How many groups of variables can be formed of non-dimensional parameters if a dimensionally homogeneous equation contains ‘n’ variables with ‘m’ primary dimensions
How many groups of variables can be formed of non-dimensional parameters if a dimensionally homogeneous equation contains ‘n’ variables with ‘m’ primary dimensions Correct Answer n - m
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.
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Feb 20, 2025