Units and Measurements in Instrumentation

INTRODUCTION:

Science, Engineering and Technology are based on experimental facts. Experiments need measurement. Naturally measurement requires instruments.

Engineering needs precision and precise control. Unless a variable is measured accurately, nothing can be done to control the variable accurately either manually or by automatic means.

Measurement of any quantity requires units and standards. The fundamental quantities are length, mass and time. There are derived quantities, like area, pressure etc. To measure any physical quantity a standard of the same quantity is essential and that is called the UNIT. Measuring any thing is to compare it with the standard. A standard is arbitrary and its virtue lies in its international agreement.
The unit of any quantity should be definite, constant and convenient for measurement. The measure of any quantity is the number of times the unit is contained in it. Two kinds of units are used in science and engineering. They are the fundamental units and derived units.

The fundamental unit is the unit of a physical quantity which is independent of any other quantity. The derived unit is the unit of a physical quantity which can be derived. Three standardized systems of units were used to measure the fundamental quantities. They are
(i) F.P.S.
(ii) C.G.S.
(iii) M.K.S systems.

Their units are as shown in the table below.

System
UNITS
Length
Mass
Time
1. FPS
foot
pound
second
2. CGS
centimetre
gram
second
3. MKS
metre
kilogram
second

In selecting suitable standards one has to bear in mind the following:

1. It should be possible to define them unambiguously.
2. They must be easy to copy.
3. They must be invariable with time and place.
4. Methods must be available for multiplying or sub-dividing each one of the standards.

A coherent, rational and comprehensive International system of units was accepted at the Eleventh International Conference of weights and measures in 1960 A.D. This system is S.I. system. System International d' Units system. We follow this system for all measurements. Other systems of units are becoming obsolete. The six basic S.I., quantities and their units of measurement and symbols are given below : (Sometimes S.I. units are called International M.K.S. system of units).

It is realised that only the three fundamental quantities are not sufficient to derive physical quantities. Four more physical quantities are taken as fundamental quantities. They are Thermodynamic temperature, Illuminating power (Luminous intensity), Strength of electric current and Quantity of matter. Additionally to these fundamental quantities, plane angle and solid angle are taken as supplementary quantities. Table shows the units and symbols.

Fundamental Quantity

Unit           

Symbol

Length
metre
m
Mass
kilogram
kg
Time
second
s
Thermodynamic temperature
kelvin
K
Illuminating power (luminous intensity)
candela
cd
Strength of electric current
ampere
A
Quantity of matter
mole
mol
Plane angle
radian
rad
Solid angle
steradian
sr

ELECTRICAL AND MAGNETIC UNITS:

Originally the electrical and magnetic units like volt, ampere, ohm, henry etc. were derived in CGS system of units. Having thought that the establishment of the practical units from the definitions of CGS system will be too difficult for laboratory work, practical units were defined. It is fairly simple to establish them.



The ampere was defined in terms of the rate of deposition of silver nitrate solution by passing a current through that solution.

The ohm was defined as the resistance of a specified column of mercury.

The above units and those derived from them were called International units. Improvement of measuring techniques has shown that there is small difference between the CGSm derived practical units and the international units. The differences are specified as follows.

The differences between CGSm and International units

1 int. ohm = 1.00049 (practical CGSm unit)
1 int. ampere = 0.99985 A
1 int. volt = 1.00034 V
1 int. coulomb = 0.99985 C
1 int. farad = 0.99951 F
1 int. henry = 1.00049 H
1 int. watt = 1.00019 W
1 int. joule = 1.00019 J

The electrical and magnetic units and their defining relationships, multiplication factors for conversion of SI units are shown below.

Quantity and Symbol
SI Unit
Conversion factors
Name, Symbol
Defining Equation
CGSm
CGSe***
Electric current, I
Ampere, A
Fz = 10-7I2dN/dz
10
10/c
Electromotive force, E
Volt, V
P** = IE
10-8
10-8c
Potential, V
Volt, V
Vp** = IV
10-8
10-8c
Resistance, R
Ohm, Ω
R = V/I
10-9
10-9c
Electric charge, Q
Coulomb, C
Q = It
10
10/c
Capacitance, C
Farad F
C = Q/V
109
109/c2
Electric field strength. E
V/m
E = V/l
10-6
10-6c
Electric flux density, D
C/m2
D = Q/l2
105
105/c
Permittivity, Ɛ
F/m
Ɛ = D/E
-
1011/4πc2
Magnetic field strength, H
A/m
∮ H dl = nI
103/4
-
Magnetic flux, Φ
weber, wb
E = dΦ/dt
10-8
-
Magnetic flux density, B
tesla, T
B = Φ/l2***
10-4
-
Inductance L, M
henry, H
M = Φ/I
10-9
-
Permeability, μ
H/m
μ = B/H
4π x 10-7
-

Note for table : * N denotes Neumann's integral for two linear circuits each carrying the current I. Fz is the force between the two circuits in the direction defined by coordinate z, the circuits being in a vacuum.

** p denotes power
** l2 denotes area.

c = velocity of light in free space in cm/s = 2.997925 x 1010

DEFINITIONS OF FUNDAMENTAL UNITS IN SI SYSTEM

1. Metre: Metre is 1,650,763,73 times the wavelength of the orange light in vacuum emitted by 36Kr86 (krypton) in the transition 2p10 to 5 d5.

In 1983 A.D. a new definition was given to metre. Metre is 1 in 299,762,458th parts of the distance travelled by light in vacuum in 1 second.

2. Kilogram: Kilogram is the mass of a platinum-iridium cylinder kept at Serves.

3. Second: One second is the time taken by 9, 192,631,770 cycles of radiation from the hyperfine transition in Cesium when unperturbed by external fields.

4. Kelvin: This is 1/273, 16 of temperature at the triple point of water measured on thermodynamic scale.

5. Candela: Candela is the luminous intensity in a direction normal to the surface of 1/6 x I05m2 of a black body at the temperature of freezing platinum at a pressure of 101325 newton per square metre.

6. Ampere: Ampere is the current which when flowing in each of two parallel conductors of infinite length and negligible cross-section and placed one metre apart in vacuum causes each conductor to experience a force exactly 2 x 10-7 newton per metre of length.

7. Mole: Mole is the amount of substance of a system that contains as many elementary entities as there are atoms in 0.012 kg of carbon - 12.

8. Radian: Radian is the angle projected at the centre of a circle by an arc whose length is equivalent to the radius.

2p radians = 360° therefore
1 radian = 360/2p = 57°17'44"

9. Steradian: The solid angle projected at the centre of the sphere of radius 1 metre by its surface of area 1 square metre.


Table of fundamental, supplementary and derived units.

Quantity
Symbol
Dimension
Unit
Unit Symbol
Fundamental length
l
L
meter
m
Mass m
M
Kilogram
kg
-
Time t
T
Second
s
-
Electric current
I
I
ampere
A
Thermodynamic temperature
T
θ
Degree, Kelvin
oK
Luminous Intensity Supplementary
-
-
candela
cd
Plane angle
α, β, γ
(L) o
radian
rad
Solid angle
-
(L2)o
steradian
sr
Derived Area
A
L2
square meter
m2
Volume
V
L3
Cubic meter
m3
Frequency
f
T-1
hertz
Hz(1/s)
Density
ρ
L-3M
kg per cubic meter
Kg/m3
Velocity
v
LT-1
meter per second
m/s
Angular Velocity
ω
(L)oT
radian per second
rad/s
Acceleration
a
LT-2
meter per second squared
m/s2
Angular acceleration
α
(L)oT-2
radian per second squared
rad/s2
Force F
LMT-2
newton
N (kgm/s2)
-
Pressure, stress
p
L-1MT-2
newton per square meter
N/m2
Work, energy
W
L2MT-2
Joule
J/Nm
Power Quantity of Electricity
P
L2MT-3
watt
W(J/s)
Potential difference, electromotive force
V
L2MT-3I-1
volt
V (W/A)
Electric field strength
E, Ɛ
LMT-3I-1
Volt per meter
v/m
Electric resistance
R
L2MT-3I2
ohm
Ω (V/A)
Electric capacitance
C
L-2M-1T4I2
farad
F(As/V)
Magnetic flux
Φ
L2MT-2I-1
weber
Wb(vs)
Magnetic field strength
H
L-1I
ampere per meter
A/m
Magnetic flux density
B
MT-2I-1
tesla
T(Wb/m2)
Inductance
L
L2MT-2I2
henry
H (Vs/A)
Magnetomotive force
U
I
ampere
A
Luminous flux
-
-
lumen
lm (cd sr)
Luminance
-
-
candela per sq. meter
cd/m2
Illumination
-
-
Lux
1 x (1m/m2)



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