Chimney Stack Height Calculation

Gaussian Plume Model Equation:

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

Emission Rate (Q):

g/s

Wind Speed (u):

m/s

Horizontal Dispersion (σ_y):

Vertical Dispersion (σ_z):

Stack Height:

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1. What is the Gaussian Plume Model?

The Gaussian plume model is a mathematical model used to predict the dispersion of air pollutants from a point source such as a chimney stack. It assumes that pollutant concentrations follow a Gaussian (normal) distribution in both horizontal and vertical directions.

2. How Does the Calculator Work?

The calculator uses the Gaussian plume equation:

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

Where:

\( Height \) — Required stack 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: The equation calculates the minimum stack height needed to achieve acceptable ground-level pollutant concentrations based on emission characteristics and atmospheric conditions.

3. Importance of Stack Height Calculation

Details: Proper stack height calculation is crucial for environmental compliance, minimizing ground-level pollution concentrations, protecting public health, and optimizing industrial facility design.

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 and greater than zero for accurate calculations.

5. Frequently Asked Questions (FAQ)

Q1: What factors affect dispersion coefficients?
A: Atmospheric stability, terrain roughness, and distance from source significantly influence σ_y and σ_z values.

Q2: How accurate is the Gaussian plume model?
A: It provides reasonable estimates for steady-state conditions over flat terrain but may be less accurate in complex terrain or unstable conditions.

Q3: What are typical dispersion coefficient values?
A: Values range from 10-100m for σ_y and 5-50m for σ_z depending on atmospheric stability class and distance.

Q4: When is this model most applicable?
A: Best suited for continuous point sources under neutral to stable atmospheric conditions over relatively flat terrain.

Q5: Are there limitations to this calculation?
A: Does not account for building downwash, complex terrain effects, or chemical transformations of pollutants.