In Case of number of variables involved in a physical phenomenon then the relations among the various variables can be determined by the following methods

1) Rayleigh methods

2) Buckingham's $\pi$ theorem

Above methods are discussed below

Raylelgh Method of Dimensional Analysis:

This method is quite convenient to use in case the expression for a variable depends upon 3 or 4 variables only when the number of independent variables exceed more than four, this method cannot be used conveniently to find the expression for the dependent variable

$x_{1},x_{2} \ \ and \ \ x_{3}$ variables Therefore according to Rayleigh method the variables xis the function of variables $x_{1}, x_{2} and x_{3}$ mathematically

X=f(x1,x2,x3)

Above expression can also be written as

x=constant (k) $x_{1}^{a}.x_{2}^{b}.x_{3}^{c}$

Where a,b, and c are arbitrary powers of the variables $x_{1},x_{2},x_{3}$

By using the concept of dimensions homogeneity i.e by equating the powers of the fundamental dimensions on both sides an expression for dependent variables (x) can be obtained in terms of variables $(x_{1},x_{2},x_{3})$