Module 1 Gec 227

GCE 227 CHAPTER 1 Lecture1:

Fundamental Concept of Metrology

Preamble:

Measurement is simply defined as the estimation or determination of extent dimension or capacity usually in relation to source standard or unit! Metrolo"y on the other hand is the study of measurement! The comparison must #e to standard as indicated #elo$! %tandard Comparision Mesurand

Process &Measurement'

&Comparision to a standard'

Result

Fundamental Units Of Measure, SI System The %( system is the latest form of metric system and has t$o supplementary units )i* radian &for solid an"le' and steradian &for plane an"le' in addition to se)en #ase units of metre +" second ampere +el)in candela and mole for len"th mass time current thermo dynamic temperature luminous intensity and amount of su#stance respecti)ely! All other units can #e deri)ed from these ,uantities! The %( system is a comprehensi)e lo"ical and coherent system desi"ned for use in all #ranches of science en"ineerin" and technolo"y! technolo"y!

The sym#ols units and dimension of )arious mechanical electrical and ma"netic ,uantities are "i)en #elo$Quantity

Symbol Unit

Area Volume Frequency Density Velocity

A V F D V

M2 M3 Hz Kg/M3 M/S

Dimension

L2 L3 T-1 ML-3 LT-1

Quantity

Symbol

Unit

Dimension

Acceleration Force or!" energy $o%er  Sur&ace tension '(arge $otential" Di&&erence em& 

A F " ) $

M/S2  +,+e%ton .,+-M ,./S

* V" )

',A-S V

ML-3 LT-1 LT-2 MLT-2 ML2T-2 T ML2T-3-1

)lectric &iel0 strengt( esistance 'aacitance n0uctance Magnetic &lu Magnetic &iel0 strengt( Magnetic &lu 0ensity

)   ' L

V/M ,V/A F H 5 A/m T,5/M2

MLT-3-1 ML2T-3-2 M-1L-2T62 ML2T-2-2 ML3T-2-1 L-1 ML-2-1

Φ

H 4

Quantity

Symbol Unit

Magnetic moti7e F &orce ,MMF S eluctance 8 $ermea5ility M $ole-strengt( Ψ )lectric &lu D )lectric &lu 0ensity  9 $ermitti7ity

Dimension

A



A /%5 H/m 5 ' '/M2 F/m

M-1L-2T22 MLT-2-2 ML2T-2-1 TL L-2T M-1L-3T62

.ote- That the dimension for the electrical current ,uantity is &('!

1! I"#$O%UC#IO"

The de)ice used for comparin" the un+no$n ,uality $ith the unit of measurement or a standard ,uality is called the measurin" instrument! Measurement "enerally in)ol)es the use of an instrument as a means of determinin" a ,uantity or a )aria#le! The instrument assists a person to determine the )alue of an un+no$n ,uantity $hich could not other$ise #e measured #y this human facilities alone! The )alue of un+no$n ,uantity can #e determined #y direct method such as measurement of current #y ammeter or #y indirect method such as determination of resistance #y ammeter )oltmeter method! /irect measurin" instruments are most $idely used in en"ineerin" practice since they are the most simple and inexpensi)e ones and ena#le the measurements to #e made in the shortest possi#le time!

Measurement $or+ employs the follo$in" termsi

Instrument:  A de)ice for determinin" the )alue or ma"nitude of a )aria#le or ,uantity!

ii Input signal:  A si"nal applied to a de)ice element or system such as pressure applied to the input connection of a pressure transmitter! iii Output signal:  A si"nal deli)ered or "enerated #y a de)ice element or system! i& 'ccuracy:  The de"ree of conformity or closeness $ith $hich an instrument readin" approaches the true )alue of the )aria#le or ,uantity #ein" measured! ( Precision: A measure of the reproduci#ility of the measurement0 that is "i)en a )alue of a )aria#le precision means the de"ree to $hich successi)e measurements of the same )alue differ from one another! (i Sensiti&ity:  The ratio of the output si"nal or response of the instrument to a chan"e of the input or measured )alue!

iiResolution: The smallest chan"e in measured

11 )$$O$S I" M)'SU$)M)"# (n practical measurement of ,uantities it is not possi#le to o#tain exact or perfect )alues! .o measurement may #e made $ith perfect accuracy the imperfections of a measurement are due to errors arisin" in course of practical measurements! Error may come from different sources and are usually classified under three main headin"s-

*a+

ross error:  These are lar"ely human errors and include0 misreadin" of instruments incorrect ad3ustments ¶llax' and improper application of instruments and mista+es in computation!

*b+ Systematic )rrors: These are errors due to short comin"s of the instrument! %ome systematic errors are-

i! Constructions Errors! This is found in an instrument as indicated #y the manufacturers! The maximum tolerances $ithin $hich ,uantities measured #y the instrument should #e as indicated e!"! ( 14! ii! Effect of the en)ironment on the instrument &Am#ient condition error' e!"! temperature attitudes pressure e!t!c! iii! Error inherent in method used Example (

(R

(

R

5

~

&r'

( A  A

6(RR 6 ( Ar  6 ( Rr  Rtr  ( A6

R Rtr 

(

and

 r  Rtr 

(R6

(

et ( 6 8A R6199R r61R ( A6 (R6

 199 199=1

8 6 :!;8A

 1 199=1

8 6 9!98A

Relati)e error 6

9!98 8

x199 614

.o$ let (68A R6199Ω  r619Ω ( A6 (R6

 199 199=19

19 199=19

8 6:!8:8A 8 69!:8A 9!:8 8

Relati)e error 6

6;!94

i)! Error due to a"ein" and $ear of e,uipment! Example- consider the measurement of a resistance #y the )oltmeter