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West Bengal University of technology
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B.Tech
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1
Introduction to
measurement
Measurement techniques have been of immense importance ever since the start of
human civilization, when measurements were first needed to regulate the transfer of
goods in barter trade to ensure that exchanges were fair. The industrial revolution
during the nineteenth century brought about a rapid development of new instruments
and measurement techniques to satisfy the needs of industrialized production techniques. Since that time, there has been a large and rapid growth in new industrial
technology. This has been particularly evident during the last part of the twentieth
century, encouraged by developments in electronics in general and computers in particular. This, in turn, has required a parallel growth in new instruments and measurement
techniques.
The massive growth in the application of computers to industrial process control
and monitoring tasks has spawned a parallel growth in the requirement for instruments
to measure, record and control process variables. As modern production techniques
dictate working to tighter and tighter accuracy limits, and as economic forces limiting
production costs become more severe, so the requirement for instruments to be both
accurate and cheap becomes ever harder to satisfy. This latter problem is at the focal
point of the research and development efforts of all instrument manufacturers. In the
past few years, the most cost-effective means of improving instrument accuracy has
been found in many cases to be the inclusion of digital computing power within
instruments themselves. These intelligent instruments therefore feature prominently in
current instrument manufacturers’ catalogues.
1.1
Measurement units
The very first measurement units were those used in barter trade to quantify the amounts
being exchanged and to establish clear rules about the relative values of different
commodities. Such early systems of measurement were based on whatever was available as a measuring unit. For purposes of measuring length, the human torso was a
convenient tool, and gave us units of the hand, the foot and the cubit. Although generally adequate for barter trade systems, such measurement units are of course imprecise,
varying as they do from one person to the next. Therefore, there has been a progressive
movement towards measurement units that are defined much more accurately.

The first improved measurement unit was a unit of length (the metre) defined as
107 times the polar quadrant of the earth. A platinum bar made to this length was
established as a standard of length in the early part of the nineteenth century. This
was superseded by a superior quality standard bar in 1889, manufactured from a
platinum–iridium alloy. Since that time, technological research has enabled further
improvements to be made in the standard used for defining length. Firstly, in 1960, a
standard metre was redefined in terms of 1.65076373 ð 106 wavelengths of the radiation from krypton-86 in vacuum. More recently, in 1983, the metre was redefined yet
again as the length of path travelled by light in an interval of 1/299 792 458 seconds.
In a similar fashion, standard units for the measurement of other physical quantities
have been defined and progressively improved over the years. The latest standards
for defining the units used for measuring a range of physical variables are given in
Table 1.1.
The early establishment of standards for the measurement of physical quantities
proceeded in several countries at broadly parallel times, and in consequence, several
sets of units emerged for measuring the same physical variable. For instance, length
can be measured in yards, metres, or several other units. Apart from the major units
of length, subdivisions of standard units exist such as feet, inches, centimetres and
millimetres, with a fixed relationship between each fundamental unit and its subdivisions.
Table 1.1 Definitions of standard units
Physical quantity
Standard unit
Definition
Length
metre
Mass
kilogram
The length of path travelled by light in an interval of
1/299 792 458 seconds
The mass of a platinum–iridium cylinder kept in the
International Bureau of Weights and Measures,
S`evres, Paris
Time
second
Temperature
kelvin
Current
ampere
Luminous intensity
candela
Matter
mole
9.192631770 ð 109 cycles of radiation from
vaporized caesium-133 (an accuracy of 1 in 1012 or
1 second in 36 000 years)
The temperature difference between absolute zero
and the triple point of water is defined as 273.16
kelvin
One ampere is the current flowing through two
infinitely long parallel conductors of negligible
cross-section placed 1 metre apart in a vacuum and
producing a force of 2 ð 107 newtons per metre
length of conductor
One candela is the luminous intensity in a given
direction from a source emitting monochromatic
radiation at a frequency of 540 terahertz (Hz ð 1012 )
and with a radiant density in that direction of 1.4641
mW/steradian. (1 steradian is the solid angle which,
having its vertex at the centre of a sphere, cuts off an
area of the sphere surface equal to that of a square
with sides of length equal to the sphere radius)
The number of atoms in a 0.012 kg mass of
carbon-12

Table 1.2 Fundamental and derived SI units
(a) Fundamental units
Quantity
Standard unit
Symbol
Length
Mass
Time
Electric current
Temperature
Luminous intensity
Matter
metre
kilogram
second
ampere
kelvin
candela
mole
m
kg
s
A
K
cd
mol
Quantity
Standard unit
Symbol
Plane angle
Solid angle
radian
steradian
rad
sr
(b) Supplementary fundamental units
(c) Derived units
Quantity
Standard unit
Symbol
Area
Volume
Velocity
Acceleration
Angular velocity
Angular acceleration
Density
Specific volume
Mass flow rate
Volume flow rate
Force
Pressure
Torque
Momentum
Moment of inertia
Kinematic viscosity
Dynamic viscosity
Work, energy, heat
Specific energy
Power
Thermal conductivity
Electric charge
Voltage, e.m.f., pot. diff.
Electric field strength
Electric resistance
Electric capacitance
Electric inductance
Electric conductance
Resistivity
Permittivity
Permeability
Current density
square metre
cubic metre
metre per second
metre per second squared
radian per second
radian per second squared
kilogram per cubic metre
cubic metre per kilogram
kilogram per second
cubic metre per second
newton
newton per square metre
newton metre
kilogram metre per second
kilogram metre squared
square metre per second
newton second per square metre
joule
joule per cubic metre
watt
watt per metre kelvin
coulomb
volt
volt per metre
ohm
farad
henry
siemen
ohm metre
farad per metre
henry per metre
ampere per square metre
m2
m3
m/s
m/s2
rad/s
rad/s2
kg/m3
m3 /kg
kg/s
m3 /s
N
N/m2
Nm
kg m/s
kg m2
m2 /s
N s/m2
J
J/m3
W
W/m K
C
V
V/m
F
H
S
m
F/m
H/m
A/m2
Derivation
formula
kg m/s2
Nm
J/s
As
W/A
V/A
A s/V
V s/A
A/V
(continued overleaf )

Table 1.2 (continued)
(c) Derived units
Quantity
Standard unit
Symbol
Magnetic flux
Magnetic flux density
Magnetic field strength
Frequency
Luminous flux
Luminance
Illumination
Molar volume
Molarity
Molar energy
weber
tesla
ampere per metre
hertz
lumen
candela per square metre
lux
cubic metre per mole
mole per kilogram
joule per mole
Wb
T
A/m
Hz
lm
cd/m2
lx
m3 /mol
mol/kg
J/mol
Derivation
formula
Vs
Wb/m2
s1
cd sr
lm/m2
Yards, feet and inches belong to the Imperial System of units, which is characterized
by having varying and cumbersome multiplication factors relating fundamental units
to subdivisions such as 1760 (miles to yards), 3 (yards to feet) and 12 (feet to inches).
The metric system is an alternative set of units, which includes for instance the unit
of the metre and its centimetre and millimetre subdivisions for measuring length. All
multiples and subdivisions of basic metric units are related to the base by factors of
ten and such units are therefore much easier to use than Imperial units. However, in
the case of derived units such as velocity, the number of alternative ways in which
these can be expressed in the metric system can lead to confusion.
As a result of this, an internationally agreed set of standard units (SI units or
Syst`emes Internationales d’Unit´es) has been defined, and strong efforts are being made
to encourage the adoption of this system throughout the world. In support of this effort,
the SI system of units will be used exclusively in this book. However, it should be
noted that the Imperial system is still widely used, particularly in America and Britain.
The European Union has just deferred planned legislation to ban the use of Imperial
units in Europe in the near future, and the latest proposal is to introduce such legislation
to take effect from the year 2010.
The full range of fundamental SI measuring units and the further set of units derived
from them are given in Table 1.2. Conversion tables relating common Imperial and
metric units to their equivalent SI units can also be found in Appendix 1.
1.2
Measurement system applications
Today, the techniques of measurement are of immense importance in most facets of
human civilization. Present-day applications of measuring instruments can be classified into three major areas. The first of these is their use in regulating trade, applying
instruments that measure physical quantities such as length, volume and mass in terms
of standard units. The particular instruments and transducers employed in such applications are included in the general description of instruments presented in Part 2 of
this book.

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