Gaussian Plume Ground-Level Concentration

\[C = \frac{Q}{\pi u \sigma_y \sigma_z}\exp\left(-\frac{y^2}{2\sigma_y^2}\right)\exp\left(-\frac{H^2}{2\sigma_z^2}\right)\]

Variables

Cground-level pollutant concentration (mass/volume)

Qpollutant emission rate (mass/s)

uwind speed at stack height (m/s)

sigmay[σ_y]horizontal dispersion coefficient (m)

sigmaz[σ_z]vertical dispersion coefficient (m)

ycrosswind distance from plume centerline (m)

Heffective stack height (m)

Description

What is this formula?

This formula estimates the ground-level concentration of a pollutant emitted continuously from an elevated stack using the Gaussian plume model.

When to use it

Use it for preliminary air pollution dispersion calculations under steady wind, continuous emission, and approximately uniform atmospheric conditions.

Example

Data:

Q = 2 g/s

u = 5 m/s

sigmay = 40 m

sigmaz = 20 m

y = 30 m

H = 50 m

Formula:

C = (Q / (π u sigmay sigmaz)) · e^(-y²/(2 sigmay²)) · e^(-H²/(2 sigmaz²))

Substitution:

C = (2 / (π · 5 · 40 · 20)) · e^(-30²/(2 · 40²)) · e^(-50²/(2 · 20²))

Result:

C = 0.0000273 g/m³

Applications

Air quality assessment, stack emission studies, environmental impact analysis, industrial permitting, and preliminary pollutant dispersion modeling.

Note

This is an empirical atmospheric dispersion model. It assumes steady-state conditions, continuous emissions, flat terrain, constant wind direction, and dispersion coefficients selected from atmospheric stability correlations. Results are estimates and may differ from regulatory dispersion models that include terrain, meteorology, deposition, building downwash, and chemical reactions.