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Qwestrum Engineering360 · Environmental Engineering · Air Pollution Control

Atmospheric Dispersion

Atmospheric dispersion estimates how emitted pollutants spread and dilute in air under varying meteorological conditions. Gaussian plume models remain a core analytical tool for stack-impact calculations.
Exam tip: keep SI units consistent end-to-end, write the governing relation symbolically before substituting, and sanity-check magnitude and sign.

Key formulas & points

Skim these first — then read the full notes below.

  • Wind speed u; σ_y σ_z from stability and distance
  • Inversion traps pollutants ground level
  • ISCST3/AERMOD regulatory models

Topic details

Introduction

Dispersion modelling links source emissions with ground-level concentrations at receptors, which is essential for EIA and consent applications. CPCB-aligned studies commonly apply AERMOD-type frameworks with site-specific meteorological inputs.

Scope in B.Tech and GATE syllabus

For exam preparation, Gaussian plume formulation is a frequent numerical question because it combines fluid mechanics, statistics, and environmental interpretation. Students must identify how wind speed, stability, and stack parameters shape concentration fields.

Key relations & formulas

Formulas (Indian textbook notation)

  • GaussianplumeC(x,y,z)=(Q2πuσyσz)exp(−y22σy2)[exp(−(z−H)22σz2)+exp(−(z+H)22σz2)]Gaussian plume C(x,y,z) = (\frac{Q}{2\pi u\sigma_{y}\sigma_{z}}) exp(-\frac{y^{2}}{2\sigma_{y}^{2}})[exp(-(z-H)\frac{^{2}}{2\sigma_{z}^{2}})+exp(-(z+H)\frac{^{2}}{2\sigma_{z}^{2}})]

Formulas (Indian textbook notation)

  • PasquillstabilityclassesA−FPasquill stability classes A-F

Formulas (Indian textbook notation)

  • effectivestackheightH=h+Δheffective stack height H = h + \Delta h

Notation and sign conventions

Relation 1 —
GaussianplumeCGaussian plume C

Formulas (Indian textbook notation)

  • GaussianplumeC(x,y,z)=(Q2πuσyσz)exp(−y22σy2)[exp(−(z−H)22σz2)+exp(−(z+H)22σz2)]Gaussian plume C(x,y,z) = (\frac{Q}{2\pi u\sigma_{y}\sigma_{z}}) exp(-\frac{y^{2}}{2\sigma_{y}^{2}})[exp(-(z-H)\frac{^{2}}{2\sigma_{z}^{2}})+exp(-(z+H)\frac{^{2}}{2\sigma_{z}^{2}})]
Write this relation with symbols exactly as in Air Pollution Control — CP Rao before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.
Relation 2 —
PasquillstabilityclassesA−FPasquill stability classes A-F

Formulas (Indian textbook notation)

  • PasquillstabilityclassesA−FPasquill stability classes A-F
Write this relation with symbols exactly as in Air Pollution Control — CP Rao before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.
Relation 3 —
effectivestackheightH=h+Δheffective stack height H = h + \Delta h

Formulas (Indian textbook notation)

  • effectivestackheightH=h+Δheffective stack height H = h + \Delta h
Write this relation with symbols exactly as in Air Pollution Control — CP Rao before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.

Fundamentals and definitions

The Gaussian model assumes steady emission, homogeneous wind, and statistically distributed plume spread represented by σ_y and σ_z. Though simplified, it captures first-order behavior for many regulatory scenarios.

Governing relations in practice

Effective stack height includes physical stack plus plume rise, and this term critically affects near-field ground concentrations. Thermal buoyancy and momentum-driven rise can significantly reduce receptor impacts when properly accounted for.

Design and analysis considerations

Atmospheric stability class governs turbulence intensity and therefore dispersion width. Stable conditions suppress mixing and raise centerline concentrations, while unstable conditions enhance dilution but may increase variability.

Assumptions and validity limits

State assumptions explicitly before using any relation for atmospheric dispersion — steady state, uniform properties, linear elastic material, ideal gas, incompressible flow, etc., as applicable.
Wrong assumptions invalidate the entire solution even when the formula is correct. In Air Pollution Control viva and GATE descriptive questions, listing valid assumptions often earns separate marks.

Step-by-step problem approach

1. Read the question and list given data with SI units (common in Air Pollution Control papers).
2. Draw a neat labelled diagram where applicable — examiners in Indian universities award diagram marks even when arithmetic slips.
3. Identify which relation from this topic applies to atmospheric dispersion.
4. Use equation 1:
GaussianplumeCGaussian plume C
.
5. Use equation 2:
PasquillstabilityclassesA−FPasquill stability classes A-F
.
6. Substitute values, compute, and verify units and sign (direction).
7. State conclusion in one line — e.g. safe/unsafe, stable/unstable, feasible/infeasible.

Applications & exam relevance

Atmospheric Dispersion appears in industry stack emissions. In Indian environmental curricula this topic is tested because it connects theory to particulate and gaseous control.
GATE and semester exams often combine atmospheric dispersion with earlier units — revise prerequisites before attempting mixed problems.
Industry interview panels sometimes ask: "Where did you use atmospheric dispersion?" — answer with a lab, mini-project, or plant visit example if possible.

Common mistakes in exams

• Substituting physical stack height directly without plume-rise correction
• Using wrong stability class for given meteorological condition
• Forgetting reflection term in Gaussian concentration expression
• Reporting concentration without unit conversion checks

Quick revision checklist

Before attempting atmospheric dispersion problems, confirm you can:
1. Wind speed u; σ_y σ_z from stability and distance
2. Inversion traps pollutants ground level
3. ISCST3/AERMOD regulatory models
Revise the solved examples in Air Pollution Control — CP Rao and one previous-year GATE or university paper for this unit.

Worked examples

Try the problem first — open the solution when you are ready to check.

For h

Problem

For h = 60 m and plume rise Δh = 18 m, effective stack height H = 78 m, which is then used in the Gaussian ground-level concentration equ...

Solution

For h = 60 m and plume rise Δh = 18 m, effective stack height H = 78 m, which is then used in the Gaussian ground-level concentration equation.

Conceptual check — Atmospheric Dispersion

Problem

In a Air Pollution Control semester or GATE paper you are asked: "State the main assumption, the governing relation, and one practical consequence of atmospheric dispersion." What should a complete answer include?

Exams & GATE

Gaussian plume ground-level concentration — standard air pollution question.

📖 Standard books (India)

  • Air Pollution Control — CP Rao

    Read: Syllabus unit

    Indian environmental engineering reference

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