Discussion
A ground level accidental release of 0.5 g/s occurs at a 4 m height in terrain with a roughness length of Z0 = 0.01 m. Assuming a wind speed of 1 m/s, what is the maximum ground level concentration 4 km downwind estimated from the Gaussian plume equation ?
Answer: A
The official key gives 0.56 µg/m3, option A. This explanation confirms the size of that value but could not reproduce it exactly, because the stem names no stability class.
For a ground-level concentration on the plume centre line the Gaussian plume equation is:
\[ \begin{aligned} C &= \frac{Q}{\pi u \sigma_y \sigma_z}\,F \\ F &= e^{-H^{2}/(2\sigma_z^{2})} \end{aligned} \]
With Q = 0.5 g/s, u = 1 m/s and H = 4 m, the factor F is almost 1 at 4 km, because the plume is hundreds of metres deep there. The value then depends on σy and σz at x = 4 km, which depend on the stability class. With Briggs open-country curves, my own calculation gives about 0.6 µg/m3 for unstable class B, about 0.3 for class A, about 14 for class E and about 40 for class F. The keyed 0.56 therefore matches an unstable, light-wind daytime atmosphere, which is what a 1 m/s wind with strong sunshine would give.
Options C and D (56 and 66) would need a very stable night-time class, and the stem does not say which applies, so the data given do not exclude them on their own. The key is kept as printed; I could not find the source of this question to confirm its assumed class.
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