Plume Behaviour and Stack Design Questions and Answers

Answer: A

Dispersion from a stack depends on stability, wind and stack height.

In the Gaussian plume model, ground-level concentration depends on the emission rate, the wind speed, the dispersion coefficients set by atmospheric stability, and the effective stack height (physical height plus plume rise). A taller stack releases pollutants higher, giving the plume more distance to spread before it reaches the ground.

Stack diameter affects exit velocity and so plume rise slightly, but it is not one of the main controls. Pollution control equipment changes how much is emitted, not how it disperses, and 'stack attachment' is not a dispersion parameter.

Answer: A

The statement that is not a weakness is that the model does not evaluate dispersion in all three dimensions.

That statement is false: the Gaussian plume model is three-dimensional. It carries the plume along the wind direction x and spreads it in the crosswind (y) and vertical (z) directions with the dispersion coefficients σ_y and σ_z, so it does evaluate all three dimensions.

The other three are real limitations: the basic model treats the pollutant as inert, so it cannot handle chemically reactive pollutants; it assumes steady-state conditions of constant emission rate, wind and stability; and it is meant for short-range, short-period estimates, not as a long-term air shed evaluator.

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 σ_y and σ_z 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.