•    Dimensional analysis is based on the principle that the variables in a physical phenomenon arranged properly to give an equation which is dimensionally homogeneous.

•    The equation in which dimensions of left hand side is equal to the dimensions of right hand side.

•    Now, check the dimensional homogeneity of the Darcy’s equation.

                                h_f = Flv² / 2gd

Dimension of L.H.S = h_f = L

Dimension of R.H.S = Flv² / 2gd = 1x L x (L/T)² / 2x (L/T²).L

                                                      = L³ /T². T²/ L² = L (Neglect 2 in denominator and consider constant f as 1.)

Dimension of L.H.S. = Dimension R.H.S.

h^f = Flv² / 2gd is the dimensionally homogenous equation, so it can be used in any system of units.

1.    It is used to determine the dimension of a physical quantity.
2.    It helps to check whether equation is dimensionally homogeneous or not.
3.    It provides the facility to convert units from one system to another.
4.    It provides a step towards dimensional analysis which is widely used for research work and model test.

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