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How It Works
Atmospheric dispersion models predict how pollutants spread downwind from a source like a smokestack. The effective stack height combines the physical chimney height with the extra rise the hot plume gains from buoyancy and momentum. Wind speed at the release height is then used with Gaussian equations to estimate ground-level concentrations.
The power-law wind profile adjusts a measured wind speed at one elevation to any other height using a stability parameter (n) that ranges from about 0.07 for unstable conditions to 0.55 for very stable atmospheres.
Example Problem
A power plant has a 60 m physical stack and the plume rise is estimated at 25 m. What is the effective stack height?
- H = 60 + 25 = 85 m
For the wind profile: if the station measures 4 m/s at 10 m height and n = 0.25, the wind speed at 85 m is 4 × (85/10)0.25 ≈ 6.8 m/s.
Frequently Asked Questions
What is effective stack height in air pollution?
Effective stack height is the sum of the physical chimney height and the plume rise caused by buoyancy and exit velocity. It determines the initial release elevation in Gaussian dispersion models and directly affects predicted ground-level concentrations.
How does atmospheric stability affect dispersion?
Unstable atmospheres promote vertical mixing and dilute pollutants faster, while stable conditions suppress mixing and can trap emissions near the surface. The stability parameter n in the wind profile equation captures this effect, with higher values indicating more stable conditions.
What is a typical plume rise for a power plant?
Plume rise varies widely but commonly ranges from 20 to 100 m depending on exit gas temperature, stack diameter, and wind speed. A 500 MW coal plant might have a plume rise of 50–80 m under moderate wind conditions.
What is the power law wind profile used for?
The power law wind profile extrapolates a wind speed measured at one height (typically 10 m at a weather station) to any other elevation. It is widely used in air quality modeling, wind energy assessments, and structural engineering.
Related Calculators
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- Venturi Scrubber Calculator -- calculate pressure drop for wet scrubbing of gas streams.
- Ideal Gas Law Calculator -- relate gas pressure, volume, and temperature for stack emissions.
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