . . . . . . . . . 229 II.2 Transient temperature measurement . . . . . . . . . . . . . . . . . . 235 II.3 Thermometric error . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237 II.4 Heat flux measurement . . . . . . . . . . . . . . . . . . . . . . . . . . 239 III Measurement of Pressure, Fluid velocity, Volume flow rate, Stagnation and Bulk mean temperatures 7 Measurement of Pressure 243 7.1 Basics of pressure measurement . . . . . . . . . . . . . . . . . . . . . 244 7.2 U - Tube manometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245 7.2.1 Well type manometer . . . . . . . . . . . . . . . . . . . . . . . . 247 7.2.2 Dynamic response of a U tube manometer . . . . . . . . . . . 249 7.3 Bourdon gauge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253 7.3.1 Dead weight tester . . . . . . . . . . . . . . . . . . . . . . . . . . 254 7.4 Pressure transducers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254 7.4.1 Pressure tube with bonded strain gauge . . . . . . . . . . . . . 255 7.4.2 Bridge circuits for use with strain gauges . . . . . . . . . . . . 259 7.4.3 Diaphragm/Bellows type transducer . . . . . . . . . . . . . . . 262 7.4.4 Capacitance type diaphragm gauge . . . . . . . . . . . . . . . . 266 7.4.5 Piezoelectric pressure transducer . . . . . . . . . . . . . . . . . 269 7.5 Measurement of pressure transients . . . . . . . . . . . . . . . . . . 269 7.5.1 Transient response of a bellows type pressure transducer . . 271 7.5.2 Transients in a force balancing element for measuring pressure273 7.6 Measurement of vacuum . . . . . . . . . . . . . . . . . . . . . . . . . 275 7.6.1 McLeod gauge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276 7.6.2 Pirani gauge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277 7.6.3 Ionization gauge . . . . . . . . . . . . . . . . . . . . . . . . . . . 278 7.6.4 Alphatron gauge . . . . . . . . . . . . . . . . . . . . . . . . . . . 279 8 Measurement of Fluid Velocity 281 8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282 8.2 Pitot - Pitot static and impact probes . . . . . . . . . . . . . . . . . . 282 8.2.1 Pitot and Pitot static tube . . . . . . . . . . . . . . . . . . . . . . 282 8.2.2 Effect of compressibility . . . . . . . . . . . . . . . . . . . . . . . 286 8.2.3 Supersonic flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . 288 8.2.4 Orientation effects and multi-hole probes . . . . . . . . . . . . 291 8.3 Velocity measurement based on thermal effects . . . . . . . . . . . . 293 8.3.1 Hot wire anemometer . . . . . . . . . . . . . . . . . . . . . . . . 293 8.3.2 Constant Temperature or CT anemometer . . . . . . . . . . . . 295 8.3.3 Useful heat transfer correlation . . . . . . . . . . . . . . . . . . 296 8.3.4 Constant Current or CC anemometer . . . . . . . . . . . . . . . 297 8.3.5 Practical aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . 299 8.3.6 Measurement of transients (velocity fluctuations) . . . . . . . 300CONTENTS xxiii 8.3.7 Directional effects on hot wire anemometer . . . . . . . . . . . 301 8.4 Doppler Velocimeter . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303 8.4.1 The Doppler effect . . . . . . . . . . . . . . . . . . . . . . . . . . 303 8.4.2 Ultrasonic Doppler velocity meter . . . . . . . . . . . . . . . . . 304 8.4.3 Laser Doppler velocity meter . . . . . . . . . . . . . . . . . . . . 307 8.5 Time of Flight Velocimeter . . . . . . . . . . . . . . . . . . . . . . . . 309 8.5.1 Simultaneous measurement of position and velocity . . . . . . 313 8.5.2 Cross correlation type velocity meter . . . . . . . . . . . . . . . 313 9 Volume flow rate 315 9.1 Measurement of volume flow rate . . . . . . . . . . . . . . . . . . . . 316 9.2 Variable area type flow meters . . . . . . . . . . . . . . . . . . . . . . 316 9.2.1 Principle of operation . . . . . . . . . . . . . . . . . . . . . . . . 316 9.2.2 Correction factor . . . . . . . . . . . . . . . . . . . . . . . . . . . 318 9.2.3 types of variable area flow meters . . . . . . . . . . . . . . . . . 318 9.2.4 Orifice plate meter . . . . . . . . . . . . . . . . . . . . . . . . . . 319 9.2.5 Flow nozzle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323 9.2.6 Venturi meter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323 9.2.7 Effect of compressibility in gas flow measurement . . . . . . . 326 9.2.8 Sonic orifice or the sonic nozzle . . . . . . . . . . . . . . . . . . 328 9.2.9 Selection of variable area flow meters . . . . . . . . . . . . . . . 330 9.3 Rotameter or Drag effect flow meter . . . . . . . . . . . . . . . . . . . 330 9.3.1 Rotameter analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 330 9.4 Miscellaneous types of flow meters . . . . . . . . . . . . . . . . . . . 334 9.4.1 Positive displacement meters . . . . . . . . . . . . . . . . . . . . 334 9.4.2 Vortex shedding type flow meter . . . . . . . . . . . . . . . . . . 334 9.4.3 Turbine flow meter . . . . . . . . . . . . . . . . . . . . . . . . . . 335 9.5 Factors to be considered in the selection of flow meters . . . . . . . 336 9.6 Calibration of flow meters . . . . . . . . . . . . . . . . . . . . . . . . . 337 9.6.1 Methods of calibration . . . . . . . . . . . . . . . . . . . . . . . . 337 9.6.2 Soap film burette . . . . . . . . . . . . . . . . . . . . . . . . . . . 337 9.6.3 Bell prover system . . . . . . . . . . . . . . . . . . . . . . . . . . 340 9.6.4 Flying start - Flying finish method with static weighing . . . 340 10 Stagnation and Bulk mean temperature 343 10.1 Stagnation temperature measurement . . . . . . . . . . . . . . . . . 344 10.1.1 Shielded thermocouple stagnation temperature probe . . . . . 344 10.1.2 Dual thin film enthalpy probe . . . . . . . . . . . . . . . . . . . 345 10.2 Bulk mean temperature . . . . . . . . . . . . . . . . . . . . . . . . . . 346 10.2.1 Flow in a rectangular duct . . . . . . . . . . . . . . . . . . . . . 348 Exercise III 351 III.1 Pressure measurement . . . . . . . . . . . . . . . . . . . . . . . . . . 351 III.2 Velocity measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . 353 III.3 Volume flow rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354xxiv CONTENTS IV Thermo-physical properties, Radiation properties of surfaces, Gas concentration, Force/Acceleration,torque and power 11 Measurement of thermo-physical properties 359 11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 360 11.2 Thermal conductivity . . . . . . . . . . . . . . . . . . . . . . . . . . . 360 11.2.1 Basic ideas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361 11.3 Steady state methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 361 11.3.1 Guarded hot plate apparatus: solid sample . . . . . . . . . . . 361 11.3.2 Guarded hot plate apparatus: liquid sample . . . . . . . . . . . 364 11.3.3 Radial heat conduction apparatus for liquids and gases . . . . 364 11.3.4 Thermal conductivity comparator . . . . . . . . . . . . . . . . . 367 11.4 Transient method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 369 11.4.1 Laser flash method . . . . . . . . . . . . . . . . . . . . . . . . . . 369 11.5 Measurement of heat capacity . . . . . . . . . . . . . . . . . . . . . . 370 11.5.1 Heat capacity of a solid . . . . . . . . . . . . . . . . . . . . . . . 370 11.5.2 Heat capacity of liquids . . . . . . . . . . . . . . . . . . . . . . . 373 11.6 Measurement of calorific value of fuels . . . . . . . . . . . . . . . . . 374 11.6.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374 11.6.2 The Bomb calorimeter . . . . . . . . . . . . . . . . . . . . . . . . 375 11.6.3 Continuous flow calorimeter . . . . . . . . . . . . . . . . . . . . 378 11.7 Measurement of viscosity of fluids . . . . . . . . . . . . . . . . . . . . 380 11.7.1 Laminar flow in a capillary . . . . . . . . . . . . . . . . . . . . . 380 11.7.2 Saybolt viscometer . . . . . . . . . . . . . . . . . . . . . . . . . . 383 11.7.3 Rotating cylinder viscometer . . . . . . . . . . . . . . . . . . . . 384 12 Radiation properties of surfaces 389 12.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 390 12.1.1 Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 391 12.2 Features of radiation measuring instruments . . . . . . . . . . . . . 393 12.2.1 Components of a reflectivity measuring instrument . . . . . . 393 12.3 Integrating sphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394 12.3.1 Hemispherical emissivity . . . . . . . . . . . . . . . . . . . . . . 395 12.3.2 Hemispherical directional reflectivity . . . . . . . . . . . . . . . 398 12.3.3 Directional hemispherical reflectivity . . . . . . . . . . . . . . . 399 12.4 Measurement of emissivity . . . . . . . . . . . . . . . . . . . . . . . . 400 12.4.1 Emissivity measurement using an integrating radiometer . . 400 12.4.2 Emissivity by transient cooling in vacuum . . . . . . . . . . . . 401 12.4.3 Calorimetric method of emissivity measurement . . . . . . . . 404 12.4.4 Commercial portable ambient temperature emissometer . . . 406 13 Gas concentration 409 13.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 410 13.1.1 Methods of gas concentration measurement . . . . . . . . . . . 412 13.2 Non separation methods . . . . . . . . . . . . . . . . . . . . . . . . . . 413 13.2.1 Non Dispersive Infrared Analyzer (NDIR) . . . . . . . . . . . . 413 13.2.2 Differential Absorption LIDAR (DIAL) . . . . . . . . . . . . . . 415 13.2.3 Chemiluminescence NOx detection . . . . . . . . . . . . . . . . 418CONTENTS xxv 13.3 Separation methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . 419 13.3.1 Gas Chromatography . . . . . . . . . . . . . . . . . . . . . . . . 419 13.3.2 Orsat gas analyzer . . . . . . . . . . . . . . . . . . . . . . . . . . 422 13.3.3 Particulate matter - Soot (or smoke) . . . . . . . . . . . . . . . 423 14 Force/Acceleration, torque and power 429 14.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 430 14.2 Force Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . 430 14.2.1 Platform balance . . . . . . . . . . . . . . . . . . . . . . . . . . . 430 14.2.2 Force to displacement conversion . . . . . . . . . . . . . . . . . 431 14.2.3 Proving ring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 435 14.2.4 Conversion of force to hydraulic pressure . . . . . . . . . . . . 435 14.2.5 Piezoelectric force transducer . . . . . . . . . . . . . . . . . . . 436 14.3 Measurement of acceleration . . . . . . . . . . . . . . . . . . . . . . . 436 14.3.1 Preliminary ideas . . . . . . . . . . . . . . . . . . . . . . . . . . . 436 14.3.2 Characteristics of a spring - mass - damper system . . . . . . 437 14.3.3 Piezoelectric accelerometer . . . . . . . . . . . . . . . . . . . . . 445 14.3.4 Laser Doppler Vibrometer . . . . . . . . . . . . . . . . . . . . . 446 14.3.5 Fiber Optic Accelerometer . . . . . . . . . . . . . . . . . . . . . 448 14.4 Measurement of torque and power . . . . . . . . . . . . . . . . . . . . 448 14.4.1 Mechanical brake arrangement - Prony brake . . . . . . . . . 449 14.4.2 Electric generator as a dynamometer . . . . . . . . . . . . . . . 449 14.4.3 Measure shear stress on the shaft . . . . . . . . . . . . . . . . . 450 14.4.4 Tachometer - Mechanical Device . . . . . . . . . . . . . . . . . . 453 14.4.5 Non contact optical RPM meter . . . . . . . . . . . . . . . . . . 453 Exercise IV 457 IV.1 Thermo-physical properties . . . . . . . . . . . . . . . . . . . . . . . . 457 IV.2 Radiation properties of surfaces . . . . . . . . . . . . . . . . . . . . . 459 IV.3 Gas concentration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 459 IV.4 Force, acceleration, Torque and Power . . . . . . . . . . . . . . . . . 459 V Data Manipulation and Examples from laboratory practice 15 Data Manipulation 465 15.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 466 15.2 Mechanical signal conditioning . . . . . . . . . . . . . . . . . . . . . . 466 15.2.1 Betz manometer . . . . . . . . . . . . . . . . . . . . . . . . . . . 467 15.2.2 Optical measurement of twist angle in a wire . . . . . . . . . . 468 15.3 Electrical/Electronic signal conditioning . . . . . . . . . . . . . . . . 468 15.3.1 Signal conditioning . . . . . . . . . . . . . . . . . . . . . . . . . . 469 15.3.2 Signal Amplification and manipulation . . . . . . . . . . . . . . 469 15.3.3 Digital panel meter or Digital voltmeter . . . . . . . . . . . . . 480 15.3.4 Current loop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 482 16 Examples from laboratory practice 487 16.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 488xxvi CONTENTS 16.2 Thermocouple calibration using a data logger . . . . . . . . . . . . . 489 16.3 Calibration of a digital differential pressure gauge . . . . . . . . . . 491 16.4 Signal conditioning for torque measurement using strain gauges . 492 16.5 Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 494 Exercise V 497 A Bibliographic Notes and References 499 A.1 Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 499 A.2 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 501 B Useful tables 505 Index R2, 55 R2 Ad j, 55 β, diameter ratio, 319 γ,ratio of specific heats, 326 acceleration, 436 accelerometer, 441 Fiber Optic , 448 Piezoelectric, 445 accuracy, 6, 44 acousto-optic cell, 413 aliases, 80 Alphatron gauge, 279 amplifier differential, 471 differentiating, 472 instrumentation, 474 integrating, 472 logarithmic, 473 summing, 470 analog to digital converter (ADC), 480, 488 angular velocity, 448 APD, 417 beat frequency, 447 Beer’s law, 416 bell prover, 340 Bernoulli principle, 283 best estimate, 8 Betz manometer, 467 bias, 6 bit, 480 black body cavity, 151 radiation, 150 Bomb calorimeter, 375 Bourdon gauge, 253 bridge full, 259, 264, 435 half, 259, 260 quarter, 259 burst signal, 308 calibration, 5, 6 Callendar correction, 132 calorific value, 360, 374 calorimetric method, 360, 370, 404 capacitance type pressure transducer, 266 capture efficiency, 424 Chauvenet’s criterion, 32 Chemiluminescence, 418 Chi Squared test, 62 circular frequency, 438 coefficient of thermal expansion, 166 cold junction, 113 Collis and Williams correlation, 296 compensated probe, 184 compressibility, 286, 326 conduction error, 184 confidence interval, 9 confounded, 81 constant head tank, 381 continuous flow calorimeter, 378 correlation index of, 55 correlation coefficient, 54 518 INDEX count, 480 covariance, 50 critical value, 64 cross section absorption, 416 extinction, 416, 426 total, 417 cubical expansion, 163 cumulative probability, 9 current loop, 482 damping coefficient, 438 critical, 438 damping ratio, 251, 440 dead weight tester, 254, 435 degrees of freedom, 15, 17, 65 derived quantity, 4, 40 Design of experiments, 74 DIAL, 415 dial gauge, 434 diaphragm/bellows gauge, 262 differential absorption, 416 diffuse, 391 digit, 481 digital data logger, 479, 488 digital panel meter (DPM), 480 digital voltmeter, 480 dimensional analysis, 74, 82 dimensionless, 83 dimensionless groups, 74 Dixon’s Q test, 39 dominant factor, 78 Doppler effect, 303 shift, 303, 447 velocimeter, 303 Laser, 307 ultrasonic, 304 drag coefficient, 331 drop resistor, 482 dual thin film probe, 345 dynamometer, 448 brake drum, 449 Electric generator, 449 electrical analog, 173 emissivity, 157, 214, 225, 390, 400 hemispherical, 391 spectral, 151, 153 total, 158 entropy, 112 equilibrium, 104 error estimator, 15 error propagation, 42 errors, 6 random, 6 systematic, 6 Euler number, 83 EXCEL, 494 Exhaust gas, 410 expansion factor, 326 factorial 2k, 75 fractional, 79 full, 74 one half, 79 quarter, 81 factors, 74 film coefficient, 224 filter, 476 high pass, 477 low pass, 477 neutral density, 155 notch, 476 red, 154 twin T, 476 fin analysis, 188, 192 first order system, 173 fit, 49 fixed point primary, 107 secondary, 108 flow coefficient, 318 flow meter calibration, 337 drag effect, 330 positive displacement type, 334 turbine, 335 variable area, 316 discharge coefficient, 318 flow nozzle, 323 irrecoverable pressure loss, 324 orifice plate, 319 pressure taps, 319 selection, 330 venturi, 323 variable area type, 346INDEX 519 vortex shedding type, 334 Flue gas, 410 fluid velocity, 282 flying start - flying finish, 340 force balancing element, 273 force measurement, 430 Fourier number, 369 full bridge, 492 Gardon gauge, 205 sensitivity, 207 gauge constant, 207 time constant, 211 transient analysis, 210 Gas Chromatography, 419 gas concentration, 409 gas thermometer, 105 gauge factor, 256 Gaussian distribution, 8, 10 global polynomial, 115 gold point, 149 goodness of fit, 54 Graphic User Interface (GUI), 490 Grashof number, 364 heat capacity, 360, 370 liquid, 373 solid, 370 heat diffusion, 110 heat flux, 205 heat flux sensor axial conduction guarded, 214 slug type, 215, 218 thin film, 212, 220 construction detail, 222 thin wafer, 213 heat transfer coefficient, 138, 223 convection, 172 cylindrical probe, 225 radiation, 200 heating value (HV), 379 high frequency transmitter, 493 high vacuum, 275 Hooke’s law, 433 hot wire anemometer, 293 constant current, 297 constant temperature, 295 hypotheses, 4 ice point, 106 ideal gas scale, 107 impact probe, 288 influence coefficient, 74 integrating radiometer, 400 integrating sphere, 394 interaction effect, 75 interpolation, 115 intrusive, 4 ionization gauge, 278 ITS90, 108 Joule heating, 110 Kelvin relations, 110, 112, 113 Kelvin sensing, 135 King’s law, 294 Kirchoff’s law, 470 Kolmogorov Smirnov two sample test, 29 LABVIEW, 494 laminar flow, 380 Laser Doppler Vibrometer, 446 LDV, 307 fringe system, 307 reference beam system, 308 lead wire model, 186 lead wires, 118 compensating, 119 least square method, 401 least squares, 11 levels, 74 Line reversal technique, 161 low pass filter, 306 LVDT, 263, 266 Mach number, 282 main effects, 76 manometer U - tube, 245 well type, 247 inclined tube, 247 mass flow rate, 316 MATLAB, 494 McLeod gauge, 276 mean, 8 measurements, 4 monochromator, 393520 INDEX multi-hole probe, 291 five hole, 292 three hole, 291 natural frequency, 438 NDIR, 413 Newtonian fluid, 380 non-intrusive, 5 non-linear fit, 60 normal distribution, 8 normal equations, 50 NTC thermistors, 140 opacity, 426 operational amplifier, 469 optical RPM meter, 453 Orsat gas analyzer, 422 orthogonal set, 79 outliers, 32 parity plot, 59 partial pressure, 410 phase lag, 181 Pierce’s criterion, 35 Pirani gauge, 277 Pitot static tube, 284 Pitot tube, 282, 347 Planck distribution, 150 platform balance, 430 Platinum 67, 121 Platinum resistance temperature scale, 132 Poisson ratio, 256, 263, 493 portable emissometer, 406 Prandtl number, 177 Prandtl tube, 284 pre-amplifier, 493 precise, 6 pressure dynamic, 283 stagnation, 282 static, 283 pressure coeffcient, 293 pressure transients, 269 primary quantity, 4 principal stresses, 450 Prony brake, 449 Propagation of errors, 40 proving ring, 435 pyrometer total radiation, 157 two color, 159 vanishing filament, 153 pyrometer equation ideal, 153 practical, 153 pyrometry, 149 QtiPlot, 67 radiation error, 194 radiation shield, 196 Rayleigh number, 176 recovery factor, 344 reentry, 209 reference ice point, 119 reflectance, 425 reflectivity bidirectional, 391 directional hemispherical, 391, 399 hemispherical directional, 393, 398 regression linear, 49 multiple linear, 57 polynomial, 54 simple model, 76 repeatability, 74 repeatable, 6 replicate, 74 resistance flow, 250, 271 specific, 255, 256 thermal, 173, 270 Resistance thermometer, 131 Platinum, 131 resolution, 44, 81, 480 response dynamic, 249 flat, 157 linear, 6 non-linear, 6, 140 periodic input, 179 ramp input, 178 steady state, 178, 181 step input, 173 transient, 178, 181, 249 Reynolds number, 55, 83, 199INDEX 521 Rotameter, 330 analysis, 330 rotating cylinder viscometer, 380, 384 RTD, 131, 346 Bridge circuit, 135 dissipation constant, 138 four wire, 132 lead wire compensation, 135 measurement circuits, 135 self heating, 138 temperature coefficient of resistance, 132 three wire, 132 sampling, 423 iso-kinetic, 424 Saybolt viscometer, 380, 383 search method, 60 Conjugate Gradient, 60 Levenberg-Marquardt, 60 steepest descent, 60 second order system, 251 Segmented or piecewise regression, 68 shear modulus, 432 shear stress, 450 shielded thermocouple, 344 signal conditioning, 492 electronic, 468 mechanical, 466 single wire model, 187 slip rings, 493 soap film burette, 337 software, 494 solar flux, 209 sonic nozzle, 328 soot, 423 spectroscope, 162 specular, 390 spring balance, 432 spring constant, 432 SRM, 368 standard error, 19 Stefan Boltzmann constant, 158, 195 Steinhart-Hart equation, 141 Stokes number, 424 Stolz equation, 319 strain gauge, 255 Strouhal number, 335 Student t distribution, 17 subsonic flow, 286 supersonic flow, 288 Tachometer, 453 temperature actual, 152 brightness, 152 bulk mean, 346 color, 159 inside a solid, 184 mixing cup, 347 moving fluid, 185, 194 solid, 191 stagnation , 344 surface, 183 systematic error, 183 transient, 171 true, 160 Test for normality, 19 χ2 test, 26 Box and whisker plot, 20 Jarque-Bera test, 24 Q-Q plot, 22 thermal conductivity, 360 comparator, 360, 367 Gaurded hot plate solid sample, 361 Guarded hot plate, 360 liquid sample, 364 Laser flash method, 360, 369 Radial heat conduction apparatus, 360, 364 thermistor circuit, 145 thermistors, 140 thermo-electricity Peltier effect, 110 Seebeck effect, 110 Thomson effect, 110 thermo-physical properties, 360 thermocouple bayonet probe, 127 differential, 128 junctions, 126 butt welding, 127 button, 127 exposed, 126 grounded, 126 separated wire, 126522 INDEX parallel, 129 types, 122 thermocouples series, 128 thermoelectric power, 121 thermometer bimetallic, 166 IC temperature sensor, 171 liquid crystal, 170 liquid in glass, 163 thermometer error, 189 thermometer well, 185, 199 thermometric error, 127, 189, 192, 199, 201 thermometric property, 105, 107 thermometry, 104 thermopile, 128, 129, 212 thermostat, 170 Thompson τ test, 38 time constant, 173 time of flight, 282 TOF, 282 velocimeter, 309 torque, 448 transmittance, 426 trend line option, 64 triple point of water, 106 USB port, 488 vacuum, 275 variance, 8 velocimeter cross correlation, 313 velocity of approach factor, 318 vena contracta, 323 viscosity, 360, 380 voltage gain, 470 volume flow rate, 316 wedge probe, 289 Wein’s approximation, 150 displacement law, 151 Young’s modulus, 166, 169, 263, 433, 493 zeroth law of thermodynamics, 104 Zhukaskas correlation, 199, 294
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