S. I. SYMBOLS AND UNITS EXPLAINED

 

 

 

 

The S. I. system is not the same as the metric system but it is based on the metric system. The correct name is Système International d'Unités and it was created in 1960. The standard provides the names, units and symbols of physical properties. It also provides a standard for multiples and sub-multiples of units and recommends the preferred method for writing down units.

 

There are only seven (7) fundamental units and only five (5) are commonly used in Engineering.  All other units are compounds of these. The only base unit that has the kilo prefix is the unit of mass (kilogramme kg). It follows from this that the kmol is also a base unit rather than the mol.

 

THE SEVEN FUNDAMENTAL UNITS
Quantity Unit Symbol and Name Quantity symbol
Length m metre l and various others
Mass kg kilogramme m
Time s second t
Temperature K Kelvin T
Electric Current A Ampere I and i
Luminous Intensity Cd Candela I or Iv
Amount of matter kmol   n

 

MULTIPLES of UNITS

 

S. I. units are often much too big or much to small to be written in sensible numbers so we use multiples as follows.

 

NAME SYMBOL EXPONENT FORM DECIMAL FORM
Exa E 1018  
Peta P 1015  
Tera T 1012 1 000 000 000 000
Giga G 109   1 000 000 000
Mega M 106  1 000 000
Kilo k 103 1 000
Basic   1 1
milli m  10-3   0.001
micro μ (Greek letter mu) 10-6   0.000 001
nano n  10-9  0.000 000 001
pico p 10-12     0.000 000 000 001
femto f 10-15   
atto a 10-18  

 

PRESENTATION OF UNITS

 

The names of units are written in lower case letters (e.g. m for metre) except when they are named after a person in which case the capital letter is used (e.g. J for Joule).

 

The S. I. standards recommend that the divisor /  be used in preference to negative indices hence m/s is preferred to ms-1.

 

The individual units should be separated by a single space in compound expressions (e.g. N m for Newton metre and not Nm).

 

The decimal point should be on the line and not in the middle hence 3.142 is correct but 3·142 is incorrect.

 

We should not write numbers larger than 1000 or smaller than 0.1 but use the appropriate multiples (e.g. 1 mm rather than 0.001 m and 1 km rather 1000 m).

 

Long numbers should be spaced in groups of 3 (e.g. 20.275 681).

 

Multiples of 1000 are preferred throughout but this produces some anomalies. For example the preferred units of length are km, m and mm. The use of decimetres (dm) and centimetres (cm) are not recommended but dm3 and cm3 are acceptable as units of volume. In some cases alternative names exist for such multiples such as the units of capacity and volume.

 

VOLUME CAPACITY
The base unit is the cubic metre  m3  
10-3 m3 is a cubic decimetre  dm3  This is also called a litre
10-6 m3  is a cubic centimetre   cm3   This is also called a millilitre
10-9 m3  is a cubic millimetre    mm3  

 

NAMES AND SYMBOLS

 

UNITS USED IN BASIC MECHANICAL ENGINEERING

Quantity

Unit Name

Unit Symbol

Base Compound Units

Quantity symbol
Acceleration :- Linear     m/s2 a
Acceleration : -Angular     rad/s2 α (Greek letter alpha)

Area

 

 

m2

A
Angle radian rad   α,β,θ and f
Coefficient of Friction       μ (Greek letter mu)
Efficiency       η (Greek letter eta)
Energy Joule J N m or kg m2/s2  

Force

Newton

N

kg m/s2

F

Force:- Resisting

Newton

N

kg m/s2

R
Modulus:-section     m3 Z
Modulus :- Elasticity     Pa  or N/m2 or kg/m s2 E
Modulus :- Rigidity (Torsion)     Pa  or N/m2 or kg/m s2 G
Moment of Force     Nm or kg m2/s2 M
Moment of Inertia     kg m2 I and J
Momentum :- Linear     kg m/s  
Momentum :- Angular     kg m2/s  
Power Watt W J/s or N m/s or kg m2/s3 P
Poisson's Ratio     Ratio ν (Greek Letter nu)
Second Moment of Area     m4 I
Second Moment of Area : Polar     m4 J
Strain : Direct     Ratio ε (Greek Letter epsilon)
Strain :- Shear     Ratio γ (Greek Letter gamma)
Stress :- Direct Pascal Pa Pa  or N/m2 or kg/m s2

σ (Greek letter sigma)
Stress : - Shear Pascal Pa Pa  or N/m2 or kg/m s2 τ (Greek letter tau)
Torque     N m or kg m2/s2 T
Velocity :- Linear     m/s v and various others
Velocity :-Angular     rad/s

ω (Greek letter omega)

Volume

None

 

m3

V or Q

Weight

Newton

N

kg m/s2

W

 

 

OTHER UNITS USED IN BASIC ELECTRICAL ENGINEERING

Quantity

Unit Name

Unit Symbol

Base Compound Units

Quantity symbol
Current Ampere A   I
Current Density - linear     A/m  
Current Density     A/m2 J
         
Charge Coulomb C A s Q
Charge - volume density     C/m3 or A s/m3 ρ (greek letter rho)
Charge - surface density     C/m2 or A s/m2 σ (Greek letter sigma)
         
Resistance Ohm

Ω

 V/A or kg m2/s3 A2 R
Reactance Ohm

Ω

 V/A or kg m2/s3 A2 X
Impedance Ohm

Ω

 V/A or kg m2/s3 A2 Z
Conductance Siemens

S

 1/Ω or  s3 A2/kg m2 G
Susceptance Siemens

S

 1/Ω or  s3 A2/kg m2 B
Admittance Siemens

S

 1/Ω or  s3 A2/kg m2 Y
Resistivity     Ω m or  kg m3/s3 A2 ρ (greek letter rho)
Conductivity     S/m or   s3 A2/kg m3 σ (Greek letter sigma)
         
Power - Active Watts W N m/s or J/s or Nm/s or kg m2/s3 P
Power - Reactive     V Ar Q
Power - Apparent     V A or Nm/s or kg m2/s3 S
         
Temperature Coefficient of Resistance     1/K or 1/oC α,β or γ
         
Voltage :- General Volt V kg m2/s3 A V
Voltage :- Electromotive Force Volt V kg m2/s3 A E
Voltage :-Potential Difference Volt V kg m2/s3 A V
         
Magnetic Flux Weber Wb kg m2/A s2 Φ(Greek letter Phi)
Magnetic Flux density Tesla T Wb/m2 or kg /A s2 B
Magneto Motive Force Ampere A   F
Magnetic Field Strength     At/m  (t is number of turns) H
Reluctance     1/H or A2 s/kg m2 S
Self  Inductance Henry H V s/A or kg m2/A2 s2 L
Mutual Inductance Henty H V s/A or kg m2/A2 s2 M
Absolute Permeability     H/m or kg m/A2 s2 μo (Greek letter mu)
Relative Permeability     Ratio μr (Greek letter mu)
         
Capacitance Farad F C/V or A2 s4 /kg m2 C
Electric Flux Coulomb C A s

Y (Greek letter psi)
Electric Flux density     C/m2 or A s/m2 D
Electric Field Strength     V/m or kg m/s3 A E
Absolute Permittivity     F/m or  A2 s4 /kg m3

εo (Greek letter epsilon)
Relative Permittivity     Ratio

εr (Greek letter epsilon)

 

 

 

 

UNITS USED IN THERMODYNAMICS AND FLUID MECHANICS
Quantity Unit Name Unit Symbol Base Compound Units Quantity symbol
Altitude metre m z
Coefficient of expansion :- linear     1/K or 1/oC α (greek letter alpha)
Coefficient of expansion :- area     1/K or 1/oC usually γ (Greek letter gamma)
Coefficient of expansion :- cubical     1/K or 1/oC

β (greek letter beta)
Coefficient of Heat Transfer     W/m2 K h
Density None   kg/m3 ρ (greek letter rho)
Enthalpy Joule J N m or  kg m2/s2 H
Enthalpy :- Specific     J/kg or N m/kg or  m2/s2 h
Entropy     J/K or N m/K or  kg m2/s2 K S
Entropy : -Specific     J/kg K or N m/kg K or m2/s2 K s
Gas Constant :-Characteristic     J/kg K or N m/kg K or m2/s2 K R
Gas Constant :- Universal     J/kmol K Ro
Heat Transfer Joule J Nm or kg m2/s2 Q
Heat Transfer Rate Watt W J/s or Nm/s  or  kg m2/s3

Φ(Greek letter Phi)
Index of expansion/compression :- Adiabatic       γ (Greek letter gamma)
Index of expansion/compression :- Polytropic     Ratio of the specific heats n
Internal Energy     J or N m or kg m2/s2 U
Internal Energy : -Specific     J/kg or N m/kg or m2/s2 u
Mass flow rate     kg/s  
Pressure Pascal Pa N/m2 or  kg/m s2 p
Pressure Head metre   m h
Specific Volume None   m3/kg v
Specific Heat Capacity     Joule/kg K or N m/kg K or m2/s2 K c
Surface Tension     N/m or kg/s2 γ (Greek letter gamma)
Temperature :-Celcius     oC θ (Greek letter theta)
Thermal Conductivity     W/m K or kg m/s3 K

λ (Greek letter lambda)
Velocity     m/s

v and others
Velocity :- sonic     m/s

α (Greek letter alpha)
Velocity :- of Vapour     m/s

C
Viscosity :-Dynamic centiPoise cP  Pa s or N s/m2 (Note 103 cP = 1 N s/m2) η (Greek letter eta)
Viscosity :- Kinematic centiStoke cSt  (Note 106 cSt = 1 m2/s) ν (Greek letter nu)
Work Joule J Nm or kg m2/s W
Work Transfer Rate (Power) Watt W J/s or N m/s or kg m2/s3 P