كتاب Theory and Design for Mechanical Measurements - Sixth Edition
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 كتاب Theory and Design for Mechanical Measurements - Sixth Edition

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أحضرت لكم كتاب
Theory and Design for Mechanical Measurements
Sixth Edition
Richard S. Figliola
Clemson University
Donald E. Beasley
Clemson University  

كتاب Theory and Design for Mechanical Measurements - Sixth Edition  T_a_d_12
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Contents
1 Basic Concepts of Measurement
Methods 1
1.1 Introduction 1
1.2 General Measurement System 2
1.3 Experimental Test Plan 5
1.4 Calibration 15
1.5 Standards 23
1.6 Presenting Data 31
1.7 Summary 35
References 35
Nomenclature 36
Problems 36
2 Static and Dynamic Characteristics of
Signals 43
2.1 Introduction 43
2.2 Input/output Signal Concepts 43
2.3 Signal Analysis 48
2.4 Signal Amplitude and Frequency 51
2.5 Fourier Transform and the Frequency
Spectrum 65
2.6 Summary 73
References 73
Suggested Reading 74
Nomenclature 74
Problems 74
3 Measurement System Behavior 81
3.1 Introduction 81
3.2 General Model for a Measurement
System 81
3.3 Special Cases of the General System
Model 85
3.4 Transfer Functions 108
3.5 Phase Linearity 110
3.6 Multiple-Function Inputs 112
3.7 Coupled Systems 114
3.8 Summary 116
References 116
Nomenclature 116
Problems 117
4 Probability and Statistics 123
4.1 Introduction 123
4.2 Statistical Measurement Theory 124
4.3 Describing the Behavior of a
Population 131
4.4 Statistics of Finite-Sized Data
Sets 135
4.5 Hypothesis Testing 141
4.6 Chi-squared Distribution 144
4.7 Regression Analysis 148
4.8 Data Outlier Detection 155
4.9 Number of Measurements
Required 156
4.10 Monte Carlo Simulations 158
4.11 Summary 160
References 161
Nomenclature 162
Problems 162
5 Uncertainty Analysis 168
5.1 Introduction 168
5.2 Measurement Errors 169
5.3 Design-Stage Uncertainty
Analysis 171
5.4 Identifying Error Sources 176
5.5 Systematic and Random Errors and
Standard Uncertainties 177
5.6 Uncertainty Analysis: Multi-Variable
Error Propagation 180
5.7 Advanced-Stage Uncertainty
Analysis 187
5.8 Multiple-Measurement Uncertainty
Analysis 193
vi5.9 Correction for Correlated Errors 205
5.10 Nonsymmetrical Systematic
Uncertainty Interval 208
5.11 Summary 209
References 210
Nomenclature 210
Problems 211
6 Analog Electrical Devices and
Measurements 219
6.1 Introduction 219
6.2 Analog Devices: Current
Measurements 220
6.3 Analog Devices: Voltage
Measurements 224
6.4 Analog Devices: Resistance
Measurements 228
6.5 Loading Errors and Impedance
Matching 235
6.6 Analog Signal Conditioning:
Amplifiers 240
6.7 Analog Signal Conditioning:
Special-Purpose Circuits 245
6.8 Analog Signal Conditioning:
Filters 250
6.9 Grounds, Shielding, and Connecting
Wires 261
6.10 Summary 264
References 264
Nomenclature 264
Problems 265
7 Sampling, Digital Devices, and Data
Acquisition 271
7.1 Introduction 271
7.2 Sampling Concepts 272
7.3 Digital Devices: Bits and Words 280
7.4 Transmitting Digital Numbers:
High and Low Signals 282
7.5 Voltage Measurements 284
7.6 Data Acquisition Systems 295
7.7 Data Acquisition System
Components 296
7.8 Analog Input-Output
Communication 301
7.9 Digital Input–Output
Communication 306
7.10 Digital Image Acquisition and
Processing 311
7.11 Summary 316
References 316
Nomenclature 317
Problems 317
8 Temperature Measurements 322
8.1 Introduction 322
8.2 Temperature Standards and
Definition 323
8.3 Thermometry Based on Thermal
Expansion 326
8.4 Electrical Resistance
Thermometry 328
8.5 Thermoelectric Temperature
Measurement 342
8.6 Radiative Temperature
Measurements 365
8.7 Physical Errors in Temperature
Measurement 373
8.8 Summary 382
References 383
Suggested Reading 384
Nomenclature 384
Problems 385
9 Pressure and Velocity
Measurements 392
9.1 Introduction 392
9.2 Pressure Concepts 392
9.3 Pressure Reference Instruments 395
9.4 Pressure Transducers 403
9.5 Pressure Transducer Calibration 410
9.6 Pressure Measurements in Moving
Fluids 412
9.7 Modeling Pressure - Fluid
Systems 416
9.8 Design and Installation: Transmission
Effects 416
9.9 Acoustical Measurements 421
9.10 Fluid Velocity Measuring
Systems 425
Contents vii9.11 Summary 435
References 436
Nomenclature 437
Problems 438
10 Flow Measurements 442
10.1 Introduction 442
10.2 Historical Background 442
10.3 Flow Rate Concepts 443
10.4 Volume Flow Rate Through Velocity
Determination 444
10.5 Pressure Differential Meters 446
10.6 Insertion Volume Flow Meters 464
10.7 Mass Flow Meters 474
10.8 Flow Meter Calibration and
Standards 480
10.9 Estimating Standard Flow Rate 481
10.10 Summary 481
References 481
Nomenclature 482
Problems 483
11 Strain Measurement 487
11.1 Introduction 487
11.2 Stress and Strain 487
11.3 Resistance Strain Gauges 490
11.4 Strain Gauge Electrical
Circuits 497
11.5 Practical Considerations for Strain
Measurement 500
11.6 Apparent Strain and Temperature
Compensation 504
11.7 Optical Strain Measuring
Techniques 514
11.8 Summary 521
References 521
Nomenclature 522
Problems 523
12 Mechatronics: Sensors, Actuators, and
Controls 527
12.1 Introduction 527
12.2 Sensors 527
12.3 Actuators 555
12.4 Controls 561
12.5 Summary 580
References 580
Nomenclature 580
Problems 581
Appendix A Property Data and
Conversion Factors 585
Appendix B Laplace Transform Basics 592
B.1 Final Value Theorem 593
B.2 Laplace Transform Pairs 593
Reference 593
Appendix (Online Only) A Guide For
Technical Writing
A Guide for Technical Writing
References
Glossary 594
Index
Index
Note: Page numbers in italics refer to illustrations
A
Absolute viscosities, 590
AC coupling, 298
AC generators, 553
Acceleration, velocity measurement from, 540–543
Acceleration measurement, 531–537
piezoelectric accelerometer, 538, 538
with a seismic instrument, 537–539
Accelerometer, 84–85, 99, 304, 538–539
piezoelectric, 538–539, 538
vibrometer, 536
Accuracy, 17
relative accuracy, 17
Acoustical measurements, 421–425
A-weighting scale, 422, 422
condenser microphone, 423, 423
C-weighting scale, 422, 422
microphones, 423–425
signal weighting, 421–423
sound level meter (SLM), 424, 424
Acoustic wave speed, 428
Active filters, 251, 258–260
inverting bandpass, 259, 260
inverting high-pass, 259, 259
inverting low-pass, 258, 259
Lowpass Butterworth Active Filter program, 260
Sallen–Key unit-gain filter, 260
Actuators, 555–561. See also Hydraulic actuators; Linear actuators;
Pneumatic actuators; Rotary actuators; Solenoids
flow-control valves, 560–561
A/D converters, 299–300
Address, 281
Advanced-stage uncertainty analysis, 187–193, 189
higher-order uncertainty, 188
Nth-order uncertainty, 188–193
single-measurement uncertainty analysis, 187
zero-order uncertainty, 188
Aleatory uncertainty, 179
Alias frequencies, 274–277
folding diagram for, 275
Alloys, properties of, 585
Alternating current measurement, using analog devices, 224
American National Standards Institute (ANSI), 31, 169
American Society of Mechanical Engineers (ASME), 31, 169, 447, 454,
454–455, 553
American Society of Mechanical Engineers’ Performance Test Code
(ASME PTC), 392, 553
American Society of Testing and Materials (ASTM), 31
ASTM E29—Standard Practice for Using Significant Digits,
33
Ammeter, 221, 228
Amontons, Guillaume, 322
Ampere (A), 26
Amplification, 296–299
Amplifiers, 240–245, 297–298
closed loop gain, 241
operational amplifier, 241, 242–243
Amplitude, 46
ambiguity, 277–278
of signal, 51–65
Analog devices, 219–264
analog signal conditioning, 240–245
special-purpose circuits, 245–250
connecting wires, 260–264
current measurements using, 220–224
alternating current, 224
D’Arsonval meter movement, 220, 221
direct current, 220–224
simple multirange ammeter, 221
grounds, 260–264
impedance matching, 235–240
loading errors, 235–240
measurements using, 219–264
potentiometer, 226–228
resistance measurements, 228–235
shielding, 260–264
shields, 263
voltage measurements using, 224–228
analog voltage meters, 225
oscilloscope, 225–226
Analog filters, 297
Analog input-output communication, 301–306
data acquisition modules, 301–306
Analog signal, 44, 45
conditioning, 250–261, 296–299. See also Filters
amplification, 296–299
Analog-to-digital converter, 285–289
conversion error, 287–289
quantization error, 286–287
resolution, 285
saturation error, 287
Analog voltage comparator, 245–246, 245
Analog voltage meters, 225
Anemometry, 431–433. See also Doppler anemometry; Thermal
anemometry
Angular velocity measurements, 544–547, 546
electromagnetic techniques, 546–547
mechanical measurement techniques, 544–545
stroboscopic, 545–546, 545
ANSI. See American National Standards Institute (ANSI)
Anti-aliasing filter, 276
Aperiodic signal, 47
Apparent strain, 504–514, 504
bridge static sensitivity, 507–508
practical considerations, 508–510
ASME. See American Society of Mechanical Engineers (ASME)
Astable multivibrator, 248
ASTM. See American Society of Testing and Materials (ASTM)
Asynchronous transmission, 307
Average value, 15, 17, 48n2, 50, 123, 342
analog signal, 45, 48
digital signal, 49–50
discrete time signal, 49–50
moving, 297
603A-weighting scale, 422, 422
Axial strain, 488
B
Balance
null, 226–227, 294, 346n3
Bandpass filter, 250
Barometer, 396–397
Fortin barometer, 396, 397
Base dimensions and units, 24–26
current, 26
frequency, 25
length, 25
luminous intensity, 26
mass, 24–25
measure of substance, 26
temperature, 26
time, 25
Basic DC-RMS Measurement program, 224
Bellows, 405–406
Bending beam load cell, 547, 548
Bernoulli, Daniel, 443, 452
Bernoulli effect, 446
Bessel filters, 251
design, 257–258
Best estimate, 127, 181–182, 200
Beta ratio, 448
Biaxial strain gauge rosettes, 510, 510
rectangular strain gauge rosettes, 511, 511
single plane type, 510
stacked type, 510
BIH. See Bureau International de l’Heure (BIH)
Bimetallic thermometers, 327–328, 327
Binary codes, 281–282
Binary numbers, 46, 280, 283–286
Bistable multivibrator, 249
Bits, 280–282
Block diagrams, 567–569
Bluetooth communications, 307–308
Boltzmann’s constant, 366
Borda, Jean, 448
Bourdon tube, 404–405
Bourdon tube pressure gauge, 405, 405
Bragg grating, 519–520, 519
Bridge circuits, 229–230, 331, 331
Callender-Griffiths 3-wire bridge, 331, 331
Mueller 4-wire bridge, 331, 331
Wheatstone bridge, 229, 230
Bridge constant, 502–504
Bridge static sensitivity, 507–508
Buffer, 307
Bulb thermometer, 3, 3
Bureau International de l’Heure (BIH), 25
Butterworth filters, 251, 251
design, 251–252
first-order low-pass resistor-and-capacitor (RC) Butterworth filter
circuit, 252, 252
improved designs, 252–257
ladder circuit for multistage high-pass LC filter, 254, 254
magnitude characteristics, 252, 253
Byte, 281
C
Calibration, 15–23
accuracy, 17
dynamic calibration, 16
errors, 17, 176, 176
hysteresis, 20–21
instrument precision, 22
instrument repeatability, 22
instrument uncertainty, 23
linearity error, 21
measured value, 17
overall instrument error, 23
random errors, 17–19
random test, 21
range, 16
reproducibility, 22
resolution, 16
sensitivity error, 21–22
sequential test, 19
span, 16
standard, 15
static calibration curve, 15, 15
static calibration, 15
static sensitivity, 16
systematic errors, 17–19
true value, 17
uncertainty, 19
validation, 23
verification, 23
zero errors, 21–22
Callender-Griffiths 3-wire bridge, 331, 331
Candella, 26
Canny method, 313, 314–315
Capacitance, 28
farad (F), 28
Capacitance elements, 407–409, 408
Capillary tube viscometer, 463n2
Capsule elements, 405–406
Cascading filters, 252
Castelli, Benedetto, 4423
Catch-and-weigh technique, 480
Celsius (°C) scale, 26, 325
Central tendency, 125
Charge, 28
coulomb (C), 28
Charge amplifier, 247
Chauvenet’s criterion, 155
Chi-squared (χ2) distribution, 144–148
Goodness-of-fit test, 147–148
precision interval in a sample variance, 145–146
Circular frequency, 53
Closed-loop control, 562
Closed-loop controller, 300–301, 301
Closed loop gain, 241
Coaxial cable, 263
Combined standard uncertainty, 195, 201
Common-mode voltage (cmv), 262, 305
Comparator, 568, 568
Complete immersion thermometer, 326
Complex periodic waveform, 46
Complex waveforms, 54
Compliance, 416
Compressibility effects, 449
Concomitant methods, 14
Condenser microphone, 423, 423
Conduction errors, 374–377
Conductive plastic potentiometer, 529, 529
Confidence interval, 123, 124n2, 139, 150, 155–157, 161, 195, 209
Connecting wires, 263–264
coaxial cable, 263
optical cable, 264
single cable, 263
triaxial cable, 264
twisted pairs, 263
604 IndexContinuous variable, 6
Controlled variable, 6
Controller model, 570–572
Controls, 561–579
block diagrams, 567–569
closed-loop control, 562
dynamic response, 564–565
feedback control, 563
Laplace transforms, 565–567
on–off control, 562, 563–564
open-loop control, 562, 562
operational blocks, 568–569
oven control model, 569–573
proportional-integral (PI) Control, 573–575
Conversion error, 287–289
Conversion factors, 585–591
Conversion resolution, 287, 287
Coriolis, Gaspard de, 475
Coriolis, 475–479
flow meter, 475–479, 476–477
turndown, 462, 464, 470–471, 475, 478
uncertainty, 471–472, 478–479
Correction for correlated errors, 205–208
Correlation, 15
coefficient, 152
photon, for LDA, 432
Coulomb (C), 28
Coupled systems, 114–116, 115
Cradled dynamometers, 553–555
AC generators, 553
DC generators, 553
eddy current dynamometers, 553
waterbrake dynamometers, 553, 554–555
Critically damped system, 99
Critical pressure ratio, 460
Current, 26
ampere (A), 26
measurement, using analog devices, 220–224
4–20mA current loop, 247–248
C-weighting scale, 422, 422
D
D/A converters, 300
D’Arsonval meter movement, 220, 221
Damping ratio, 101
Data-acquisition errors, 176–177, 177
Data acquisition modules, 301–306
differential-ended connection, 304–305, 305
self-contained, portable multipurpose, 303
single-ended connection, 304–305, 304
special signal conditioning modules, 305–306
USB-based, 303
Data acquisition systems (DAS), 271–316
analog signal flow scheme using, 296, 296
components, 296–301
A/D converters, 299–300
amplifiers, 297–298
analog filters, 297
closed-loop controller, 300–301
D/A converters, 300
digital filters, 297
digital input/output, 300
filters, 296–299
multiplexer, 299
offset nulling circuit, 299
shunt resistor circuits, 298–299
Data acquisition triggering, 306
Data outlier detection, 155–156
Data presentation, 31–35
full log, 32–33, 32
numerical operations, 34
plotting, 32, 32
rectangular, 32
rounding, 33–34
semi-log, 32–33, 32
significant digits, 33–35
Data-reduction errors, 177, 177
Data transmission, 307
DC component, 48
DC generators, 553
Dead volume, 407, 416
Deadweight Testers, 402–403, 402
Deflection method, 231–235
Degrees of freedom, 136
Dependent variable, 6
Derived dimensions and units, 26–30
electrical dimensions, 28–30
energy, 27
force, 27
power, 28
pressure, 28
stress, 28
Design of experiments, 82, 171
Design-stage uncertainty analysis, 171–176
in combining uncertainties, 173, 173
elemental errors, combining, RSS method, 172–173
Detailed uncertainty analysis, 171
general versus, 171
Deterministic signal, 46
Deviation, 136
Deviation plot, 145
DFT. See Discrete Fourier transform (DFT)
Diaphragms, 406–409
capacitance elements, 407–409, 408
diaphragm meters, 473
piezoelectric crystal elements, 409, 409
pressure transducer using four active resistance strain gauges, 407, 407
strain gauge elements, 407
Differential-ended connection, 304–305, 305
Digit, 33
least significant digit, 33
most significant digit, 33
significant digit, 33
Digital devices, 280–282
address, 281
bits, 280–282
offset binary, 281
ones-complement binary code, 281
twos-complement binary code, 281
words, 280–282
Digital filters, 297
Digital image acquisition and processing, 311–316
Canny method, 313
edge detection methods, 314
image acquisition, 312–313, 312
image processing, 313–316
Sobel method, 313
Digital input/output, 300
Digital input–output communication, 306–311
asynchronous transmission, 307
bluetooth communications, 307–308
data transmission, 307
parity, 307
RS-232C protocol, 308
synchronous transmission, 307
Universal Serial Bus (USB), 307
Index 605Digital numbers, transmitting, 282–284
high and low signals, 282–284
methods for, 283, 283
Digital signal, 45, 46, 49–50
Digital-to-analog converter, 284–285
Digital voltmeters, 294–295
Dimension, 24
base, 24–26
derived, 26–30
electrical, 28–30
length, 25
mass, 24–25
temperature, 25–26
time, 25
Direct current measurement, using analog devices, 220–224
Direct current offset, 50–51
Discharge coefficient, 448
Discrete Fourier transform (DFT), 67–71, 272
fast Fourier transform (FFT), 68
one-sided or half-transform, 68
Discrete-time signals, 44, 45, 49–50
Discrete variable, 6
Displacement sensors, 528–531
conductive plastic potentiometer, 529, 529
dynamic response, 530–531
linear variable differential transformer (LVDT), 529–530, 529
rotary variable differential transformer (RVDT), 531
Displacement, velocity measurement from, 540–543
Distortion, 110
Doppler, Johann, 431
Doppler (ultrasonic) flow meters, 471–472
Doppler anemometry, 431–433, 435
laser Doppler anemometer (LDA), 431, 431
phase Doppler anemometry, 432
Dynamic calibration, 16
Dynamic error, 97
Dynamic measurements, 82–83
Dynamic pressure, 426
in moving fluids, 413
transducer calibration, 410–412
shock tube facility, 410, 410
Dynamic response, 564–565
Dynamic signal, 46, 47, 48
analog representations of, 48
discrete representations of, 48
Dynamometer, 550, 553
absorbing, 553
ac and dc generators, 553
cradled, 553–555
eddy current, 553
engine, 550
waterbrake, 553–555
E
Earth ground, 262
Eddy current dynamometers, 553
Edge detection methods, 313, 314
Elastic behavior of materials, 489
Elastic load cell designs, 547, 548
Electrical dimensions, 28–30
capacitance, 28
charge, 28
electrical potential, 28
resistance, 28
Electrical potential, 28
volt (V), 28
Electrical resistance thermometry, 328–342
practical considerations, 335–336
resistance temperature device resistance measurement, 331–335
Electrodynamometer, 224
Electromagnetic flow meters, 464–467
Electromagnetic spectrum, 365, 365
Electromagnetic techniques, 546–547
Electronic reference junction compensation, 347
Elemental errors:
combining, RSS method, 172–173
propagation of, 194–200
Emissive power, 366–367, 371–372
Energy, 27
joule, 27
Epistemic uncertainty, 180
Error(s), 17
calibration errors, 176, 176
conversion error, 287–289
data-acquisition errors, 176–177, 177
data-reduction errors, 177, 177
error fraction, 89
hysteresis error, 20, 20
linearity error, 20
overall instrument error, 23
propagation of error, 180–182
random errors, 17–19, 179
repeatability error, 20
saturation error, 287
sensitivity error, 20
sources, identifying, 176–177
systematic errors, 17–19
zero shift (null) error, 20
Euler, Leonhard, 443
Euler formula, 59
Even functions, 59–65
Expanded uncertainty, 195, 201
Expansion factor, 449–450, 452
Experimental test plan, 5–15. See also Randomization; Variables
concomitant methods, 14
data reduction design plan, 6
interference, 9–10
noise, 9–10
parameter design plan, 6
repetition, 14
replication, 14
steps in, 6
system and tolerance design plan, 6
Extraneous variables, 7
F
Fahrenheit, Gabriel D., 323
Fahrenheit (°F), 26
Farad (F), 28
Faraday, Michael, 465, 530
Fast Fourier transform (FFT), 68
Feedback control, 4, 563
Fiber Bragg strain measurement, 519–520, 519
Filter band, 106
Filters, 250–261, 296–299. See also Bessel filters; Butterworth filters
active filters, 251, 258–260
analog, 297
bandpass filter, 250
Butterworth filters, 251
cascading filters, 252
characteristics, 250, 250
digital, 297
high-pass filter, 250
low-pass filter, 250
notch filter, 250
passband, 250
606 Indexpassive analog filter circuits, 251
roll-off, 251
stopband, 250
Final value theorem, 593
Finite-sized data sets, statistics of, 135–141
finite statistics, 135
inferential statistics, 135
repeated tests and pooled data, 140–141
standard deviation of the means, 136–140
Finite statistics, 135
First-order systems, 87–98
frequency response, 95
determination of, 98
magnitude ratio, 96, 97
phase shift, 96, 97
simple periodic function input, 94–98
step function input, 88–90
time constant, 88
First-order uncertainty, 188–190
Fixed point temperatures, 323–324
Flip-flop circuits, 248–250
Flip-flop multivibrator, 249, 249
Flow coefficient, 448–449, 451, 561
Flow-control valves, 560–561, 560
Flow measurements, 442–481. See also Insertion volume flow meters;
Mass flow meters; Pressure differential meters
Bernoulli effect, 446
flow meter calibration and standards, 480–481
historical background, 442–443
mass flow rate, 442
standard flow rate, estimating, 481
volume flow rate, 442
through velocity determination, 444–446
Flow nozzle, 447, 454–460
Flow rate concepts, 443–444
Fluid velocity measuring systems, 425–435
particle image velocimetry (PIV), 433–434, 433
pitot–static pressure methods, 434–435
pitot-static pressure probe, 426–428, 427
thermal anemometry, 428–431, 429
velocity measuring methods, 434–435
Folding diagram, 275–276, 275
Force, 27
load cells, 547–550
measurement, 547–550
Newton, 27
Fortin barometer, 396, 397
Fossilization, 194
Fourier analysis, 51
Fourier coefficients, 58–59
Fourier series, 57–58
Cosine Series, 59
fundamental, 58
Sine Series, 59–65
Fourier transform, 65–73
discrete Fourier transform (DFT), 67–71
inverse Fourier transform, 66
Francis, James, 452
Freeman, John Ripley, 455
Frequency, 25, 43. See also Nyquist frequency
Frequency analysis, 54–57
Frequency bandwidth, 97
Frequency distribution, 126
Frequency of signal, 51–65
Frequency response, 95
Frequency spectrum, 65–73
Frontinius, Sextus, 443
Full field IR imaging, 372–373
Full-log coordinate format, 33
Functions:
even function, 59–65
odd function, 59–65
with T= 2π, 59
Fundamental Fourier series, 58
Fundamental frequency, 58
G
Galvanometer, 222, 227, 227
Gases, transmission effects, 418–420
Gauge factor, 494–495
Gauge length, 493, 496
General measurement system, 2–5
components, 4, 5
General model for measurement system, 81–85
General purpose interface bus (GPIB), 307–308, 308
General system model, 85–108
first-order systems, 87–98. See also individual entry
second-order systems, 98–108. See also individual entry
static sensitivity (K), determination, 86
zero-order systems, 85–87
General template for measurement system, 4–5
General versus detailed uncertainty analysis, 171
Goodness-of-fit test, 147–148
Gosset, William, 136, 136n5
GPIB. See General purpose interface bus (GPIB)
Ground loops, 262
Grounds, 260–264
H
Hall effect, 224
Handshake, 306
Harmonics, 58
Heat flux, 359–362
heat flux sensor, 359
Heat flux sensor, 359
construction of, 359, 359
thin-film heat flux sensor, 360, 360
Heavily damped systems, 420–421
Hero of Alexandria, 442
Herschel, Clemens, 452
Herschel venturi meter, 451, 453
Hierarchy of standards, 30–31
Higher-order uncertainty, 188
High-pass filter, 250
Histogram, 126
Hooke’s law, 489
Hot-film sensor, 429, 435
Hot-wire sensor, 429, 431, 435
Hydraulic actuators, 556–558
Hypothesis testing, 141–144
p-value, 143
t-test, 143
z-test, 142
Hypsometer, 388
Hysteresis, 20–21
Hysteresis error, 20, 20
I
Image acquisition, 312–313, 312
Image processing, 313–316
Impact cylinder, 414, 414
Impedance matching, 235–240
Imread function, 313
Imshow function, 313
Inch-pound (I-P) unit system, 24
Inclined tube manometer, 398, 399
Index 607Independent variables, 6
Inertance, 416
Inferential statistics, 135
Infinite statistics, 135
Input, 43
Input/output signal concepts, 43–47
generalized behavior, 44
measurement system selection, 43, 44
signal waveforms, 46–47
waveforms, classification, 44–46
Insertion errors, 373–374
Insertion volume flow meters, 464–474
diaphragm meters, 473
Doppler (ultrasonic) flow meters, 471–472
electromagnetic flow meters, 464–467
positive displacement meters, 472–474
rotameters, 469–470, 469
rotating vane meters, 473
transit time flow meters, 471–472
turbine meters, 470–471
vortex shedding meters, 467–469, 467–468
wobble meters, 473
Instrument error:
common elements of, 20, 20
hysteresis error, 20
linearity error, 20
repeatability error, 20
sensitivity error, 20
zero shift (null) error, 20
Instrument Precision, 22
Instrument repeatability, 22
Instrument uncertainty, 23, 172
Interference, 9–10, 10
International Bureau of Weights and Measures (BIPM), 24
International Organization for Standardization (ISO), 31, 169, 179
International Temperature Scale of 1990 (ITS-90), 325
Interpolation, 324
standards for, 325–326
Interstage loading errors, 236–240
Inverse Fourier transform, 66
Inverting bandpass active filter, 259, 260
Inverting high-pass active filter, 259, 259
Inverting low-pass active filter, 258, 259
J
Joule, 27
Junction, 312
K
Kelvin (K) scale, 26, 325
K-factor, 468
Kiel probe, 414, 414
Kinematic viscosities, 591
King’s law, 429
L
Laminar flow elements, 463–464
Laplace transform analysis, 571
Laplace transform basics, 592–593
Laplace transform pairs, 593
Laplace transforms, 565–567
Laser Doppler anemometer (LDA), 431, 431, 435
Lateral strains, 489–490
Law of homogeneous materials, 345
Law of intermediate materials, 345
Law of successive or intermediate temperatures, 346
LDA. See Laser Doppler anemometer (LDA)
Leakage, 278–280
Least significant digit, 33
Least-squares regression analysis, 149–152
Leibniz, Gottfried Wilhelm, 57n4
Length, 25
Level of significance, 142
Light, characteristics, 515
Linear actuators, 555–556
screw-drive linear motion, 556
slider–crank mechanism, 555–556
using lead screw, 556, 556
Linear polynomials, 152–155
Linear variable differential transformer (LVDT), 405, 529–530, 529
LVDT gauge head, 531, 532
Linear velocity measurements, 539
Linearity error, 20, 21
Linkwitz–Riley high-pass or low-pass filter, 256, 257
Linnaeus, Carolus, 323
Liquid-in-glass thermometer, 324, 324, 326, 326–327
complete immersion thermometer, 326
partial immersion thermometer, 327
total immersion thermometer, 327
Liquids, transmission effects, 418
Load cells, 547–550
bending beam load cell, 547, 548
elastic load cell designs, 547, 548
piezoelectric load cells, 547–550
design, 548, 549
proving ring, 549–550, 550
shear beam load cell, 547, 549
strain gauge load cells, 547
Loading errors, 235–240
interstage loading errors, 236–240
for voltage-dividing circuit, 236–237, 236
Lowpass Butterworth Active Filter program, 260
Low-pass filter, 250
low-pass Butterworth filter, 251, 251
Luminous Intensity, 26
candella, 26
LVDT. See Linear variable differential transformer
M
Mach number, 381–382, 411
Magnitude, 43
magnitude ratio, 96
Manometer, 397–402
inclined tube manometer, 398, 399
micromanometer, 398, 399
U-tube manometer, 397, 398
Mass, 24–25
Mass flow meters, 474–480
Coriolis flow meter, 475–479, 476–477
thermal flow meter, 474–475
McLeod gauge, 395–396, 396
Mean value, 48, 48n2, 123–125, 127, 130–131, 136–141, 155, 170, 180–
182, 186, 200, 202–205, 298
digital signal, 49–50
discrete time signal, 49–50
sample mean, 124, 135–140, 155, 170, 180
true mean, 7, 125, 130–131, 136, 138–141
Measurand, 124
Measured value, 17
Measured variable, 2, 124
Measurement errors, 169–171
repeated measurements, distribution of errors on, 169, 170
Measurement methods, 1–35. See also Calibration; Experimental test plan;
Standards
basic concepts, 1–35
experimental test plan, 5–15
608 Indexfeedback-control stage, 4
general measurement system, 2–5
general template for, 4–5
output stage, 4
sensor, 2–4
signal conditioning stage, 4
transducer, 2–4
Measurement random standard uncertainty, 195
Measurement system behavior, 81–116. See also General system model
coupled systems, 114–116, 115
dynamic measurements, 82–83
general model for, 81–85
multiple-function inputs, 112–114
phase linearity, 110–112
transfer functions, 108–110
Measurement systematic standard uncertainty, 195
Mechanical measurement techniques, 544–545, 544
Mechanical power measurements, 551–555
cradled dynamometers, 553–555
prony brake, 552, 552
rotational speed, 551–552
shaft power, 551–552
torque, 551–552
Mechatronics, 527–579. See also Actuators; Controls; Force:
measurement; Sensors; Velocity measurements
Metallic gauges, 491–493
metallic foil strain gauge, 493, 493
Method of least-squares, 149
Metrology, 169
Micromanometer, 398, 399
Microphones, 423–425
Modified three-sigma test, 155
Moiré methods, 517–519, 518
Mole, 26
Monostable multivibrator, 249
Monte Carlo simulations, 158–160, 158, 187
Most significant digit, 33
Moving coil transducers, 543–544, 543
Moving fluids, 412–415. See also Pressure measurements in moving fluids
Mueller 4-wire bridge, 331, 331
Multiple-function inputs, 112–114
Multiple gauge bridge, 501–502
Multiple-junction thermocouple circuits, 357–359
Multiple-measurement uncertainty analysis, 193–205, 194
combined standard uncertainty, 195, 201
elemental errors, propagation of, 194–200
expanded uncertainty, 195, 201
propagation of elemental systematic uncertainties, 194–195
propagation of uncertainty to a result, 200–205
Welch–Satterthwaite formula, 201
Multiplexer, 299, 300
Multi-variable error propagation, 180–187
Monte Carlo method, 187
propagation of error, 180–182
sensitivity index, approximating, 182–184
sequential perturbation, 184–186
Multivibrator, 248–250, 248
astable, 248
flip-flop/bistable multivibrator, 249, 249
monostable, 249
TTL signal, 248
N
Narrow band infrared temperature measurement, 370–373
full field IR imaging, 372–373
fundamental principles, 370–371
two-color thermometry, 371–372
National Institute of Standards and Technology (NIST), 326, 347, 350,
355, 363–365, 480–481
Natural frequency, 101
Negative temperature coefficient (NTC), 328
Newton, Sir Isaac, 443
Newton, 27
NIST. See National Institute of Standards and Technology (NIST)
Noise, 9–10, 10
Nondeterministic signal, 47
Nonsymmetrical systematic uncertainty interval,
208–209
Normal (or gaussian) distribution, 131
Normal error function, 132
Normal stress, 487
Notch filter, 250
NTC. See Negative temperature coefficient (NTC)
Nth-order uncertainty, 188–193
Null method, 230–231
Numerical operations, 34
Nyquist frequency, 275, 297
O
Obstruction meters, 447–449
compressibility effects, 449
selection, 461–463
accuracy, 462
costs, 461
placement, 461
pressure loss, 461
turndown, 462–463
square-edged orifice plate meter, 447, 447
standards for, 449
Odd functions, 59–65
Offset binary, 281
Offset nulling circuit, 299
Ohm (Ω), 28
Ohmmeter circuits, 228–229
multirange ohmmeter circuits, 228, 229
Ones-complement binary codes, 281
One-shot circuit, 249
One-sided or half-transform, 68
On–off control, 562, 563–564
Open-loop control, 562, 562
Operational amplifier, 241, 242–243
Operational blocks, 568–569
single-input, single-output amplifier block, 568, 568
temperature-input, voltage-output amplifier block, 568,
568
Optical cable, 264
Optical fiber thermometer, 370, 370
Optical strain measuring techniques, 514–515
Orifice meter, 449–451
square-edged orifice meter, 449, 450–451
Orifice plate, 447
Oscilloscope, 225–226
Outlier, 155–156
Chauvenet’s criterion, 155–156
three-sigma test, 155
Output, 4, 43
Output stage, 4
Oven control model, 569–573, 570, 573
controller model, 570–572
Laplace transform analysis, 571
plant model, 569–570
step response, 572–573
Overall instrument error, 23
Overdamped system, 99
P
Parallel communications, 308–311
Parallel converters, 293–294
Index 609Parameter, 6
Parity, 307
Partial immersion thermometer, 327
Particle image velocimetry (PIV), 433–435, 433
Pascal (Pa), 28
Passband, 250
Passive analog filter circuits, 251
Peltier, Jean Charles Athanase, 344
Peltier coefficient, 344
Peltier effect, 344
Period, 53
Periodic signals, 52–54
spring-mass system, 52, 53
Perturbation, sequential, 184–186
Phase Doppler anemometry, 432
Phase linearity, 110–112
Phase shift, 95
Photoelastic measurement, 515–517
plane polariscope, 516, 517
Physical errors in temperature measurement, 373–382
conduction errors, 374–377
errors associated with temperature sensors, 374
insertion errors, 373–374
probe design, 376–377
radiation errors, 377–379
radiation shielding, 379–380
random errors, 374
recovery errors, 380–382
systematic errors, 374
PI. See Proportional-integral (PI) control
PID. See Proportional integral–derivative (PID) control
Piezoelectric accelerometer, 538, 538
Piezoelectric crystal elements, 409, 409
Piezoelectric load cells, 547–550, 549
Pitot–static pressure methods, 434–435
Pitot-static pressure probe, 426–428, 427
Pitot tube, 414, 414
PIV. See Particle image velocimetry (PIV)
Place value, 33
Planck’s constant, 366
Plane polariscope, 516, 517–518
Plant model, 569–570
Platinum resistance temperature device (RTD), 331–336
PLC. See Programmable logic controller (PLC)
Plotting formats, 32, 32
full-log coordinate format, 33
rectangular coordinate format, 32
semilog coordinate format, 32–33
Pneumatic actuators, 556–558, 558
Poiseulle, Jean, 463
Poisson’s ratio, 406, 489, 491, 495
Polarization of light, 515, 515
Pooled data, 140–141
Pooled mean, 140
Pooled standard deviation, 140
Pop test, 411
Population behavior, 131–135
Positive displacement meters, 464, 472–474
Positive temperature coefficient (PTC), 328
Potentiometer pressure transducer, 405, 406
Potentiometer, 226–228
instruments, 227–228
voltage divider circuit, 227, 227
Power, 28
watt (W), 28
Prandtl tube for static pressure, 415, 415
Precision interval in a sample variance, 145–146
Pressure, absolute, 87, 392–394, 396, 404, 411
Pressure concepts, 28, 392–395
pascal (Pa), 28
relative pressure scales, 393, 393
Pressure differential meters, 446–464
flow nozzles, 454–460
laminar flow elements, 463–464
obstruction meters, 447–449
selection, 461–463
orifice meter, 449–451
sonic nozzles, 460–461
venturi meter, 451–454
Pressure-fluid systems, modeling, 416
Pressure measurements, 392–435. See also Transmission effects
in moving fluids, 412–415
dynamic pressure, 413
stagnation, 413
static pressure, 413–415
total pressure measurement, 413–414
total pressure, 413
Pressure reference instruments, 395–403
barometer, 396–397
deadweight testers, 402–403, 402
inclined tube manometer, 398, 399
manometer, 397–402
McLeod gauge, 395–396, 396
micromanometer, 398, 399
U-tube manometer, 397, 398
Pressure sensors, elastic elements as, 403, 404
Pressure transducers, 403–410. See also Diaphragms
bellows, 405–406
Bourdon tube, 404–405
calibration, 410–412
dynamic Calibration, 410–412
static calibration, 410
capsule elements, 405–406
diaphragms, 406–409
potentiometer pressure transducer, 405, 406
pressure sensors, elastic elements as, 403, 404
Primary standard, 24
Primary unit standards, 24
Probability, 123–167. See also Chi-squared (χ2) distribution; Probability
density functions; Regression analysis
Monte Carlo simulations, 158–160
number of measurements required, 156–158
Probability density functions, 125–131
standard statistical distributions, 128–129
binomial, 129
log normal, 128
normal, 128
Poisson, 129
rectangular, 128
triangular, 128
Programmable logic controller (PLC), 4
Prony brake, 552, 552
Propagation:
of elemental systematic uncertainties, 194–195
of uncertainty to a result, 200–205
Property data, 585–591
thermophysical properties, 586–587
Proportional integral–derivative (PID) control, 575–579,
579
proportional control, 578–579
of a second-order system, 575–579, 577
Proportional-integral (PI) control, 573–575, 574
integral control, 573–574
time response, 575
Provers, 480
Proving ring, 549–550, 550
610 IndexP-value, 143
Pyranometer construction, 368
Pyrometry, 369–370
Q
Quantization, 45, 285
quantization error, 286–287
R
Radiation
blackbody, 325, 366
detectors, 366–368
emissive power, 366–367, 371–372
errors, 377–379
shield, 379–380
temperature measurement, 365–373
wavelength distribution, 366
Radiative temperature measurements, 365–373
narrow band infrared temperature measurement, 370–373
optical fiber thermometer, 370, 370
pyrometry, 369–370
radiation detectors, 366–368
radiation fundamentals, 365–366
radiometer, 367–369, 367
Radiometer, 367–369, 367
pyranometer construction, 368
Ramp (integrating) converters, 291–293, 291–292
Random errors, 17–19, 18, 179, 374
Random standard uncertainty, 179
Random test, 21
Random uncertainty, 124, 139, 179
Random variable, 125
Randomization, 10–13
Range, 16, 43
Rayleigh relation, 428
Recovery errors in temperature measurement, 380–382
Rectangular coordinate format, 32
Rectangular distribution, 159, 171, 179n5, 187, 193, 209
standard uncertainty, 187
Reference junction, 347
Regression analysis, 148–155
least-squares regression analysis, 149–152
linear polynomials, 152–155
Relative accuracy, 17
Relative pressure scales, 393, 393
Repeatability, 22
Repeatability error, 20
Repeated measurements, distribution of errors on, 169, 170
Repeated tests, 140–141
Repetition, 14
Replication, 14
Reproducibility, 22
Resistance, 28, 416
ohm (Ω), 28
Resistance measurements, 228–235
bridge circuits, 229–230
deflection method, 231–235
Null method, 230–231
ohmmeter circuits, 228–229
Resistance strain gauges, 490–497
configurations, 494
delta rosette, 494
diaphragm pattern, 494
linear pattern, 494
rectangular rosette, 494
residual stress pattern, 494
stacked rosette, 494
tee pattern, 494
torque rosette, 494
gauge factor, 494–495
metallic gauges, 491–493
semiconductor strain gauges, 495–497
strain gauge construction and bonding, 493–495
Resistance temperature detectors (RTDs), 328–330, 329, 428, 475
platinum RTDs, 331–336
Resistance temperature device resistance measurement, 331–335
Resolution, 16, 285
conversion resolution, 287, 287
Resonance band, 104
Resonance frequency, 105
Reynolds number, 6
Ringing frequency, 101
Rise time of system, 89, 101
Roll-off, 251
Root-mean-square
analog signal, 49
Root-sum-squares (RSS) method, 172
Rotameters, 469–470, 469
Rotary actuators, 558–560
stepper motors, 558–560, 559
Rotary variable differential transformer (RVDT), 531, 533
Rotating vane meters, 473
Rotational speed, 551–552
Rounding, 33–34
RS-232C protocol, 308
RTDs. See Resistance temperature detectors (RTDs)
Ruge, Arthur, 491
RVDT. See Rotary variable differential transformer (RVDT)
S
Sallen–Key unit-gain filter, 260–261, 260
Sample-and-hold circuit (SHC), 246–247
Sample mean value (), 135
Sample standard deviation (sx), 135
Sample variance (s2x), 135
Sampling, 271–316
alias frequencies, 274–277
amplitude ambiguity, 277–278
anti-aliasing filter, 276
concepts, 272–280
leakage, 278–280
sample rate, 272–274, 272–273
waveform fidelity, 280
Sampling theorem, 274
Saturation error, 287
Screw-drive linear motion, 556
Second-order systems, 98–108
ringing frequency, 101
rise time, 101
settling time, 101
simple periodic function input, 103–104
step function input, 100–103
system characteristics, 104–108
Seebeck, Thomas Johann, 343
Seebeck effect, 343–344
Seismic transducer, 531–537, 534–535
Semiconductor strain gauges, 495–497
Semilog coordinate format, 32–33
Sensitivity error, 20, 21–22
Sensitivity index, approximating, 182–184
Sensors, 2–4, 527–555. See also Displacement sensors; Load cells
acceleration measurement, 531–537
atomic force microscope, sensor stage of, 2–3
displacement sensors, 528–531
potentiometer construction, 528, 528
rotary variable differential transformer, 531, 533
Index 611Sensors (Continued )
seismic transducer, 531–537
torque measurements, 550–551
vibration measurement, 531–537
Sequential perturbation, 184–186
Sequential test, 19
Settling time, 101
Shaft power, 551–552
SHC. See Sample-and-hold circuit (SHC)
Shear beam load cell, 547, 549
Shielding, 260–264
Shields, 263
Shock tube facility, 410, 410
Shunt resistor circuits, 298–299
Signal, 43–73. See also Input/output signal concepts
amplitude, 51–65
analysis, 48–51
digital signals, 49–50
direct current offset, 50–51
discrete-time signals, 49–50
signal root-mean-square value, 49
conditioning, 4
strain measurement and, 512–514
definition, 44
dynamic characteristics of, 43–73
frequency, 51–65
periodic signals, 52–54
static characteristics of, 43–73
Signal root-mean-square value, 49
Signal waveforms, 46–47
aperiodic, 47
deterministic signal, 46
dynamic signal, 46, 47
nondeterministic signal, 47
simple periodic waveform, 46
static signal, 46
steady periodic signal, 46
Signal weighting, 421–423
A-weighting scale, 422, 422
condenser microphone, 423, 423
C-weighting scale, 422, 422
Signals analysis in frequency space, 71–73
Significant digits, 33–35
Simmons, Edward, 491
Single cable, 263
Single-ended connection, 304–305, 304
Single-measurement uncertainty analysis, 187, 189
Single-tailed test, 142
Slider–crank mechanism, 555–556
Simple multirange ammeter, 221
Simple periodic function input, 94–98, 103–104
Simple periodic waveform, 46
Sobel method, 313, 314–315
Solenoids, 557–558, 558
Sonic nozzles, 460–461
Sound level meter (SLM), 424, 424
Span, 16
Special-purpose circuits, 245–250
analog voltage comparator, 245–246, 245
astable multivibrator, 248
charge amplifier, 247
4–20mA current loop, 247–248
flip-flop circuits, 248–250
multivibrator, 248–250
sample-and-hold circuit (SHC), 246–247
Special signal conditioning modules, 305–306
Square-edged orifice meter, 449, 450–451
Square-edged orifice plate meter, 447, 447
Stagnation in moving fluids, 413
Standard, 15
Standard cubic feet per minute (SCFM), 481
Standard cubic meters per minute (SCMM), 81
Standard deviation, 22, 130
of the means, 136–140
Standard error of the fit, 150
Standard flow rate, estimating, 481
Standard statistical distributions, 128–129
binomial, 129
log normal, 128
normal, 128
Poisson, 129
rectangular, 128
triangular, 128
Standard thermocouple voltage, 349–350, 350
Standardized normal variate, 131
Standards, 23–31. See also Base dimensions and units; Derived
dimensions and units
hierarchy, 30–31
primary, 24
temperature, 26
test, 31
Static calibration, 15
Static pressure in moving fluids, 413, 413n2
Static pressure measurement in moving fluids, 414–415
Prandtl tube for static pressure, 415, 415
static pressure wall tap, 414, 414
Static pressure transducer calibration, 410
Static sensitivity (K), 16, 86
determination, 86
Static signal, 46
Statistical measurement theory, 124–131. See also Probability Density
Functions
Steady periodic signal, 46
Step function input, 88–90
Stepper motors, 558–560, 559
Stiffness, 416
Stopband, 250
Strain, 487–490. See also Resistance strain gauges
axial strain, 488
lateral strains, 489–490
Strain gauge
electrical circuits, 497–500
elements, 407
interface, 305, 306
load cells, 547
Wheatstone bridge circuit, 498
Strain measurement, 487–520
apparent strain, 504–514
biaxial strain gauge rosettes, 510, 510
bridge constant, 502–504
fiber Bragg strain measurement, 519–520
Moiré methods, 517–519
multiple gauge bridge, 501–502
optical strain measuring techniques, 514–515
photoelastic measurement, 515–517
practical considerations for, 500–504
signal conditioning, 512–514
strain gauge data, analysis, 510–512
temperature compensation, 505–507
Stream pressure, 413n2
Stress, 28, 487–490
biaxial state of stress, 489, 490
normal stress, 487
pascal (Pa), 28
Stroboscopic angular velocity measurements, 545–546, 545
Student’s t distribution, 136
612 IndexSubstance measure, 26
mole, 26
Successive approximation converters, 289–295, 290
digital voltmeters, 294–295
parallel converters, 293–294
ramp (integrating) converters, 291–293, 291
Synchronous transmission, 307
Systematic errors, 17–19, 124n1, 177–179, 374
Systematic standard uncertainty, 177
Systematic uncertainty, 178
T
Temperature, 26
celsius (°C), 26
and definition, 323–326
fahrenheit (°F), 26
kelvin (K), 26
standards, 323–326
Temperature compensation
bridge arrangements for, 507, 507
common gauge mountings, 506
and strain measurement, 505–507
Temperature measurements, 322–382. See also Electrical resistance
thermometry
fixed point temperatures, 323–324
historical background, 322–323
interpolation, 324
liquid-in-glass thermometer, 324, 324
physical errors in, 373–382. See also individual entry
scales and standards, 325–326
t estimator, 136
Test plan, 5–14. See also Experimental test plan
Test standards and codes, 31
The principle of superposition, 112
Thermal anemometer, 435
Thermal anemometry, 428–431, 429
hot-wire probe, 429, 429
operating modes, 429
Thermal flow meter, 474–475
Thermistors, 336–342, 336
circuits, 336, 337
Thermocouple, 342, 343
basic temperature measurement with, 346–347, 347
multiple-junction thermocouple circuits, 357–359
in parallel, 358–359, 358
Thermocouple voltage measurement, 350–357
thermocouple reference table, 351–353
Thermoelectric temperature measurement, 342–365
applications for, 359–362
data acquisition considerations, 362–365
fundamental thermocouple laws, 345–346
Peltier effect, 344
reference junction, 347
Seebeck effect, 343–344
standard thermocouple voltage, 349–350, 350
thermocouple standards, 347–350
Thomson effect, 344–345, 345
Thermometer
bimetallic, 327–328
complete immersion, 326
electrical resistance, 328–342
liquid-in glass, 326–327
optical fiber, 370
partial immersion, 327
platinum resistance, 31, 325–326, 331
radiation, 365
total immersion, 327
Thermometry based on thermal expansion, 326–328
bimetallic thermometers, 327–328
liquid-in-glass thermometers, 326–327
Thermophysical properties, 586–587
of air, 589
of metallic solids, 586–587
of saturated water (liquid), 588
Thermopiles, 357–358, 357
Thin-film heat flux sensor, 360, 360
Thomson, William (Lord Kelvin), 26, 344, 491
Thomson effect, 344–345, 345
Three-sigma test, 155
Thresholding, 313
Time, 25
time constant, 88, 90
Tolerance design plan strategy, 6n3
Torque, 551–552
measurements, 550–551
shaft instrumented for, 551, 551
Torricelli, Evangelista, 396, 451
Total immersion thermometer, 327
Total pressure in moving fluids, 413
Total pressure measurement, 413–414
impact cylinder, 414, 414
Kiel probe, 414, 414
Pitot tube, 414, 414
Transducers, 2–4
atomic force microscope, transducer stage, 3
for shock and vibration measurement, 538–539
Transfer functions, 108–110
operation of, 108, 109
Transit time flow meters, 471–472
Transmission band, 105
Transmission effects, 416–421
design and installation, 416–421
equivalent lumped parameter network, 417, 417
gases, 418–420
heavily damped systems, 420–421
liquids, 418
Triangular distribution, 128
Triaxial cable, 264
True mean value, 130
True value, 17
True variance, 130
T-test, 143
TTL signal, 248
Turbine meters, 470–471
Twisted pairs, 263
Two-color thermometry, 371–372
Twos-complement binary codes, 281
Two-tailed test, 142
Type A uncertainty, 179
Type B uncertainty, 179
U
Uncertainty, 19
propagation, 172
Uncertainty analysis, 168–209. See also Advanced-stage
uncertainty analysis; Multiple-measurement uncertainty analysis;
Multi-variable error propagation
advanced-stage, 187–193
aleatory uncertainty, 179
correction for correlated errors, 205–208
design-stage, 171–176
epistemic uncertainty, 180
error sources, identifying, 176–177
general versus detailed, 171
measurement errors, 169–171
multiple-measurement, 193–205
Index 613Uncertainty analysis (Continued )
nonsymmetrical systematic uncertainty interval, 208–209
standard uncertainties, 177–180
systematic error, 177–179
Type A uncertainty, 179
Type B uncertainty, 179
Underdamped system, 99–101, 104–105, 261, 410
Unit, 24
Unit step function, 88, 88
Universal Serial Bus (USB), 307
U.S. Engineering Unit System, 24–25
U-tube manometer, 397, 398
V
Validation, 23
Valves, 560–561
Variables, 6–9
continuous, 6
controlled variable, 6
dependent, 6
discrete, 6
extraneous, 7
independent, 6
parameter, 6
Velocity measurements, 392–435, 539–544. See also Angular velocity
measurement; Fluid Velocity measuring systems
Doppler anemometry, 435
laser Doppler anemometer (LDA), 435
linear velocity measurements, 539
particle image velocimetry (PIV), 435
pitot–static pressure methods, 434–435
selection of, 434–435
thermal anemometer, 435
velocity from displacement or acceleration, 540–543
Venturi, Giovanni, 452, 460
Venturi meter, 447, 451–454
Herschel venturi meter, 451, 453
Verification, 23
Vibration measurement, 531–537
transducers for, 538–539
Vibrometer, 536
Viscosity
absolute, 437, 533, 590
kinematic, 427, 444, 470, 591
Volt (V), 28
Voltage
analog measurement, 224–228
digital measurement, 284–295
Voltage divider circuit, 227, 227
Voltage measurements, 284–295
analog-to-digital converter, 285–289
digital-to-analog converter, 284–285
quantization, 285
using analog devices, 224–228
Voltage-divider principles, 528n2
Voltage-dividing circuit, loading errors for, 236–237, 236
Voltmeters, 225
Volt-ohmmeters (VOMs), 225
Volume flow rate through velocity determination, 444–446
von Karman, Theodore, 467
Vortex shedding meters, 467–469, 467–468
W
Water, thermophysical properties, 588
Waterbrake dynamometers, 553, 554–555
Watt (W), 28
Waveforms, 43
classification, 44–46, 47. See also Signal waveforms
analog signal, 44, 45
analog-to-digital (A/D) converter, 46
digital signal, 45, 46
discrete time signal, 44, 45
fidelity, 280
Weisbach, Julius, 460
Welch–Satterthwaite formula, 201
Wheatstone bridge, 229, 230
voltage-sensitive Wheatstone bridge, 231,
231
Wobble meters, 473
Words, 280–282
Y
Young’s modulus, 489
Z
Zero errors, 21–22
Zero-order systems, 85–87
Zero-order uncertainty, 171, 188
Zero shift (null) error, 20
Zeroth law of thermodynamics, 323
z-test, 142
z variable, 131, 136, 142
614 IndexCONVERSION FACTORS*
MASS
1 lb
m = 0.4536 kg
1 slug = 14.5939 kg
LENGTH
1 inch = 0.0254 m
1 ft = 0.3048 m
1 km = 1000 m = 1 × 103 m
1 cm = 0.01 m = 0.3937 in. = 0.0328 ft
1 mm = 0.001 m = 1 × 103 m
1 μm = 0.000001 m = 1 × 106 m
1 nm = 0.000000001 m = 1 × 109 m
1 mi = 5280 ft = 1.6093 km
1 l.y. = 9.4605 × 1015 m
AREA
1 ft2 = 0.0929 m2
1 cm2 = 1 × 104 m2 = 0.155 in.2
VOLUME
1 L = 1000 cm3 = 0.2642 gal = 1 × 103 m3
1 gal = 231.0 in.3 = 0.1337 ft3
1 gal = 3.7854 L = 0.003785 m3
1 ft3 = 28.3168 L = 0.0283 m3
TIME
1 min = 60 s
1 h = 60 min = 3600 s
1 day = 8.6400 × 104 s
FORCE
1 N = 1 kg-m/s2 = 1 × 105 dynes
1 lb = 4.4482 N
1 kgf = 9.80665 N
PRESSURE OR STRESS
1 Pa = 1 N/m2
1 lb/in2 = 6894.757 Pa
1 atm = 14.6959 lb/in.2 = 760 Torr
= 101,325 Pa
1 bar = 14.5038 lb/in.2 = 1 × 105 Pa
= 750 Torr
1 dyn/cm2 = 0.10 Pa
1 inch Hg = 3386.38 N/m2
1 inch H2O = 2.54 cm H2O = 249.089 Pa
= 0.0361 lb/in.2
1 Torr = 1 mm Hg = 133.322 Pa
1 μstrain = 106 m/m = 106 in/in
TEMPERATURE
K = °C + 273.15
1°C = 1.8°F = 1 K
°F = 1.8°C + 32
°R = °F + 459.67
VOLUME FLOW RATE
1 gal/min = 0.00223 ft3/s = 0.06309 L/s
1 m3/min = 35.315 ft3/min = 1 × 106 cm3/min
ANGLE
1° = 0.01745 rad
1´ = 2.909 × 104 rad
1 revolution = 2π rad
ROTATION
1 rev/s = 2π rad/s = 6.2832 rad/s
1 rpm = 1 rev/min = 0.1047 rad/s
FREQUENCY
1 Hz = 2π rad/s
*
Many of these conversion factors have been rounded off.MOMENT OR TORQUE
1 lb-ft = 1.3558 N-m
POWER
1 W = 1.0 J/s = 860.42 cal/hr
1 hp = 550.0 ft-lb/s = 745.6999 W
1 kW = 1 × 103 W
1 Btu/hr = 778.1692 ft-lb/hr = 0.2931 W
ENERGY
1 J = 1.0 N-m = 1 × 107 ergs
1 erg = 1 dyne-cm
1 cal = 4.1868 J
1 ft-lb = 1.3558 J
1 Btu = 1055.0558 J
VISCOSITY
1 lb-s/ft2 = 47.880 N-s/m2
1 centipoise = 0.01 dyne-s/cm2 = 0.001 Pa-s
SPECIFIC HEAT
1 Btu/lbm-°F = 4.1868 kJ/kg-°C
GAS CONSTANT
1 ft-lb/lbm-°R = 5.380 J/kg-K
THERMAL CONDUCTIVITY
1 Btu/hr-ft-°F = 1.7307 W/m-°C
HEAT TRANSFER COEFFICIENT
1 Btu/hr-ft2-°F = 5.6786 W/m2-°C
BULK MODULUS
1 × 106 psi = 6.895 × 109 Pa
PHYSICAL CONSTANTS
Standard Acceleration of Gravity
g = 9.80665 m/s2 = 32.1742 ft/s2
Speed of Light
c = 2.998 × 108 m/s
Planck’s Constant
h
p = 6.6261 × 1034 J-s
Stefan-Boltzmann Constant
σ ˆ 5:6704  108 W/m2-K4
ˆ 0:1712  108Btu/h-ft2-°R4
Universal Gas Constant
R ˆ 8:3143 J/gmole-K
ˆ 1:9859 Btu/lbmole-°R


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