Fund

amentalofm

easurements

7Mar

15

Introd

uctio

n

Cou

rse

2015

6

Toen

sure

afairexchange

fortrading

Tosatisfythene

edsfor

indu

stria

lized

prod

uctio

ntechniqu

eTo

provideaccurate

physicalvaria

bleinform

ationfor

scientificstud

y,processc

ontrolandmon

itorin

g.

English

andMetric

System

sUnita

ndmeasuresa

rede

velope

dfore

ffectivecommun

ication.

512kilobyte

persecon

ddata

rate,a

1600

meter

runw

ay,110

kilometer

perh

ourspe

edlim

itApint

ofmilk,96mile

perh

ourfastballs,

a15

ston

esman

TheEnglish

system

ofun

itsoriginated

from

Babylonian.It

was

theRo

man

swho

introd

uced

thebase

of12

intheEnglish

system

.Themetric

system

arou

sedarou

ndtheen

dof

18thcentury,its

developm

entfollowed

amoreratio

naland

scientificapproach

than

anthropo

metric

.

System

sofu

nits

Aun

itisaparticular

physicalqu

antity(le

ngth,w

eight,etc),

defin

edandadop

tedby

conventio

n,with

which

othe

rparticular

quantitieso

fthe

samekind

arecomparedto

express

theirv

alue

.Thevalueof

aph

ysicalqu

antityisthequ

antitativeexpression

ofaparticular

physicalqu

antityas

theprod

ucto

fanu

mbe

randaun

it,thenu

mbe

rbeing

itsnu

mericalvalue.

Fore

xample,thecircum

ferenceof

theeartharou

ndthe

equatorisg

iven

by:

C e=40

,074

103m

(meter)

quantity(dim

ensio

n):len

gth

unit:

meter

measure(m

agnitude

):40

,074

103

System

sofu

nits

Exam

ple:

Asheeto

fEurop

eanA4

pape

ris2

10millim

etersw

idth

by29

7millim

eterslon

g. quantity(dim

ensio

n):len

gth

unit:

millim

eter

measures:

210,29

7To

avoidmisinterpretations

theuseof

theinternationa

lsystem

ofun

its(SystrmeInternationald'unitrs,SI)ish

ighly

recommen

dedwhe

npresentin

gmeasurementresults.

Asystem

units

iscomprise

dof

based,supp

lementary

and

deriv

edun

its.B

ased

units

aredimen

sionally

inde

pend

ent.

Base

Units

7ba

seun

its:m

eter,kilo

gram

,secon

d,am

pere,K

elvin,

mole

andcand

ela.

Thefoun

datio

nforthe

SIsystem

was

laiddu

ringtheFren

chRe

volutio

n,with

thecreatio

nof

ametric

decimalsystem

ofun

itsandof

twoplatinum

standardsrep

resentingthemeter

andthekilogram

(179

9).The

unitof

timewas

basedon

the

astron

omicalsecond

(1/86,40

0of

ameansolard

ay).

In19

60the11

thCo

nfrren

ceGrnrralede

sPoids

etMesures

adop

tedtheam

pere

asthebasic

unitfore

lectric

current.Tw

oothe

rbasicun

itshave

been

adde

dto

thesystem

,for

tempe

rature

(Kelvin)

andlight

(cande

la),andin19

71anothe

rforsub

stance

(mole).

Meter

andKilogram

Themeter

(m)isthe

length

ofthepath

travelledby

light

invacuum

durin

gatim

eintervalof

1/29

979

245

8of

asecond

[17t

hGe

neral

Conferen

ceon

WeightsandMeasuresC

GPM

(1983),Res.1].The

speedof

light

invacuum

atexactly

299,792,458metersp

ersecond

.Thekilogram

(kg)istheun

itof

mass;itiseq

ualtothemasso

fthe

internationalprototype

ofthekilogram

[1stCG

PM(1889)].

A C

GI o

f the

inte

rnat

iona

l pr

otot

ype

kilo

gram

(the

inch

ru

ler

is fo

r sc

ale)

. The

pro

toty

pe

is m

anuf

actu

red

from

a

plat

inum

–iri

dium

allo

y an

d is

39

.17

mm

in b

oth

diam

eter

and

he

ight

, its

edg

es h

ave

a fo

ur-a

ngle

ch

amfe

r to

min

imiz

e w

ear

Second

andAm

pere

Thesecond

(s)isthe

duratio

nof

919

263

177

0pe

riods

ofthe

radiationcorrespo

ndingto

thetransitionbe

tweenthetw

ohype

rfinelevelsof

thegrou

ndstateof

thecesiu

m(Cs)133

atom

[13thCG

PM(1967),Res.1].

Theam

pere

(A)isthatcon

stantcurrent

which,ifm

aintaine

din

twostraight

parallelcon

ductorso

finfinite

length,ofn

egligible

circular

crosssection,andplaced

1meter

apartinvacuum

,wou

ldprod

ucebe

tweenthesecond

uctorsaforceeq

ualto2x

107ne

wtonpe

rmeter

oflength

[9th

CGPM

(194

8)].

the

ampe

re is

a m

easu

re o

f the

am

ount

of e

lect

ric

char

ge

pass

ing

a po

int

in a

n el

ectr

ic c

ircui

t pe

r un

it tim

e w

ith

6.24

110

18el

ectr

ons,

or o

ne c

oulo

mb

per

seco

nd

cons

titut

ing

one

ampe

re. A

mpe

res

can

be v

iew

ed a

s a

flow

ra

te, i

.e. n

umbe

r of

(cha

rged

) par

ticle

s tr

ansi

ting

per

unit

time.

KelvinandMole

TheKelvin(K),un

itof

thermod

ynam

ictempe

rature,isthe

fraction1/273.16

ofthethermod

ynam

ictempe

rature

ofthe

triplepo

into

fwater

[13thCG

PM(1967),Res.4].

Themole(m

ol)isthe

amou

ntof

substanceof

asystem

which

contains

asmanyelem

entary

entitiesa

sthe

reareatom

sin

0.01

2kilogram

ofcarbon

12[14thCG

PM(1971),Res.3]. Lord

Kel

vin

In c

hem

istr

y an

d ph

ysic

s, th

e A

voga

dro

cons

tant

(sym

bols

: L, N

A)

is d

efin

ed a

s th

e nu

mbe

r of

con

stitu

ent

part

icle

s (u

sual

ly a

tom

s or

mol

ecul

es) i

n on

e m

ole

of a

giv

en s

ubst

ance

. It

has

dim

ensi

ons

of r

ecip

roca

l mol

and

its

valu

e is

equ

al t

o 6.

0221

4129

(27)

1023

mol

1

Am

edeo

Avo

gadr

o

Cand

ela

Thecand

ela(cd)

istheluminou

sinten

sity,inagivendirection,

ofasource

that

emits

mon

ochrom

aticradiationof

freq

uency

54010

12he

rtza

ndthat

hasa

radiantinten

sityinthat

directionof

1/68

3wattp

ersteradian[16thCG

PM(1979),

Res.3].

A10

0wattlight

bulbhasthe

luminou

sinten

sityof

approxim

ately13

5cd.

Theradian

(rad)

andthesteradian(sr)aretw

oSI

supp

lementary

units.The

reare2

radianso

verthe

circum

ferenceof

acircleand4

steradians

over

thesurfa

ceof

ashpe

re.

A g

raph

ical

rep

rese

ntat

ion

of 1

ste

radi

an. T

he

sphe

re h

as r

adiu

s r,

and

in t

his

case

the

are

a of

th

e pa

tch

on t

he s

urfa

ce is

A=r2

.

Defin

ition

sofstand

ardun

its

Cou

rse

2015

16

Fund

amen

talSIunits

Cou

rse

2015

17

Deriv

edSIun

its(examples)

Cou

rse

2015

18

Conversio

nfactorsb

etweenun

itsystem

s

Exam

ple

Assume10

0Calare

expe

nded

fore

achmile

jogged

Acupof

icecream

contains

400Cal

1gof

fatp

rodu

ces9

Calofe

nergy

ToJog4miles

400Cal/9

Cal/g

=44

.4gbo

dyfat

Exam

ple

Volumeof

theair1

440ft3

Thede

nsity

ofaira

t1atm

and30

0Kis1.16

kg/m

3=0.00226

slag/

ft3

Themasso

fthe

air3

.25slu

gs(TE)

=47

.5kg

(SI)

Theweighto

fair3.25

slugs

32.174

ft/s

2=10

4.6lbf

47.5kg

9.81

m/s

2=465

.4N

Accuracy

ofthebase

units

Other

quantitiesthanthebase

quantitiesa

recalledderiv

edqu

antities.They

aredefin

edinterm

softhe

sevenbase

quantitiesv

iaasystem

ofqu

antityeq

uatio

ns.

Decimalprefixe

s(form

ostp

opular

cases)

Scientificno

tatio

n:to

avoidwritingvery

large

andvery

smallnum

bers

Exam

ple:

3250

00=3.2510

5 =3.25

E+5

The

SI p

refe

renc

e is

to

expr

ess

a nu

mbe

r us

ing

a pr

efix

suc

h th

at it

s nu

mer

ical

va

lue

is b

etw

een

0.1

and

1000

. (

2.4G

Hz,

300

kW)

Significant

Figures

Thenu

mbe

rofSignificantF

igures

shou

ldcorrespo

ndwith

the

uncertaintyinthemeasurement.(digits

upto

andinclud

ing

thefirstun

certaindigit).

Fore

xample,iftheun

certaintyinameasurementis

0.05

,then

themeasurementsho

uldbe

expressedas

2.55

0.05

Rulesfor

roun

ding

offa

numbe

rTrun

cate

thenu

mbe

rtoits

desired

length

Expressthe

excessdigitas

ade

cimalfra

ction

Roun

dup

theleastsignificantd

igitby

1,ifthefra

ction>½or

thefra

ctioniseq

ualto½andthe

leastsignificantd

igitisod

d.Itisleftalon

e,othe

rwise

.Exam

ple:

5.6850

103be

come5.68

103forthree

significant

digit

Exam

ple

Exam

ple

Exam

ple

54.0

0.5=?K

273.15+54.0=327.2K

0.5K

forthe

samelevelofp

recisio

n273.15+54.0=327K

form

aintaining

3sig

nificantfigures

Elem

entsof

ameasurementsystem

Cou

rse

2015

31

Prim

arysensor:gives

anou

tput

that

isafunctio

nof

the

measurand

liquidinglassthe

rmom

eter,a

thermocou

ple,andastrain

gauge

Elem

entsof

ameasurementsystem

Cou

rse

2015

32

Varia

bleconversio

nelem

ents:con

vertso

utpu

tvariableof

aprim

arytransducer

toamoreconven

ient

form

.thedisplacemen

tmeasurin

gstraingaugehasa

nou

tput

intheform

ofavaryingresistance.Be

causetheresistancechange

cann

otbe

measuredeasily,itisconvertedto

achange

involta

geby

abridge

circuit

Elem

entsof

ameasurementsystem

Cou

rse

2015

33

Signalprocessin

gelem

entsim

provethequ

ality

oftheou

tput

ofameasurement(no

iseredu

ction,sensitivity

and

resolutio

n)Prim

arysensor

andvaria

bleconversio

nelem

enta

recombine

d;this

combinatio

nisknow

nas

atransducer.

Insomecases,theword“sen

sor”

isused

gene

ricallyto

refertobo

thtransducersa

ndtransm

itters.

Choo

singAp

prop

riate

Measurin

gInstruments

Cou

rse

2015

34

specificatio

nof

theinstrumentcharacteristicsreq

uired

accuracy,resolution,sensitivity,and

dynamicpe

rform

ance

theenvironm

entalcon

ditio

nsInstrumentd

urability

andmainten

ance

requ

irements

Tradeoffb

etweenpe

rform

ance

andcost

thetotalpurchasecostandestim

ated

mainten

ance

costso

fan

instrumento

veritslifearedivide

dby

thepe

riodof

itsexpe

cted

life.

newtechniqu

esandinstrumentsarebe

ingde

velope

dallthe

time,andthereforeagood

instrumentatio

nen

gine

ermust

keep

abreasto

fthe

latestde

velopm

entsby

readingthe

approp

riate

technicaljou

rnalsregularly.

Exam

plefora

pplications

Cou

rse

2015

35

Applications

ofmeasurin

ginstruments

regulatin

gtrade

mon

itorin

gfunctio

nsandcalibratin

gtheinstruments

Toform

afeed

back

controlsystems

Endof

theCh

apter

Cou

rse

2015

36