Gaussian Air Pollutant Plume Ground-Level Concentration (μg/m³) Calculator

Compute downwind ground-level pollutant concentration (μg/m³) from stack emission Q and effective height H.

Centerline Ground Concentration C(x,0,0)
290.75 μg/m³
Ground-Level Concentration in mg/m³ 0.29 mg/m³
Zero-Height Ground Release Plume (H=0) 445.19 μg/m³
Stack Elevation Attenuation Factor 65.31 %
Inputs
⚡ Scenarios:
g/s
Pollutant mass emission rate Q from stack in grams/second (g/s).
m/s
Wind speed u at effective stack height in m/s.
m
Effective stack height H (physical stack + plume rise) in meters.
m
Pasquill-Gifford horizontal dispersion coefficient σ_y at downwind x (m).
m
Pasquill-Gifford vertical dispersion coefficient σ_z at downwind x (m).
Results & Graph
Centerline Ground Concentration C(x,0,0)
290.75 μg/m³
Ground-Level Concentration in mg/m³
0.29 mg/m³
Zero-Height Ground Release Plume (H=0)
445.19 μg/m³
Stack Elevation Attenuation Factor
65.31 %

Centerline Ground Concentration C(x,0,0)

Graph 1 • Gaussian Plume Dispersion • Domain Architecture & Live Telemetry Maps Emission Rate Grams Per Sec, Wind Speed At Stack Meters Sec, Effective Stack Height Meters through Gaussian Plume Dispersion Formula.
INPUT PARAMETERS • Emission Rate Gram: 45 g/s • Wind Speed At Stac: 4.5 m/s • Effective Stack He: 60 m ∑ F(x) Gaussian Plume Dispersion DESIGN OUTPUT 290.75 μg/m³ Ground-Level Concentrati: 0.29 mg/m³ Zero-Height Ground Relea: 445.19 μg/m³
Graph 2 • Centerline Ground Concentration C(x,0,0) Across Emission Rate Grams Per Sec Sweep (40% → 160%) Evaluates C(x, 0, 0) = [ Q / (π × u × σ_y × σ_z) ] × exp( −H² / (2 × σ_z²) ) across 7 operating points (current input highlighted).
0 μg/m³ 255.9 μg/m³ 511.7 μg/m³ 116.3 18g/s 174.4 27g/s 232.6 36g/s 290.8 45g/s 348.9 54g/s 407.1 63g/s 465.2 72g/s
Graph 3 • Joint Sensitivity: Emission Rate Grams Per Sec × Wind Speed At Stack Meters Sec Compares Centerline Ground Concentration C(x,0,0) when Wind Speed At Stack Meters Sec is shifted +25% (solid) vs. −25% (dashed).
0 μg/m³ 277.2 μg/m³ 554.4 μg/m³ --- Wind Speed At Stack Meters Sec @ 75% 162.8 -30% 197.7 -15% 232.6 +0% 267.5 +15% 302.4 +30%
Summary: At σ_y=110 m and σ_z=65 m (Q=45 g/s, u=4.5 m/s, H=60 m), ground-level plume centerline concentration is 290.75 μg/m³.
Summary: At σ_y=110 m and σ_z=65 m (Q=45 g/s, u=4.5 m/s, H=60 m), ground-level plume centerline concentration is 290.75 μg/m³.
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Formula & Mathematical Methodology: Gaussian Plume Dispersion Formula

C(x, 0, 0) = [ Q / (π × u × σy × σz) ] × exp( −H² / (2 × σz²) )
C(x, 0, 0) = [ Q / (π × u × σ_y × σ_z) ] × exp( −H² / (2 × σ_z²) )
  • emissionRateGramsPerSec: Emission Rate Grams Per Sec (g/s)
  • windSpeedAtStackMetersSec: Wind Speed At Stack Meters Sec (m/s)
  • effectiveStackHeightMeters: Effective Stack Height Meters (m)
  • crosswindDispersionSigmaYM: Crosswind Dispersion Sigma Y M (m)
  • verticalDispersionSigmaZM: Vertical Dispersion Sigma Z M (m)

Rounding: Engineering outputs round to 2–3 decimal places; discrete material bag/unit counts round up via ceiling.

Worked Example: Engineering Scenario: Gaussian Plume Dispersion

Compute downwind ground-level pollutant concentration (μg/m³) from stack emission Q and effective height H.

  1. Enter your system dimensions, electrical/RF ratings, or environmental conditions.
  2. Evaluate the governing equation: C(x, 0, 0) = [ Q / (π × u × σ_y × σ_z) ] × exp( −H² / (2 × σ_z²) ).
  3. Inspect the primary design output, supporting allowances, and 3 SVG schematics.
Result: Computes Gaussian Plume Dispersion via C(x, 0, 0) = [ Q / (π × u × σ_y × σ_z) ] × exp( −H² / (2 × σ_z²) ).

Frequently Asked Questions

How does the Gaussian Air Pollutant Plume Ground-Level Concentration (μg/m³) Calculator calculate results?

It evaluates C(x, 0, 0) = [ Q / (π × u × σ_y × σ_z) ] × exp( −H² / (2 × σ_z²) ) directly in your browser and updates three custom SVG visualizations in real time.

Can I use Goal Seek to solve backwards for a required dimension or rating?

Yes. Click "🎯 Goal Seek" in the results toolbar to solve backwards for any numeric input parameter.

Does this engineering calculator work offline?

Yes. All calculations run 100% locally in your browser and work offline via the CalculatorGraph PWA.

Science & Engineering · Environmental & Agricultural Science

Gaussian Air Pollutant Plume Ground-Level Concentration (μg/m³) Calculator: inputs, method, and how to read the result

Compute downwind ground-level pollutant concentration (μg/m³) from stack emission Q and effective height H.

Choose inputs for the case you are checking

The defaults are illustrative. Replace them with values for your case and keep the units shown beside each field.

  • Emission Rate Grams Per Sec: Pollutant mass emission rate Q from stack in grams/second (g/s).
  • Wind Speed At Stack Meters Sec: Wind speed u at effective stack height in m/s.
  • Effective Stack Height Meters: Effective stack height H (physical stack + plume rise) in meters.
  • Crosswind Dispersion Sigma Y M: Pasquill-Gifford horizontal dispersion coefficient σ_y at downwind x (m).

What the calculation includes

With the default values shown, Centerline Ground Concentration C(x,0,0) is 290.75 μg/m³. The calculation follows Gaussian Plume Dispersion Formula; the formula and variable definitions above show how the inputs combine.

One-input check: With the other defaults held constant, changing Emission Rate Grams Per Sec from 45 g/s to 49.5 g/s changes Centerline Ground Concentration C(x,0,0) from 290.75 μg/m³ to 319.82 μg/m³. This is a comparison inside the calculator's stated model, not a prediction.

Where to use caution

  • Uses standard NREL, IEEE, ASHRAE, and IRC design equations.
  • Verify final structural, electrical, and mechanical specifications against local building codes.

Scope: Global Engineering & Building Code Standard Check the assumptions and limitations against your situation before relying on the estimate.

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