Write the three-dimensional Gaussian model dispersion for the atmospheric pollution problem. Modify the model under the following assumptions: 

(i) Wind velocity is in only y -direction.

(ii) Mass transfer due to bulk motion in the y -direction overshadows the contributions due to mass diffusion.

(iii) Motion is in steady state.

(iv) Wind speed is constant.

(v) Diffusivities are constant in all the directions

The three-dimensional Gaussian model dispersion for atmospheric pollution can be expressed as:

\[C(x, y, z) = \frac{Q}{2\pi \sigma_x \sigma_y \sigma_z} e^{-\frac{1}{2}\left(\frac{(x-x_0)^2}{\sigma_x^2} + \frac{(y-y_0)^2}{\sigma_y^2} + \frac{(z-z_0)^2}{\sigma_z^2}\right)}\]

Where:
- \(C(x, y, z)\) is the concentration of pollutants at point \((x, y, z)\).
- \(Q\) is the emission rate of pollutants.
- \((x_0, y_0, z_0)\) are the coordinates of the source.
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