Dimensions

•    Various physical quantities used in fluid phenomenon is formed by some fundamental quantities or primary quantities. Such as mass, length, time and temperature.

•    The unit of physical quantities which does not depends on the unit of any other physical quantities is called as fundamental dimensions.

•    The unit of physical quantity which depends on the unit of other physical quantities is called as derived or secondary dimensions.

Dimensions of Some Physical Quantities:

Example dimension of the following quantities:

1)    Force
2)    Angular velocity
3)    Discharge
4)    Torque
5)    Power
6)    Viscosity
7)    Density.

1.    Force = Mass x Acceleration
                                            F = M x Length x (Time)² = ML/T² = MLT^-2

2.                             Angular = Angle covered in radian / Time

                                          ω = 1/T = T ^-1

3. Discharge,           Q = Area x Velocity = L² x Length/Time = L². L/T L³ T ^-1


4. Torque (Moment),  T = Force x Distance = Mass x Acceleration x Distance
                                             = Mass x Length/ (Time) x L = M.L.L / T²

                                                         T = ML²T ^-2

5. Power,                      P = Work done/Time = Force x Distance/Time
                                             = Mass x Acceleration x Distance/Time
                                       
                                               P = M.L / T².L / T = ML²T ^-3

6. Viscosity,                 μ = Shear stress / Shear strain = Force/Area / du/dy
                                              = Mass x Acceleration / Area x du/dy = M.L/T² /L².L/T.I/L
                                                  = MLT / L²T²

                                                  μ = ML^-1T ^-1

7. Density,                    ρ = Mass/Volume = M/L³ = ML^-3


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