$2\mathrm{.}7$ Smoke stack. A chemical plant has a smoke stack $75m$ tall that discharges a continu$-$

ous flux of carbon monoxide $(CO)$ of $0\mathrm{.}01k\frac{g}{s}.$ The wind blows with a velocity of $1\frac{m}{s}$

due east $($from the west to the east$)$ and the transverse turbulent diffusion coefficient is

$4\mathrm{.}5\frac{m^2}{s}.$ Neglect longitudinal $($downwind$)$ diffusion.

Write the unbounded solution for a continuous source in a cross wind.

Add the appropriate image source$($s$)$ to account for the no$-$flux boundary at the ground

and write the resulting image$-$source solution for concentration downstream of the re$-$

lease.

Plot the two$-$dimensional concentration distribution downstream of the smoke stack for

the plane $2m$ above the ground.

For radial distance $r$ away from the smoke stack, where do the maximum concentrations

occur?