Fig. 8. A plan view of a plume of pollutant from a continuous point source S.
Consider a slice of air 1 m thick moving in the -direction, extending
to infinity in the and directions and moving with the mean wind .
The time taken for the slice to pass a fixed point is seconds. If the
source emits kgs of pollutant, then the amount in the slice is
The pollutant diffuses in the , and directions. But since
the source is continuous, about the same amount of pollutant diffuses into
the sheet in the -direction as diffuses out through the opposite side.
Diffusion in the -direction therefore has negligible effect. The diffusion
problem reduces to that of 2-dimensional diffusion in the , plane but
in a frame of reference moving in the -direction with speed . The
2-dimensional diffusion solution Eq. (22) therefore applies, but with .
In other words