18-Env-A5 Air Quality and Pollution Control Engineering · May 2013
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
National Exams — May 2013 — 04-Env-A5 / Air Quality and Pollution Control Engineering. 3 hours duration; closed book with a candidate-prepared 8.5×11 in double-sided aid sheet; Casio or Sharp approved calculator only. Any five (5) questions constitute a complete paper (the first five answers as they appear are marked); all seven are solved below for completeness. Each question is worth 20 marks with section marks shown in brackets.
Reference texts. Cooper & Alley, Air Pollution Control: A Design Approach (4th ed.); Wark, Warner & Davis, Air Pollution: Its Origin and Control (3rd ed.); Davis & Cornwell, Introduction to Environmental Engineering (6th ed.); Canadian Environmental Protection Act, 1999 (CEPA) and the Canadian Ambient Air Quality Standards (CAAQS) administered by Environment and Climate Change Canada.
Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.
Stable conditions occur on clear nights with light wind, when the ground radiates heat away faster than it is replenished, producing a temperature inversion (temperature increasing with height) that actively suppresses vertical air motion. A plume released into a stable layer barely spreads vertically and instead fans out nearly horizontally in a thin, ribbon-like layer that can travel long distances at roughly plume height without touching the ground — low ground-level concentration directly under the plume, but potentially high concentration far downwind if the layer later mixes down (fumigation).
Very unstable conditions occur on sunny days with strong solar heating and light wind, producing a large negative (superadiabatic) lapse rate that drives vigorous convective turbulence. A plume released here loops: large convective eddies swing the plume up and down erratically, occasionally bringing a concentrated "blob" of high concentration to the ground close to the stack before it lifts away again — producing high but intermittent peak ground-level concentrations near the source.
Slightly unstable conditions occur under moderate sun with some cloud cover and moderate wind, giving mild convective mixing without the violent looping of the very-unstable case. The plume disperses in a classic coning shape — a steadily widening cone downwind — which is the typical, well-behaved daytime dispersion pattern textbooks use as the Gaussian-model baseline.
A point source (an isolated stack) is modelled directly at its physical (x,y) coordinates with an effective release height $H$ = physical stack height + plume rise, exactly as in the Gaussian formula of part (iii) — the simplest and most exact case.
Line sources (a busy roadway, a rail corridor) are handled either by integrating a continuous row of infinitesimal point sources along the line (numerically or via a closed-form line-source Gaussian integral when wind is roughly perpendicular to the line), or, for a wind blowing parallel to the line, by treating it as an infinite line source with a simplified crosswind-integrated form of the Gaussian equation (the $\sigma_y$ term effectively drops out because the source is already continuous in $y$).
Area sources (a tailings pond, a stockpile yard, fugitive dust from an open storage area) are approximated either by dividing the area into a grid of point sources and superposing their individual plumes, or by the virtual point source technique: an imaginary point source is placed upwind of the area at the distance that would give a Gaussian plume the same initial lateral spread ($\sigma_{y0}$) as the physical area's width, after which the standard point-source equation is applied from that virtual origin.
(1) Wind speed, $u$. $C$ is inversely proportional to $u$ in the denominator: doubling wind speed halves the ground-level concentration everywhere along the plume centreline, because the same emission rate $Q$ is diluted into twice the volumetric flow of air per unit time. Low wind speed is therefore one of the classic conditions (alongside night-time stability) that produces the worst-case ground-level concentrations.
(2) Atmospheric stability class (via $\sigma_y,\sigma_z$). Unstable conditions give large $\sigma_y,\sigma_z$ (vigorous mixing spreads the plume quickly), which appears in BOTH the denominator (larger $\sigma_y\sigma_z$ dilutes more) and the exponential $\exp(-H^2/2\sigma_z^2)$ (larger $\sigma_z$ makes this term closer to 1, i.e., less attenuation) — the net effect is that unstable conditions usually bring the plume to the ground sooner (smaller $x_{max}$) but at a lower peak concentration, while stable conditions (small $\sigma_y,\sigma_z$) keep the plume aloft longer (larger $x_{max}$, further from the stack) but produce a sharper, more concentrated peak on the rare occasion the tightly confined plume does reach the ground.
(3) Effective stack height, $H$ (physical height + plume rise). $H$ enters only through $\exp(-H^2/2\sigma_z^2)$: increasing $H$ shrinks this exponential term sharply (it is the dominant lever on ground-level $C$), pushing both $C_{max}$ down and $x_{max}$ (the distance to the peak) further downwind, since the plume must travel farther, and $\sigma_z$ must grow larger, before it spreads enough vertically to reach the ground with any appreciable concentration. This is the physical basis for using taller stacks and hot, buoyant plume rise as a ground-level-concentration control strategy.
