Mechanical Measurements - 2nd Edition
S.P. Venkateshan
Professor Emeritus Department of Mechanical Engineering Indian Institute of Technology Madras
Chennai, INDIA
Mechanical measurements 2nd Edition
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 unitW
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
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 unitW
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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