Mechanical Measurements
Mechanical Measurements
Cal Poly Pomona
Engineering
Contents
1 The Process of Measurement: An Overview
Thomas G. Beckwith/Roy D. Marangoni/John H. Lienhard V .
2 Standards and Dimensional Units of Measurement
Thomas G. Beckwith/Roy D. Marangoni/John H. Lienhard V 15
3 Assessing and Presenting Experimental Data
Thomas G. Beckwith/Roy D. Marangoni/John H.Lienhard V 35
4 The Analog Measurand: Time-Dependent Characteristics
Thomas G. Beckwilh/Roy D. Marangoni/John H. Lienhard V 111
5 The Response of Measuring Systems
Thomas G. Beckwith/Roy D. Marangoni/John H. Lienhard V . 145
6 Sensors
Thomas G. Beckwith/Roy D. Marangoni/John H. Lienhard V . 191
7 Signal Conditioning
Thomas G. Beckwith/Roy D. Marangoni/John H. Lienhard V . 239
8 Digital Techniques in Mechanical Measurements
Thomas G. Beckwith/Roy D. Marangoni/John H. Lienhard V . 301
9 Strain and Stress: Measurement and Analysis
Thomas G. Beckwith/Roy D. Marangoni/John H. Lienhard V 347
10 Measurement of Pressure
Thomas G. Beckwilh/Roy D. Marangoni/John H. Lienhard V . 393
11 Measurement of Fluid Flow
Thomas G. Beckwith/Roy D. Marangoni/John H. Lienhard V . 431
12 Temperature Measurements
Thomas G. Beckwith/Roy D. Marangoni/John H. Lienhard V . 483
13 Measurement of Motion
Thomas G. Beclcwith/Roy D. Marangoni/John H. Lienhard V . 563
14 Appendix: Standards and Conversion Equations
Thomas G. Beckwith/Roy D. Marangoni/John H. Lienhard V . 59915 Appendix: Theoretical Basis for Fourier Analysis
Thomas G. Beckwith/Roy D. Mara11go11VJoh11 H. Lienhard V . 603
16 Appendix: Number Systems
Thomas G. Beckwith/Roy D. Marongo11VJoh11 H. Lienhard V 609
17 Appendix: Some Useful Data
Thomas G. Beckwith/Roy D. Marangoni/John H. Lienhard V . 615
18 Appendix: Stress and Strain Relationships
Thomas G. Beckwith/Roy D. Mara11gonVJohn H. Lienhard V . 621
19 Appendix: Statistical Tests of Least Squares Fits
Thomas G. Beckwith/Roy D. MarangonVJohn H. Lienhard V . 637
Index
A
Abeorpthllly. 522-523
–
.lion. 184, 419-420, 584
p1eme-, 212, 575-679
theory, 564
Allasing, 131-132, 328
Amsican National 5-.ds lnsllule (ANSI). 2
Ampltt- al .,.,,.,,., 111
Analog signals, 303
Analog-lo-digital CIXlversion
. 11, 42-44, 318. 312, 394, 473, 507
palllllel encador, 335
quanlizalion . 337-338
resolution, 43, 131-132, 337-338, 459. 517, 579
Ample rale, 1 31-135, 328
signal cordtlaning for, 338
An- c:hlmber. 138
An-r hol .n and
ullfBlonlo.Dapp, 432
ASCII, 319-321
? -. 22, 84-85. 3113-384, *· 491 ,
599, 817
8
Balance analytical (bum)
cum1nl 17-18, 102, 180, 218-221, 253, 347, 496,
565
·- cin:uil, 239, 347
llllr, 20, 47, 322, 387, 394, 800
–
anllOid, 403
Bell pnwer, 457
llemouli’s eqllllion. 434
Bias anor. 38-41 , 225, 555
Blas uncertainty, 44-45
Binary codes
alphanumeric, 303
bar code, 322
llaudol, 318-319
Gray code. 317-319
1n1-.1 Mana. 318
parily, 321?
?. 321
Btt lnlerval, 303
Boda plol. 284
Bourdon lube. 8, 194, 403
Bridge
ac. 259
balancing ogamanll, 252
CIXllllalll 231 , 245, 347, 409, -7. 498-500
a.illanl .,._ 256-257, 347, 498-499
.-. 242-243, 360
de-. 252-253. 358, 405, 487, 498
faclar, 242, 357. 408, 501
lour_ _ _ 498-499
llol-wil9 -. 488
null, 252-253, 358, 498
raaclance, 203, 253
–· 202-203. 242-243. 347. 407-410. 487,
495-502
-in -· 241. 351-352
lempaiahn ,.,_sa11on, 230, 347, 405
-. 253-255, 358, 487
wi.ais1one. 251-252, 351, 552
. 265, 598
Bue
exlemal. 287, 328-329
1- i. 328-329
llyla, 303
c
?llan
al accallramal . 564
of liquid?n-9m 549
of prmai-ng ayslafM, 393
ol aailllllc ?Is, 575
of aysl8rn -· 1″41
or _ -. 519
of .,_, 584
. and dynarric, 393-394
Celoriasympllltic. 547
-l capacilanca, 547
Cspacitenc:e, 6, 18, 100-101, 154, 197, 240, 407, 544.
575
Conni llmll 111-. 58
Cenlnl pracaulng un? (CPU), 329
Qlalced llow, 448-449
Clrallls
bdal, 239, 359, 501
brtclge. 242. 359-381 , 501
lnl8graled. 222. 285-288. 304, 517
239
?. 258, 305, 381
,._. d_, 248-248
Qua lnlarvlla. 0.70
Clock
– . 21, 230-231, 302-304
.-, 231, 313
–
iilgMI, 231 , 302-304
? .
dllclialVe. 187
hmnonlc. 148, 584
Coi1mHnOde nolla nijecticn
nijecaon rallo (CMRR? 268
Compllralar dspllcemenl
“”””””· 8, 74, 180, 193, 239-240, 383, 407. 449.
565
Coupling malhcxll, 239
Cilllcal pt9llUi9 ratic, 448
Clyoganlc .,iemanll liquid halum –
– . 2. 44-45, 143, 192, 241 , 305, 347-348, 396,
479, 495, 621 -4i22
2. 15, 41-42, 143, 185-187, 198-197.
268. 328. 347. 393, 453. 483-510,
618-817
D
Demping
allical, 158, 570
ratic, 158-157, 218, 570-671
undeRlamping, 188
Dale
d- of. 38-39. 638
gqpllical — ol. 38
pracaulng of. 304
Ample of, 11-12, 44, 324, 383
Dabt
singl&-lampla, 38
Deacl-weighl -. 388
Daliouncar, 309
Decl>al. 283
Daftaclfon conatanl. 107, 161 , 223-224, 404, 588
DlmodoAallon. 241
Demulllpl-. 312
Dllvilllon
-· 44, 200, 405, 520, 838
Dllleranllld .- r. 192-193, 240. 585
Digilll
– 304, 531-632
codal, 302
Imaging. 339, 531
–. 8, 129, 241, 304, 360-381. 579
lignels, 8, 129, 239-240, 303-305. 473
-. 331’333, 385, 531
Olgllal dil:ui _
. displays, 304, 508
Dlgllml ciR:uilry
11181og–igilol, 130, 253, 302
digll9l-lcHlnlkig, 274, 302-303
.,, c:cunlor, 309
INquancy -· 324
microprac11w. 130, 302. 508-509
mullfplexw, 32&327
-· 7. 253. 304, 508. 577
w hoping, 325
Digllal lmoglng
hlgh ?. 340
Olgbl mlgnal – (DSP), 343
Discltvgo coefticienl. 437
Dilc:nila Ampllng. 129
Dillrtbulian
chi-sq . 38
?llly. 45, 840
Weibul, 69
Doppler burst, 472
Doppler llequency lhift, 470
Drill, 5, 21, 40, 200, 251, 313. 407. 452, 5
E
Edllan ellec:l, 285
– . . 25
ElmQanlc caunter, 519
ElmQanic -. 204-205
e-.,. 488
Encador
biMry, 318-320
dilplacemanl. 317
E.,., _ Ma.Id, 21-22
Enor
biaa, 1 1 , 38, 225. 555-558
hyslefelia, 40-42, 494
–. 259. 381
loading, 38, 247-248. 379. 426, 573
-. 4, 38, 494, 597. 837-839
pyromtllry, 528
-ng. 4, 4 1 , 225, 248. 490-492
-· 4, 41 , 225-226. 248. 489-492
lamperature drill. 78
lamperature maa -.nant. 5, 82-43, 4
zero ollaa? 11
EV81’11 ccunler, 324
e.n.omaior. 350
F
Fadar bttdge
expansion, 230, 382. 448-447. 490-49:
lrequency encl . disloltion. 149
v-.y of appioecll, 435
Fsaday’s law, 206, 451
Filler (alaclrical)
aclive. 239, 408
nllaliallng. 338-339
band-. 278-277
-. 11
cutoll froquancy, 277-21111
digital, 4. 73, 212, 240, 301-303, 386, ?
531-532, 579
high–. 182. 278-277
LC , 183
,, _, 1 53-154, 278-280. 338. 558
-. 290
o_,. of, 100. 215, 352, 429, 559, 588
lu-. 282
Flip.flop
S-R, 309
Flow visuallmlion
— lluoroocanc:e. 432
Flowmelers
calilnllon of, 431
Coriolis. 432e11uca1 now n111d, 432
eleclrOmagnellc, 432
obstrucllon, 431-433
olifice. 434-435
ftow nozzle. 435
posllive displ ,.1111111, 449-4llO
lherm1I, 431-432
turbine, 432
ul”-‘lc, 432
venlud, 432
Flu: ‘:shedcfng, C53
clla-rl$tics of, 449-460
cllolced. 448-449
ioc;ry ., urernent, 475
Fluid velocily, — of
? nulds, 445
Doppler-shill me.-. 432
frequency response, 41, 151-153. 219, 240, 397,
459, 548
Klellube, 462
luer-Ooppler ,omal8r, 432
Pilot lube, 198, 4!58
pressure probes, 431-432
ulllasonlc-Oopple -. 432
Force measurement of
lnlnsducers, 5, 152-153, 192·195, 292, 342, 363,
393, 454, 565
Forcing !Unction
genero? 23, 1 59-160, 195. 288-289, 351-352,
399-400, 455, 493, 588. 604
sbtpped, 151, 422
Fourier a,.lysis
dlacrale, 10, 1 29-132, 608-e!7
.mplesof, 38, 118, 561
Fourier-· 115, 160, 64l!MI07
F-beat
drculer, 31-32, 111-114, 155, 304, 402, 586
cydlc, 111, 165
damped 1u . 188
_.1111 -. a
!Un-? 4, 15-18, 120, 149, 20f, 302, 417,
585, 808
meuurement ol, 23. 184, 208. 239-240, 398-396,
452-455, 521 , 583-679 .
merer, 12, 1&-17, 158, 207, 302, 545
Nyqui? 131-132, 340, 807
reson.,co, 143, 163, 210, 261-262, 339, 41 7, 566
response, 1 1 , 16, 40-42, 122, 145-159, 201 ,
239-240, 312, 39&-397, 458-459,
541-645, 584
s”91’1rum, 1 1 1 , 328, 423, 521
undamped natural, 159, 589-570
Fringe (interference)
laser-Ooppler, 470-471
Funcdon generolllr, 579
G
Gage -r. 1 1 , 259, 353-355, 408
Gate, 307-309
Gausaian or normal diotribufion, 99
G-ral Conleftlnce on Weighla and Measures, 17
Goodness-ol.fil, 66
Graphlcal p .,,lallon ofdola
choosing coonlinalas, 87
genaral rules for, 65
slraight-line lnlnlformations, 92
Grounding, 239, 309
H
Hall ellecl
quanlum, 28, 108
Harmonic>
analysis, 1 1 1 , 151, 584, 604
coelllclont, 588
Older, 122, 146, 277, 589-570
slmple. 111-114, 146, 565
HolmhollZ fllOllBlor, 417
HerlZ, 17, 113, 155, 324, 4 1 7-418
Hislogram, 47
Hurricane Bob, 84-85
Hl’POU-is lellting
I
large sample, 63
of sample meens, 64
1 11,,.,ie, &1
Impedance bridge, 253
Impedance, input and output ampllllors
and noise, 287, 304, 380
mlllchfno, 6, 74, 209, 272, 576
ind=15, 250, 325, 350, 435, 599
mulull, 1 0 1 , 201
sall, 195, 241
transclucor, &-7, 195-1 96. 239,408
lnd.-ice
– raluc:tance, 201, 406. 575
Infrared l8diation (lghl) and hoot
sensing. 7, 186, 199, 243-244, 31 7, 380. 397,
431-432, 483-485. 587
lnlelfae, communications
··-· 331-333
parallel, 264, 330
eerill, 332-333
wireleoa, 332-333
lnlafacing, 305
1nl8lfenlmetiy
holographic, 351 , 475
lnlam11ian1I T “1*’81ure Scale of 1990, 23, 494
lnlarvll d1u
conlldonco, 37, 639-840
J
Josophoon Juncdon, 28
JPEG, 341
L
Laser
In- ftUOfHClllco, 432
Wllodly 431
wa”81englhs of, 20, 108
Laich, 309-310
Law “‘ inlermedlele .- . 504-505
Law ol inlennedllle lemperelureo, 504
Laall lqUllW (lln- 19g18Ulon)
conftdenco lnllmlls lor. 639
otllllstical lells ol, 637
Langlll Light -. 4
monochromatic, 529
? of. 4, 31-32, 42-43, 217-218, 489, 522
Lighl delecling lransduoers
avalanche photadlode, 219
pholodlodes, 215-220
pholomultipler lube (PMT), 471
pholon dllectars, 21 7-219, 521 -522
pho1onns111ors, 218
p)’IOelllClric. 212, 521
lhannal deleClors, 21 7, 521
Lino filting, 94
Linearily
ol polenliomeler, 249
Laad cel
h,., lc and pneumalic, 564
tempenlture sensitivity of, SOB
Loading “””‘· 41 , 247
Logarilhmlc decremon? 596-597
Lagle etomenra, 305
Laudnou. 262
M
Manomerer, 82. 397-402, 481, 816
Mcleod gage, 412-413
Mean (a¥8rageJ, definition of
for population, 53
lorsample. 53
Measurand
analog, 10, 1211-131 . 304
MeMUremont
molhods ol, 2, 73, 231 , 356. 396, 531
Mendenhall onlor, 16
–
lnoquoncy, 1 1 , 15, 155, 207. 302, 544-645
time interval, 20
Miclucompuler, 302
miCloproce1SOr, 130, 302, 489, S06-509
Madu1us
reaislors,409
Mohr’s cn:le, 622
Morse code. 318
MPEG, 341
mulllpllll8r, 32&-327
Muhlvibnitor, 31 2-313
N
642
National Bureau of Slandmda (NBS) 2 16
National ‘r”””9f Slandanla and ?nology INSI’?
Nibble, 303
Noire, 5, 42. 153, 265-287. 304-305, ·- 51
Nonnar probablly plol, 69-71 -· 9 57tl
NOZZie, now, 435-438
N.- ., .
. 15
=??;?;??12. !589.110M12
aclal, 316, 61CMl11
0
Otm’s law, 178, 243-244
Oplailolator, 221
Order
ol mechanical syslem1, 185, 240
Orlice llawrr8W, 436
Osclllosc:opo (CRO)
=??· 129, 152-153, 253, 304-306
p
Parlly, 321-322
Pellier ellecr, 504
Podod, 1? 120, 158, 1 118, 324, 350, 457, 51JO,
Phase ambiguity, 132
Phue response, 148, 240, 573
PholoconduClive malarials, 217
pholadiado, 197, 296, 522
? stic:ill\ 351
“‘-IClric lllled, 217
Ph- Ulliplier lube, 122, 218, 471-472
.,_,-“‘· 217-219, 521-522
“‘-anoistor, 219-220
Plezoeleclric _ 172, 192, 407, 575
Plozonlslsavlly, 213 .
Plranl gage, 414
Pilch lllde. 483
pbml, 341
-. 370. 626
pr>Junctions, 213
– reoistanoe
voltage-diWllng, 180, 193, 239, 367, 585
Practical lemperalure ICllle, 23, 74, 483
Precision error
unte11ainly. 3-4, 20, 38-37, 224, 389, 5116, 63!M!40
Preaaure absolule
cl)onamlc, 5, 18, 114, 158, 196, 261 , 356-358,
393-395, 434, 560, 588
gage, 5, 64, 157, 192, 354-358, 383-394,465
hood, 457, 590
sound, 41, 121, 212, 282, 395, 448, 538
slagnation, 395, 460-482, 535
standards, 1 0, 1&-18, 40, 397, 458, 540, 599
static, 8, 196, 362, 394-395, 432, 5311-539, 588
lolll, 54, 229, 368. 395, 432, 484, 570
vacuum, 22, 42, 214, 3!13-3M, 486
vllaclly, 8. 18, 114, 158, 19&-197, 395, 431-435,
533, 587, 801
Pressuro capsule, 405
P””‘oure lnlnod\lcors
bu modulus, 410
dynamic> reoponoe ol, 158, 404, 560
high pre$8’1f8, 422, 589
row pressure. 412
menometers, 412
oemlc:onducmrdiaphragm, 213, 405
lire gage, 7, 1 57
PlllllablNly dlsbibulion, 47-48
Pftlvlng inslnlmon? 10
Pftlvlng ring, 8, 198
Pulse-code modulation {PCM), 303
Pyrooleclric sensors, 217, 531
Pytometty
Q
disappearing fil81T11111? 529
enor in, 526
infrared, 484
Quantum Hall -. 26
R
Radiation shield, 536
Radix, 316, 60!M10
Rudlng onor, 43, 337522
Alec, 304
192, 406. 449, 565
lemperalure d- (RTD>
. cold-wlte. ?
inS1Nmenlallon for, 3118, 496
typkal ptOpertieS ol, 497
lllSiSIMIY
— cOeftlcionl of, 354
llOlislOl’I
and. 200. 248-250, 305, 408-410
rnoduu, 409-410
AoM>lution
NO .-
. 336-339
inSll\llMfl? 37. 200, 337. 429, 566-567
pollnltomelers. 200
–” cln:ulls, 239
flllpol1H
amplilllde, 10. 1 2 1 . 148-147, 240-241 , 337, 381 ,
419, 542, 570
experimenlal delermlnation of, 186
phaH. 146. 240-241 , 484, 571-573
Roynalds nu-. 29, 88. 434
time, 148, 423
Roi angle, 478
floOl-mean-square (RMS). 128
_ ,,, 455
s
_.,
– ol. 79
– led. 43
oingle, 10-13, 36-37. 325. 378-379
. – devlatlon ol. 53
Selle (for welgllklg)
ballnce, 7-8. 25, 61, 155-156, 254, 380, 396, 434,
496
pendulum, 158, 592
spring, 6-7, 113-114, 146, 223, 404, 492, 587
Sc:lrnidllrlgger, 312
Soolcll yoloe, 113
Seebeck coelliclenl, 502
Segorconea, 532
–or
claphrogm pressure .,_,., 213, 405
n-lype and p-lype, 213
pn-junctions. 213
oonsors. 191-193, 405, 483-484. 575
lemperalura ,._,., 213. 483-484
Sonsitivily
denned, 37, 256, 410, 564
Ser-
Pf8SSIR, 83-85, 1 73, 193-194, 366, 395-396,
431-432. 483-485
semiQondudOr, 192, 405, 483-484, 576
vari- inductance. 195, 406-407
– ·-· 195, 299
Sealingtime, 151
llielclng, 239, 535
SllOd< -ng. 564
SllOd< lube, 420
SI (Sys!’ me lnlamalional d’Unir. >
system of unns . 31-32, 428
Signol condilionlng, 6-7, 176, 212, 239-240, 337-338,
405, 452, 484. 578
lllgnilicance, laval ol, 103
Slew rate, 148, 267
Sound lllenuation of
inlenslly, 121 . 197, 340, 470
-· 42, 285-287, 304-305, 565
?:;.:?63, 305-306, 466-468, 585
calibration melhods. 393, 577
?ii:.?46
?ral ?manalyzer, analysil, 12126, 8 328
?scalo, 223
l1mosphao1c prenure, 22, 393-394, 464, 617
COii, 458, 508, 597
lloctrtcal, 3, 22, 100-101 , 199, 285, 343, 404,
487-488, 483-484, 578
lot -.ure, 405
:glavialenglh,tional2, 20acceleralion, 225, 618
al 2, 76, 457, 578
al lemperalure, 22. 399, 467, 463
lier. 77, 274, 334, 378. 519
standanl
lolal rad-. 529
lw<M:olor, 484
Slandald devlalion
of samplo, 55
of the rMan, 56, 640
Slalan·llollzmann law, 525
Slraighl-line 1ran.m-., 92
Strain al a point
Mohr’s cin:le lor, 622
Strain gage
configurellono, 251, 351 , 495
conslruCtion ol, 351 , 495
for pressure eels, 410
orienlatlan ol, 374. 478. 626
poslyield, 380
18Sls1ance-type, 11, 193, 245, 353
roselles, 389
-. 575
Slress blalCial
hoop, 102, 369-370, 634
plane, 18, 351, 822-823
principal, 212, 358, 427, 622
uniaxial, 349
Surface roughnas, 212
Survey fool. 20
Syslam
analogous, 4, 114. 156, 192. 285, 305
of unlls, 17, 393, 434
sec:ond-onlar, 146, 419
zero-order, 146
T
Temperature
standard for, 26, 398, 457. 485
fixed poinls, 25. 549
Temperature sensors
blmetal, 196, 485
?. 25, 526-529
resiolanca lype, 501
– ol, 42, 151-154. 203, 240, 397, 459, 493.
574
Hmiconductar-jundion, 215, 483-484
1’1ennislor, 196, 292, 487-488
1’1ennocouple, 8. 82. 180, 192, 328, 414-415. 468
Thermal anemomeler
hol-wire and hol-ftlm. 432
thermal ftowmetenl, 469
ThOITNll imaging, 484
Tharmal 1Bdiation, 24, 212, 414, 468, 484
Thermocouple
high-valoclty, 5311-537
ice point 556
polynomial . 507
Thermometer constant-volume gas
liquid?n-glass, 484
Thermopile, 84, 217, 5111-519
Time con&lanl. 91, 161-163, 54 1
Time coonlinaled universal (UTC)
standard of, 2, 15-16
Time dependence, 8
Transducers
secondaiy. 4, 192-195, 383. 396, 585
Transmissivily, 522-523
Triple point, 22-24, 549
Trul’1 !ables, 307-309
u
UART. 327
Ulltasonic
enamornelet’, 432
Unceflainly
intn>duc:lion to, 36, 550
odds for. 73
propagation or. 36
Units of measurement
conversion or, 395
v
V.cwm. 20, 42, 214, 285, 306, 393-394. 486
vacuum lube, 308
Velocily measuremenl by variable reluclence
lransd”‘*11
Doppler-shift, 431-432
Vena oonlracta, 441
Venluri mater. 399. 448
Vibrallon excilars
leSling, 581-582
643
w
Wave shaping, 325
waveforms
ampliludes of, 111
complex. 111 . 146, 578
special, 122-123, 147, 312, 581, 804-806
lranslenl, 111, 174, 581
weigh .k, 80, 457
Weighl, 1 1 , 26, 63, 112, 225, 315, 398, 431 ,
Whole-field mea –
of displacemen? 390, 403, 564
or ftuid flow, 479
Wien dlsplacemenl law, 525
Wold, 2, 36, 265, 303-304. 347-348, 521
y
Yaw angle, 481-462
Young’s mod?ua
values of, 226, 383. 412, 550, 618
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