Gaussian Plume Calculator
A 100 g/s release from a 50 m effective stack in a 5 m/s wind under neutral conditions gives 923.238 µg/m³ at ground level 1 km downwind.
923.237624215732 µg/m³
Full answer, then cut to fewer decimals (not rounded):
- 923.237624215732 µg/m³
- 923.23762421573 µg/m³
- 923.2376242157 µg/m³
- 923.237624215 µg/m³
- 923.23762421 µg/m³
- 923.2376242 µg/m³
- 923.237624 µg/m³
- 923.23762 µg/m³
- 923.2376 µg/m³
- 923.237 µg/m³
- 923.23 µg/m³
- 923.2 µg/m³
- σ_y (Briggs, open country)
- 76.27700714 m
- σ_z
- 37.94733192 m
- Ground-level centreline at this x
- 923.2376242 µg/m³
- In mg/m³
- 0.9232376242 mg/m³
Step-by-step solution
- σ_y = 76.27700714 m, σ_z = 37.94733192 m at x = 1000 m (class D)
- C = Q/(2πuσ_yσ_z) e^(−y²/2σ_y²)[e^(−(z−H)²/2σ_z²) + e^(−(z+H)²/2σ_z²)]
- C = 0.0009232376242 g/m³ = 923.2376242 µg/m³
Gaussian Plume Formula
C = Q/(2πuσ_yσ_z) e^(−y²/2σ_y²)[e^(−(z−H)²/2σ_z²) + e^(−(z+H)²/2σ_z²)]
σ_y, σ_z from Briggs open-country formulas; ground reflection included
Worked Example
100 g/s from a 50 m effective stack, 5 m/s wind, neutral (D) stability, 1 km downwind at ground level:
- σ_y = 76.27700714 m, σ_z = 37.94733192 m at x = 1000 m (class D)
- C = Q/(2πuσ_yσ_z) e^(−y²/2σ_y²)[e^(−(z−H)²/2σ_z²) + e^(−(z+H)²/2σ_z²)]
- C = 0.0009232376242 g/m³ = 923.2376242 µg/m³
σ_z: 37.94733192 m · Ground-level centreline at this x: 923.2376242 µg/m³ · In mg/m³: 0.9232376242 mg/m³
GATE tip
Maximum ground-level concentration occurs roughly where σ_z = H/√2. Doubling the wind speed halves concentrations, though it also reduces plume rise.
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Frequently asked questions
What is effective stack height?
Physical height plus plume rise from the gas’s buoyancy and momentum (Briggs or Holland formulas). It is the H in the plume equation.
Which stability gives the highest ground concentration?
Unstable conditions bring the plume down close to the stack (looping); stable conditions keep it aloft but carry it far, so the worst case depends on distance.
Sources
- The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures .
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
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APA
Scientific Converters. (2026, October 15). Gaussian Plume Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/gaussian-plume-calculator/
IEEE
Scientific Converters, "Gaussian Plume Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/gaussian-plume-calculator/