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

The equation in which dimensions of left hand side is equal to the dimension of right hand side is called the dimensional homogeneity

Example: Check the dimensional homogeneity of the Darry's equation

$hf=\frac{flV^{2}}{2gd}$

Dimension of L.H.s = hf=L

Dimension of R.H.s $\frac{fLV^{2}}{2gd}=\frac{1\times L\times (L/T)^{2}}{2\times (L/T^{2}).L}-\frac{L^{3}}{T^{2}}.\frac{T^{2}}{L^{2}}$=L

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

hf=$\frac{fLV^{2}}{2gd}$ is dimension-ally homogeneous equation , so it can be used in any system units