Question

A phenomenon is modeled using n dimensional variables with k primary dimensions. The number of non-dimensional variables is

1. k
2. n
3. n - k
4. n + k

Answer 1

Correct Answer - Option 3 : n - k

Explanation:

Buckingham's Pi Theorem:

Assume, a physical phenomenon is described by n number of independent variables like x1, x2, x3, ..., xn

The phenomenon may be expressed analytically by an implicit functional relationship of the controlling variables as:

f(x1, x2, x3, ……………, xn) = 0

Now if k be the number of fundamental/primary dimensions like mass, length, time, temperature etc., involved in these n variables, then according to Buckingham's Pi theorem -

The phenomenon can be described in terms of (n - m) independent dimensionless/non-dimensional groups like π1, π2, ..., πn-m, where p terms, represent the dimensionless parameters and consist of different combinations of a number of dimensional variables out of the n independent variables defining the problem.