Chimney Height Calculation Formula

Gaussian Dispersion Model:

\[ H = \left( \frac{Q}{2\pi u \sigma_y \sigma_z} \right)^{1/2} \]

Emission Rate (Q):

g/s

Wind Speed (u):

m/s

Horizontal Dispersion (σ_y):

Vertical Dispersion (σ_z):

Chimney Height (H):

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1. What is the Gaussian Dispersion Model?

The Gaussian dispersion model is a mathematical approach used to predict air pollution dispersion from point sources like chimneys. It assumes pollutant concentrations follow a normal distribution in both horizontal and vertical directions downwind from the source.

2. How Does the Calculator Work?

The calculator uses the Gaussian dispersion equation:

\[ H = \left( \frac{Q}{2\pi u \sigma_y \sigma_z} \right)^{1/2} \]

Where:

\( H \) — Chimney height (m)
\( Q \) — Emission rate (g/s)
\( u \) — Wind speed (m/s)
\( \sigma_y \) — Horizontal dispersion coefficient (m)
\( \sigma_z \) — Vertical dispersion coefficient (m)

Explanation: This equation calculates the minimum chimney height required to achieve acceptable ground-level pollutant concentrations based on emission characteristics and atmospheric conditions.

3. Importance of Chimney Height Calculation

Details: Proper chimney height design is crucial for environmental protection, regulatory compliance, and minimizing health impacts from industrial emissions. It ensures pollutants are adequately dispersed before reaching ground level.

4. Using the Calculator

Tips: Enter emission rate in g/s, wind speed in m/s, and dispersion coefficients in meters. All values must be positive numbers. The dispersion coefficients depend on atmospheric stability and distance from the source.

5. Frequently Asked Questions (FAQ)

Q1: What factors affect dispersion coefficients?
A: Atmospheric stability (Pasquill classes), surface roughness, and distance from source significantly influence σ_y and σ_z values.

Q2: When is this model most accurate?
A: The Gaussian model works best for flat terrain, steady wind conditions, and continuous emissions over 1-2 hours.

Q3: What are typical dispersion coefficient values?
A: σ_y and σ_z range from 10-500 meters depending on stability class and distance (100m to 10km from source).

Q4: Are there limitations to this model?
A: Less accurate for complex terrain, building wake effects, calm conditions, and reactive pollutants.

Q5: How does wind speed affect chimney height?
A: Higher wind speeds generally allow for lower chimney heights as pollutants disperse more effectively.