Discussion
Effect of effective stack height on maximum ground level concentration, other things equal.
| Effective height (m) | Relative maximum concentration |
|---|---|
| 50 | 1.00 |
| 75 | 0.44 |
| 100 | 0.25 |
| 150 | 0.11 |
What relationship do the figures follow?
Answer: C
Correct answer: Concentration goes as height to the minus two
Test the figures against an inverse-square law. Going from \( 50 \) to \( 100 \) m doubles the height and the relative concentration falls from \( 1.00 \) to \( 0.25 \), a factor of four. From \( 50 \) to \( 75 \) m the ratio is \( (75/50)^2 = 2.25 \), and \( 1/2.25 = 0.44 \), matching the table; from \( 50 \) to \( 150 \) m, \( (150/50)^2 = 9 \) and \( 1/9 = 0.11 \), which also matches.
So \( C_{max} \propto H^{-2} \). A simple inverse relation would have given \( 0.50 \) at \( 100 \) m rather than \( 0.25 \), and a direct square dependence would have made concentration rise with height.
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