Effective Stack Height

This is an addition, and the reason it deserves a page of its own is what sits downstream of it. Ground-level concentration from an elevated source falls with the SQUARE of effective height, so the arithmetic here is worth more than it looks. A 60 m stack whose plume rises 45 m disperses from 105 m, and the peak ground-level concentration is not 75 percent better than the bare stack, it is $(105/60)^2 = 3.06$ times lower. In the units North American drawings are still dimensioned in, a 200 ft stack with 150 ft of rise gives an effective height of 350 ft. Plume rise is cheap and steel is not, which is why raising exit velocity or exit temperature is almost always the first thing a plant looks at.

That same arithmetic is exactly why regulators put a ceiling on it. Through the 1960s and 1970s, tall stacks were used to move a local problem somewhere else, and the acid deposition that followed in eastern Canada and the northeastern United States was the result. The 1977 Clean Air Act amendments answered with Good Engineering Practice stack height, which caps the height a dispersion model may CREDIT rather than the height a plant may build. GEP is the greater of 65 m or $H + 1.5L$, where H is the height of a nearby structure and L is the lesser of that structure's height or its projected width. Build taller if you like, but model at GEP, and the emission limit is set from the modelled result.

Effective height can also be less than the physical stack, which surprises people. If a stack does not clear nearby buildings by a comfortable margin, the plume is entrained into the recirculating cavity behind them and brought to ground within a few building heights. The rule of thumb is that a stack should reach 2.5 times the height of the tallest structure within roughly five building heights, and below that a building-downwash treatment such as PRIME is required rather than a plain Gaussian model. There is a smaller correction at the stack itself: when the exit velocity is under 1.5 times the wind speed, Briggs' stack-tip downwash adjustment is $2d(v_s/u - 1.5)$, which is negative. A 2 m stack exhausting at 6 m/s into an 8 m/s wind loses $2 \ imes 2 \ imes (0.75 - 1.5) = 3$ m of effective height before dispersion even begins.

One definitional point that causes real errors. The rise term here should be the FINAL rise, the height at which the plume has levelled off, not a transitional rise evaluated at whatever distance you happened to be interested in. Using the transitional Briggs rise at 5 km in a Gaussian calculation credits the source with a plume that climbed for the whole journey, which it did not. Compute the final rise first, add it once, and then let the dispersion coefficients do the work of distance.