Stack Plume Rise and Effective Stack Height (Briggs)

Which is what governs ground-level concentration rather than the height of the stack. Briggs computes a buoyancy flux from the stack gas velocity, the stack diameter and the temperature difference, and the final rise in neutral conditions follows that flux to a fractional power divided by the wind speed. The rise is frequently LARGER than the stack itself: a hot plume from a modest stack can rise well over a hundred feet on a light wind, so the effective release height can be double the physical one. Ignoring plume rise makes a dispersion estimate wildly conservative; assuming too much makes it dangerously optimistic, and since ground-level concentration falls roughly with the square of effective height, the error compounds. Wind is the term that trades against itself, and that is the counterintuitive part. A strong wind dilutes the plume more, but it also bends it over and reduces the rise, lowering the effective height -- and the rise is exactly inverse in wind speed, so doubling the wind halves it. The two effects work in opposite directions and the worst-case wind for ground-level concentration is neither the calmest nor the strongest, which is why a real dispersion analysis runs a full year of hourly meteorology rather than a design condition. Two limits bound this hard. Stability is not modelled: the neutral-condition relations used here are suppressed by stable air, where a plume can be trapped, and enhanced by unstable air. And DOWNWASH is not modelled at all -- a stack too short relative to nearby buildings has its plume pulled down into the building wake, which can eliminate the rise entirely and is why the good engineering practice stack height rules exist. A plume that downwashes has an effective height at or below the stack, and no buoyancy calculation will say so. This is a screening estimate of FINAL rise in neutral conditions on a buoyant plume; it does not compute momentum rise for a cool high-velocity plume, transitional rise close to the stack, stability effects, downwash, or any ground-level concentration. A regulatory dispersion model, the applicable modelling guideline, and a qualified meteorologist or air quality professional govern.

buoyancy flux F = g v d^2 (Ts - Ta) / (4 Ts) in SI; neutral-condition final rise = 21.425 F^0.75 / u below a 55 m^4/s^3 flux and 38.71 F^0.6 / u at or above it; effective height = stack height plus that rise, and rise is exactly inverse in wind speed.

The Briggs plume rise relations by name, published in SI and converted at 0.3048 m per foot and 1,609.344 m per mile, both exact. A screening estimate for a BUOYANT plume: it does not compute momentum rise for a cool high-velocity plume, transitional rise close to the stack, atmospheric stability effects, building DOWNWASH, or any ground-level concentration.

One published correlation and two exact length conversions.

Estimate. AHJ and licensed professional govern.

Field names used by the API: stack_height_ft, stack_diameter_ft, exit_velocity_fps, exit_temp_f, ambient_temp_f, wind_mph, buoyancy_flux, plume_rise_ft, effective_height_ft, height_ratio, concentration_factor, double_wind_rise_ft

• Neutral conditions, final rise stability suppresses or enhances rise and is not modelledthe applicable modelling guideline
• Buoyant plumes only momentum rise for a cool high-velocity plume is a different relationa regulatory dispersion model
• Downwash is not modelled a short stack near buildings can lose its rise entirelygood engineering practice stack height rules