Units and Dimensions

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