Dimensional analysis using Buckingham π theorem is applied when:
Choose the correct answer
Exact analytical solution exists
Physical problems are too complex for direct mathematical solution — dimensionless groups simplify analysis and model-prototype scaling
Only for flow in pipes
When all variables have the same units
Correct Answer
B. Physical problems are too complex for direct mathematical solution — dimensionless groups simplify analysis and model-prototype scaling
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Buckingham π theorem: if a physical relationship involves n variables with m fundamental dimensions, it can be reduced to (n−m) dimensionless π groups. Helps in planning experiments and generalising results. Example: pipe friction: 4 variables (hf, V, D, ρ, μ, L) with 3 dimensions → 3 π groups → friction factor f, Re, L/D.
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