Question

CO is released from a point source on a level ground at a rate of 25 g/s. The average wind speed is 5 m/s. The dispersion coefficients are 150 m and 200 m in horizontal and vertical directions, respectively, at a receiver station located on the ground along the downwind direction. Assuming the plume follows Gaussian dispersion model, the concentration of CO, in \, \mu g/m^3 at the station is \(\underline{\hspace{2cm}}\) (round off to 2 decimal places).

Hint:

For the Gaussian dispersion model, the concentration is inversely proportional to the wind speed and dispersion coefficients.

Answer 1

Correct Answer: 50

Given: \[ Q = 25 \, \text{g/s}, u = 5 \, \text{m/s}, \sigma_x = 150 \, \text{m}, \sigma_y = 200 \, \text{m} \] The Gaussian dispersion model for concentration at a downwind station is: \[ C = \frac{Q}{2\pi u \sigma_x \sigma_y} \exp\left( -\frac{y^2}{2\sigma_y^2} \right) \] For simplicity, we assume \( y = 0 \) (ground-level concentration), so: \[ C = \frac{25}{2\pi \times 5 \times 150 \times 200} = \frac{25}{471238.9} \approx 0.000053 \] Converting to \(\mu g/m^3\) (since \(1 \, \text{g} = 1000000 \, \mu g\)): \[ C \approx 0.000053 \times 1000000 = 0.053 \, \mu g/m^3 \] Thus, the concentration of CO is approximately: \[ \boxed{0.05 \, \mu g/m^3} \]