Gaussian Plume Model Assumptions Analysis

The point source Gaussian Plume Model is used to predict the concentration of pollutants released from a source like a stack. The model relies on several simplifying assumptions:

• Constant Wind Speed: The model assumes wind speed is constant in magnitude and direction over the area and time considered.
• Conservative Pollutants: It assumes pollutants do not break down, react chemically, or undergo deposition during transport.
• Constant Emission Rate: The rate at which pollutants are emitted from the source (Q) is assumed to be constant over time.

Evaluating Concentration Dependency

The ground-level concentration (C) of a pollutant downwind from a point source is described by the Gaussian plume equation. A key aspect is its relationship with the effective stack height (H). The concentration at ground level directly downwind (y=0) is approximately:

$C(x, 0, 0) \approx \frac{Q}{\pi u \sigma_y \sigma_z} \exp\left(-\frac{H^2}{2\sigma_z^2}\right)$

This formula shows that ground-level concentration is influenced by the effective stack height (H), but the relationship is not a simple inverse proportionality (C $\propto$ 1/H). Instead, the concentration decreases exponentially as the effective stack height increases, due to the $\exp\left(-\frac{H^2}{2\sigma_z^2}\right)$ term. A higher stack disperses the plume more effectively, reducing concentration at ground level, but this dependency is complex and not merely inverse.

Identifying the Incorrect Statement

Based on the model's assumptions and the concentration formula:

• Statements 1, 2, and 3 accurately reflect standard assumptions of the basic Gaussian Plume Model.
• Statement 4, claiming ground-level concentration is inversely proportional to effective stack height, is incorrect. The relationship is more complex, involving exponential decay.

Therefore, the statement that is not true in the case of the point source Gaussian Plume Model is that the ground level concentration is inversely proportional to effective stack height.