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# Units and Dimensions

The word dimensions are used to describe basic concepts like mass, length, time, temperature and force.Units are the means of expressing the value of the dimension quantitatively or numerically.

UNITS AND DIMENSIONS

The word dimensions are used to describe basic concepts like mass, length, time, temperature and force.Units are the means of expressing the value of the dimension quantitatively or numerically.

Example - Kilogram, Metre, Second, Kelvin, Celcius.

The four examples are the fundamental units; other derived units are

Density       =       mass per unit volume = kg/m3

Force =                 mass x acceleration =     kg.m/s2             = Newton or N

Pressure      =                 force per unit area          =       N/m2  =Pascal or Pa

Other unit is‘ bar’ ,

where 1 bar =1 X105 Pa  =100 Kpa  = 0.1 Mpa

Work =                 force x distance    = Newton x metre = N.m==J or Joule

Power         =                 work done per unit time=        J/s     = Watt or W

Term                    Dimension  Unit

Area                     L*L   m2

Volume                          L*L*L         m3

Velocity                         L* T-1          m/s

Acceleration                            L*T-2 m/s2

Force                    M*L*T-2      N

Pressure                         M*L-1*T-2    N/m2 = Pa

Work                    M*L2*T-2    Nm    = J

Power                            M*L2*T-3    J/s     = W

Density                          M*L-3          kg/m3

Viscosity                        M*L-1*T-1    kg/ms = N s/m2

Surface Tension   M*T-1          N/m

Quantity                        Representative symbol           Dimensions

Angular velocity            w                 t-1

Area                     A                L2

Density                          r                 M/L3

Force                    F                 ML/t2

Kinematic viscosity                           n                 L2/t

Linear velocity                         V                L/t

Linear acceleration                  A                L/t2

Mass flow rate                         m.               M/t

Power                   P       ML2/t3

Pressure               P       M/Lt2

Sonic velocity                C       L/t

Shear stress                   t        M/Lt2

Surface tension              s       M/t2

Viscosity              m       M/Lt

Volume                V       L3

Dimensions:

Dimensions of the primary quantities:

Fundamental dimension  : Symbol

Length        L

Mass M

Time           T

Temperature                  T

Dimensions of derived quantities can be expressed in terms of the fundamental dimensions.

1.SYSTEM OF UNITS

1. CGS Units

2. FPS Units

3. MKS Units

4. SI Units

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