18-Env-A5 Air Quality and Pollution Control Engineering · December 2014
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
National Exams — December 2014 — 04-Env-A5 / Air Quality and Pollution Control Engineering. 3 hours duration; closed book with a candidate-prepared 8½×11 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.
Class A (extremely unstable) occurs under strong incoming solar radiation (clear skies, high sun angle) combined with light surface wind (<2 m/s). Intense surface heating drives strong convective (thermal) turbulence that overwhelms mechanical (wind-shear) turbulence, producing large vertical eddies. The resulting plume shows looping behaviour — large, erratic vertical excursions as the plume is caught in individual thermals — which gives excellent dilution on average but can bring instantaneous high concentrations to the ground when a loop happens to touch down nearby. Class F (moderately stable) occurs at night under clear skies (strong radiative cooling, <3/8 cloud cover) with light wind (<3 m/s); the ground cools faster than the air aloft, creating a stable temperature profile that suppresses vertical motion. The plume shows fanning behaviour — it spreads horizontally in a thin ribbon with almost no vertical growth — travelling long distances aloft with little ground-level impact directly downwind, but posing a hazard if the plume intercepts elevated terrain.
The Gaussian plume model assumes a continuous point-source release into a wind field of constant mean speed and direction, with pollutant concentration in the crosswind ($y$) and vertical ($z$) directions each following a normal (Gaussian) distribution about the plume centreline. The dispersion coefficients $\sigma_y$ and $\sigma_z$ grow with downwind distance $x$ according to empirical curves that are keyed to the Pasquill stability class (unstable classes spread faster than stable ones), so the SAME governing equation is reused for every stability condition simply by substituting the appropriate $\sigma_y(x)$, $\sigma_z(x)$ pair. Deposition is handled by adding an image-source term (reflecting the plume at the ground, $z=0$, to enforce no net flux through an impermeable surface) or, for pollutants that deposit, by applying a deposition velocity that removes mass from the plume as a function of downwind distance. The model's core strength is that it collapses a complex turbulent-diffusion problem into a closed-form algebraic expression, at the cost of assuming steady, uniform meteorology over the modelled domain.
(1) Cause. A temperature inversion is a layer in which air temperature increases with height (the reverse of the normal environmental lapse rate), most commonly formed by strong nocturnal radiative cooling of the ground surface (radiation inversion) or by a warm air mass subsiding and settling over a cooler surface layer (subsidence inversion). Because the normal buoyancy-driven overturning of the atmosphere depends on temperature decreasing with height, an inversion is thermodynamically very stable and essentially shuts off vertical mixing across it.
(2) Effect on the Gaussian plume model. An inversion acts as a lid (or, if present below the stack as well, a floor) that the Gaussian dispersion coefficient $\sigma_z$ cannot grow past — physically, the plume's vertical spread is capped at the inversion height $L$ rather than continuing to grow with distance $x$ as the unconstrained $\sigma_z(x)$ curve predicts. Once $\sigma_z$ reaches roughly $L/2.15$, the model is normally modified to a limited-mixing form (an infinite series of image sources reflecting between the ground and the inversion) that produces a UNIFORM vertical concentration profile below the lid rather than a decaying Gaussian tail — this raises the predicted ground-level concentration well above what the unconstrained equation would give at the same $x$. The most severe case is fumigation: pollutant emitted into a stable layer aloft overnight accumulates above a shallow surface inversion, and when morning solar heating erodes the inversion from below, that entire accumulated mass is rapidly mixed down to ground level over a short period, producing the highest short-term ground-level concentrations the model predicts for the day.
