ENV-26

Gaussian plume (ground axis)

C = Q /(π u σy σz) exp(−H² /(2 σz²)) at y = 0.

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Air qualityPasquill–Gifford

Governing equation

C=\dfrac{Q}{\pi u\sigma_y\sigma_z}\exp\!\left(-\dfrac{H^2}{2\sigma_z^2}\right)

where

Q: Emission rate (g/s)
u: Wind speed (m/s)
\sigma_y: Lateral σ (m)
\sigma_z: Vertical σ (m)
H: Effective height (m)
C: Centreline concentration (mg/m³)

Lecture brief

Historical brief

Streeter–Phelps (1925) oxygen sag, settling theory and Guldberg–Waage kinetics made water and air quality a rate problem. The lab computes sag, overflow and a snapshot of reactor mass balance. This sheet (ENV-26 — Gaussian plume (ground axis)) is the form associated with Pasquill–Gifford. Working symbols: $Q$ , $u$ , $\sigma_y$ , $\sigma_z$ , $H$ $\rightarrow$ $C$ . Steady advection–diffusion with Gaussian closures. Total reflection at the ground doubles the image source.

Purpose

Purpose: compute

C

from

Q

u

\sigma_y

\sigma_z

H

in Environmental via

C=\dfrac{Q}{\pi u\sigma_y\sigma_z}\exp\!\left(-\dfrac{H^2}{2\sigma_z^2}\right)

C = Q /(π u σy σz) exp(−H² /(2 σz²)) at y = 0. Use it when a real environmental question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

Q = 10.000\,\mathrm{g/s}

u = 4.000\,\mathrm{m/s}

\sigma_y = 80.000\,\mathrm{m}

\sigma_z = 30.000\,\mathrm{m}

H = 50.000\,\mathrm{m}

, the governing relation

C=\dfrac{Q}{\pi u\sigma_y\sigma_z}\exp\!\left(-\dfrac{H^2}{2\sigma_z^2}\right)

yields

C = 0.0827\,\mathrm{mg/m^{3}}

. A stack, a Gaussian lobe, a ground axis. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Emission rate Q10 g/sWind speed u4 m/sLateral σ \sigma_y80 mVertical σ \sigma_z30 mEffective height H50 m

Outputs

Centreline concentration C0.0827 mg/m³

Reading speed

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Narration of this film

A stack, a Gaussian lobe, a ground axis.

Steady advection–diffusion with Gaussian closures. Total reflection at the ground doubles the image source.

Reading speed

Watch on YouTube