Question 5 of 7: Gaseous Pollutant Behaviour and Particulate Monitoring/Control

Question 5: Gaseous Pollutant Behaviour and Particulate Monitoring/Control (20 marks)

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.

(i) Terminal Settling Velocity and the Limits of Gravity Settling

Given. A particle settling under gravity in air at 25°C:

Find. The Stokes terminal settling velocity $v_t$.

Approach. Substitute directly into the supplied (simplified Stokes) formula, then check the particle Reynolds number to confirm the laminar (Stokes) regime assumed by the formula is valid.

1. Terminal velocity. $$v_t=\frac{g\rho_p d_p^2}{18\mu_g}=\frac{(9.81)(4000)(30\times10^{-6})^2}{18(1.81\times10^{-5})}=\boxed{0.108\ \text{m/s}\ (10.8\ \text{cm/s})}.$$
2. Confirm the Stokes (laminar) regime. With air density $\rho_g\approx1.18\ \text{kg/m}^3$ at 25°C, $$Re_p=\frac{\rho_g v_t d_p}{\mu_g}=\frac{(1.18)(0.108)(30\times10^{-6})}{1.81\times10^{-5}}=\boxed{0.21}.$$ Since $Re_p\ll1$, Stokes' law applies and the simplified formula is valid as used.

Limitation of gravity-only settling. Because $v_t\propto d_p^2$, settling velocity collapses rapidly as particle size falls — a chamber sized to capture this 30 µm particle in a reasonable footprint would need an impractically long residence time (and therefore chamber length) to capture particles even a few times smaller. Simple gravitational settling chambers are consequently only effective for coarse particles (roughly >50 µm); the fine, respirable fraction that dominates health risk passes through essentially uncaptured.

Potential solutions. Replace or follow the settling chamber with a device that either boosts the effective driving force well beyond 1 g (a cyclone, using centrifugal force, easily reaching tens of g's) or relies on a size-independent capture mechanism (an electrostatic precipitator, which charges and collects particles across a very wide size range including sub-micron, or a fabric filter/baghouse, which captures by physical straining and cake filtration regardless of settling velocity).

(ii) Stack Emission Monitoring — Particulate and SO_x

Particulate: a continuous opacity monitor (transmissometer) shines a light beam across the stack and measures the fraction absorbed/scattered by particulate, giving a real-time PM surrogate signal; for a direct mass measurement, isokinetic Method 5 sampling (Question 3(ii)) remains the reference method.

SO_x: a continuous UV-fluorescence (or pulsed-fluorescence) SO₂ analyzer extracts a stack gas sample and measures the characteristic fluorescence emitted when SO₂ molecules are excited by UV light, giving a continuous, specific SO₂ concentration reading for CEMS compliance reporting.

(iii) Point and Line Source Dispersion Models

Point source: emissions are modelled as originating from a single, fixed location (e.g. a stack outlet) and dispersing per the Gaussian plume equation of Question 2. Real-life example: a single power-plant or industrial stack, where the Gaussian plume model predicts ground-level concentration as a function of downwind distance.

Line source: emissions are distributed continuously along a line rather than concentrated at one point, modelled either as an integrated series of adjacent point sources along the line or with a dedicated line-source Gaussian formulation (integrating the crosswind Gaussian term along the line's length). Real-life example: vehicle exhaust along a busy urban highway or arterial road, where near-road NO_x/PM concentrations are predicted for corridor air-quality and land-use planning (e.g. siting schools or residences away from a high-traffic corridor).