The 'Buckingham pi theorem' gives the number of independent dimensionless parameters as:
Choose the correct answer
n × m
n − m (number of variables minus number of fundamental dimensions)
n + m
Always 3 groups
Correct Answer
B. n − m (number of variables minus number of fundamental dimensions)
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Number of π groups = n − m where n = total number of variables, m = number of fundamental dimensions (MLT system: M=mass, L=length, T=time, θ=temperature). For pipe friction: variables are hf, ρ, V, D, μ, L → n=6, m=3 → 3 π groups: friction factor f, Re, L/D. This reduces experimental work significantly.
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