Stack Emissions Dispersion Calculator
Our air water pollution calculator computes stack emissions dispersion accurately. Enter measurements for results with formulas and error analysis.
Reviewed by Daniel Agrici, Founder & Lead Developer
Formula
C = Q / (pi*u*sigY*sigZ) * exp(-H^2 / (2*sigZ^2))
Ground-level concentration from simplified Gaussian plume with emission rate Q, wind speed u, and dispersion coefficients.
Worked Examples
Example 1: Coal Plant Stack
Problem:Q=50 g/s, H=75 m, u=5 m/s, x=1000 m.
Solution:sigY = 191.7 m, sigZ = 174.3 m exp = 0.9132 C = 50/(6.28*5*191.7*174.3)*0.9132*1e6
Result:C = 43.3 ug/m3
Example 2: Small Boiler
Problem:Q=10 g/s, H=30 m, u=3 m/s, x=500 m.
Solution:sigY = 104.7 m, sigZ = 95.2 m exp = 0.9519 C = larger due to lower H
Result:C = 101.2 ug/m3
Frequently Asked Questions
What are sigma Y and sigma Z dispersion coefficients?
Sigma Y and sigma Z describe the horizontal and vertical spread of the pollutant plume as it travels downwind from the source. They increase with distance and depend on atmospheric stability class ranging from A (very unstable) to F (stable). Unstable conditions produce larger sigma values meaning faster dilution while stable conditions trap pollutants near the ground.
What is effective stack height?
Effective stack height is the sum of the physical stack height and the plume rise caused by buoyancy and momentum of hot exhaust gases. Plume rise can add 50-200 meters depending on exit temperature, velocity, and ambient conditions. Greater effective height reduces ground-level concentrations significantly because dispersion has more distance to act.
How does wind speed affect dispersion?
Wind speed directly influences ground-level concentration as the plume is diluted by the volume of air passing the source per unit time. Higher wind speeds reduce concentrations at any given point by stretching the plume and providing more dilution air. However very low wind speeds allow pollutants to accumulate near the source especially under stable atmospheric conditions.
What are emissions factors and how are they used?
Emissions factors convert activity data into greenhouse gas emissions. For example, burning one gallon of gasoline emits about 8.887 kg CO2. Electricity emissions vary by grid region from 0.2 to 1.0 kg CO2/kWh. Multiply the activity quantity by the emission factor to get total emissions.
References
Reviewed by Daniel Agrici, Founder & Lead Developer · Editorial policy