Class DWorst ground 0 µg/m³ at 0 mMonitor 0 µg/m³Effective height 0 m—FPS 0

Drag to orbit, wheel or pinch to zoom. The coloured ground map is the time-mean concentration at breathing level (µg/m³, log scale from 1 to 1000); the blue pole is the monitor you place with the sliders. The plume is steady: the particles show where the exhaust goes.

Smokestack Plume: Gaussian Dispersion, Stability Classes and Ground-Level Concentration

A factory chimney releases an exhaust gas into the wind. How far away, and how high, is the worst air quality at ground level?

Atmosphere (Pasquill stability class)

Source

Include Briggs plume rise (buoyancy of the hot gas)

Monitoring station

Live readouts

1101001000 µg/m³

Ground concentration along the plume axis

Height profile above the monitor

Crosswind profile at the monitor distance

Missions

Predict: with plume rise switched off, by what factor does the worst ground concentration fall when the stack height is doubled (current stability and wind)?

Hint: the peak is where the plume spread σz reaches about 0.7 times the effective height, and C falls as 1/H² in the ideal case.

Experiments

Each button recomputes the worst ground value and its distance for five settings, changing one variable and keeping the rest.

Independent numerical checks

Controls

Drag / one finger: orbit; wheel / pinch: zoom; three camera views.
Pick a stability class (A unstable ... F stable), then set wind, emission and stack. The map, plume and charts update at once.
The monitor sliders move the blue pole and the two profile charts.

The science

Gaussian plume. For a continuous point source of strength Q (g/s) in a steady wind u the time-mean concentration is C(x,y,z) = Q / (2π u σ_y σ_z) · exp(-y²/2σ_y²) · [exp(-(z-H_e)²/2σ_z²) + exp(-(z+H_e)²/2σ_z²)]. The second exponential is the mirror source that makes the ground reflect the gas. At the ground on the centre line this gives C = Q / (π u σ_y σ_z) · exp(-H_e²/2σ_z²).

Stability classes. Pasquill's letters A to F describe how turbulent the air is. Here σ_y and σ_z use the Briggs (1973) open-country fits, e.g. class D: σ_y = 0.08 x (1+10^-4 x)^-1/2, σ_z = 0.06 x (1+0.0015 x)^-1/2. Unstable air (A, B) mixes the plume down quickly, so the worst ground value is close to the stack and high; stable air (E, F) keeps the plume aloft far downwind. These are statistical fits for flat open land over about 100 m to 10 km, not for towns, hills, sea breezes or buildings.

Plume rise. Hot flue gas rises. The buoyancy flux is F = g v_s d²/4 · (T_s-T_a)/T_s (m⁴/s³). Briggs: bent-over rise Δh(x) = 1.6 F^1/3 x^2/3 / u until the final distance x_f = 119 F^0.4 m (F ≥ 55) or 49 F^5/8 m; in stable air the final rise is 2.6 (F / (u s))^1/3 with s = (g/T_a) dθ/dz. Exit speed 15 m/s, stack diameter 4 m and ambient 288 K are fixed. Effective height H_e = H + Δh.

Ideal peak. For σ_y and σ_z both proportional to x, the worst ground value is at σ_z = H_e/√2 and equals C_max = 2Q / (π e u H_e²) (σ_z/σ_y = 1). The check panel verifies this. Doubling H_e then divides C_max by four; with the real fits the factor is somewhat larger because σ_z grows more slowly with distance.

Guideline. The pollutant is treated as sulphur dioxide with no chemical conversion, deposition or washout. The Gaussian model gives roughly 10-min to 1-hour averages, so it is compared with the 350 µg/m³ 1-hour limit of the EU air quality directive (a limit, not a safe level; the WHO 24-hour guideline is 40 µg/m³).

Simplifications. Steady wind of constant speed and direction, flat ground, no buildings, no inversion lid or mixing-height reflection, no wind shear, wind speed taken at stack height, source of constant strength. Emission rates are illustrative. Do not use this for permitting or health assessment. Assets built with Blender; scene by Three.js.