Buckingham pi-Theorem states that,"If there are in variables (dependent and independent variables)in a dimension-ally homogeneous equation and if these variables contain m fundamental dimensions (M,L,T) the the variables are arranged into (n-m) dimensionless terms These dimensionless terms are called $\pi$ terms

Step1: Mathematically, if any variable x,depends on idependent variables $x_{2},x_{3},x_{4}....x_{n}$ then the functional relationship between dependent variable is expressed as

$X_{1}=f(x_{2},x_{3},x_{4}.....x_{n})$

equation can be written as

$f_{1}(x_{1},x_{2},x_{3},x_{4},.......x_{n})$=0

It is dimension-ally homogeneous equation and contains n variables.

Step 2:- The equation can be written in terms of number of dimensionless $\pi$ term which is equal to (n-m)

f$(\pi_{1},\pi_{2}...\pi-m)$=0

Step:-3 Each $\pi$ term contains m+1 variables, where m is the number of fundamental dimensions and it is also called as repeating variables

Step:-4 If $x_{2},x_{3},x_{4}$ are repeating variables then each $\pi$ is written as

$\pi_{1}=x_{2}^{a_{1}}.x_{3}^{b_{1}}.x_{4}^{c_{1}}x_{1}$

$\pi_{2}=x_{2}^{a_{2}}.x_{3}^{b_{2}}.x_{4}^{c_{2}}x_{5}$

$\pi_{n-m}=x_{1}^{a_{n-m}}.x_{2}^{b_{n-m}}.x_{3}^{c_{n-m}}x_{n-m}$

where $x_{1},x_{5.......,x_{n-m}}$are numerating variables

Step:-5 Where each equation is solved by principle of dimensional homogeneity and the values a,b,c are obtained

Step:-6 Substitute the value of a,b,c in their corresponding $\pi_{1},\pi_{2},\pi_{3}.....,$ etc. in equation

Step:-7 The value of $\pi_{1},\pi_{2},\pi_{3}$ are are substitute inequation

Step:-8 The required expression cab be obtained by expressing any one of the x-terms as a function of others