Calculator Inputs
Example Data Table
| Scenario | Q | Wind | x | y | z | Stack + Rise | Class | σy | σz | Concentration |
|---|---|---|---|---|---|---|---|---|---|---|
| Example A | 120 g/s | 5 m/s | 1000 m | 0 m | 2 m | 60 m | D | 76.28 m | 37.95 m | 0.758 mg/m³ |
| Example B | 80 g/s | 4 m/s | 500 m | 25 m | 1.5 m | 40 m | C | 54.32 m | 37.26 m | 2.807 mg/m³ |
Formula Used
Gaussian plume equation:
C(x,y,z) = Q / (2πuσyσz) × exp[-y² / (2σy²)] × [exp(-(z-H)² / (2σz²)) + exp(-(z+H)² / (2σz²))]
Where:
- C = concentration at the receptor
- Q = emission rate
- u = wind speed
- σy = lateral dispersion coefficient
- σz = vertical dispersion coefficient
- H = effective stack height = physical stack height + plume rise
When you choose automatic sigma mode, the calculator uses common Pasquill-Gifford style approximations for stability classes A to F. Manual mode lets you enter σy and σz directly when measured or modeled values are already available.
How to Use This Calculator
- Enter the source emission rate and choose its unit.
- Enter wind speed and select the correct wind unit.
- Choose one distance unit for x, y, z, stack height, plume rise, and manual sigma values.
- Enter receptor position and source geometry.
- Select automatic sigma mode for stability class estimation, or manual mode for direct σ values.
- Press Calculate Dispersion.
- Review concentration, centerline values, dilution factor, and plume spread.
- Use the export buttons to save the result as CSV or PDF.
Gaussian Dispersion in Chemical Air Studies
Why this model matters
A Gaussian dispersion calculator helps estimate how a released chemical spreads through air. It is widely used in environmental chemistry, stack emission screening, and exposure review. The model is fast. It is also practical. You can test how wind, distance, and stack height affect concentration at a receptor point.
What the calculator evaluates
This calculator focuses on plume concentration from a continuous point source. It uses emission rate, wind speed, receptor position, and effective stack height. It also uses lateral and vertical spread terms. These spread terms are called sigma y and sigma z. They control how quickly the plume widens and mixes.
Automatic and manual dispersion options
In many chemistry and air quality tasks, users start with stability classes. Those classes describe atmospheric turbulence. Unstable air mixes more strongly. Stable air mixes less. Automatic mode estimates sigma values from the selected class and downwind distance. Manual mode is useful when field data, software outputs, or permit documents already provide sigma values.
How to interpret the output
The main result is concentration at the chosen receptor. The page also shows centerline ground concentration, dilution factor, plume width, and plume depth. These outputs help compare scenarios quickly. A higher emission rate usually increases concentration. A higher wind speed often lowers concentration. A taller effective stack can shift the peak farther downwind.
Best use cases
Use this tool for screening studies, classroom chemistry work, emission planning, and fast scenario comparison. It is ideal for first-pass decisions. It is not a full replacement for advanced regulatory modeling. Terrain, building downwash, chemistry changes, and deposition can alter real results. Still, the Gaussian approach remains a strong starting point for structured air dispersion analysis.
FAQs
1. What does a Gaussian dispersion calculator do?
It estimates pollutant concentration at a receptor using a Gaussian plume model. The tool combines source strength, wind speed, plume spread, and receptor location in one structured calculation.
2. What is effective stack height?
Effective stack height is the physical stack height plus plume rise. This value affects how high the plume starts mixing and strongly changes ground-level concentration predictions.
3. When should I use manual sigma values?
Use manual sigma inputs when another model, field study, or technical report already gives you sigma y and sigma z. This avoids re-estimating dispersion spread from stability class assumptions.
4. What does stability class mean?
Stability class describes atmospheric turbulence. Class A is very unstable and mixes strongly. Class F is stable and mixes weakly. The selected class changes plume spread and concentration.
5. Why does higher wind speed often reduce concentration?
Faster wind moves the plume through the air volume more quickly. That usually increases dilution at a fixed receptor point, which lowers the predicted concentration from the same emission rate.
6. What units does this calculator support?
The calculator supports several emission, wind, and distance units. It converts everything internally before calculation, so you can compare scenarios without manual unit conversion mistakes.
7. Is this tool suitable for regulatory compliance work?
It is best for screening and learning. Regulatory work often needs more advanced models that include terrain, building effects, deposition, chemistry, and detailed meteorological data.
8. Why include the reflected plume term?
The reflected term accounts for plume reflection near the ground. It helps estimate concentration more realistically, especially for near-surface receptors and standard Gaussian plume applications.