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# Canarina DISPER software · air pollution mapping · algorithms 9

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Canarina DISPER software · air pollution mapping

9.1.4 Plume Rise Formulas

The plume height is used in the calculation of the Vertical Term. The distance dependent momentum plume rise equations are used to determine if the plume is affected by the wake region for building downwash calculations.

Stack-tip Downwash.

In order to consider stack-tip downwash, modification of the physical stack height is performed. The modified physical stack height hs is found from:

hs’=hs+2ds[(vs/us)-1.5]   for  vs<1.5us      (5

or

hs’=hs                   for vs> o =1.5us   (6)

where hs is physical stack height (m), vs is stack gas exit velocity (m/s), and ds is stack top diameter (m). If stack tip downwash is not considered, hs’= hs in the following equations.

Buoyancy and Momentum Fluxes.

For most plume rise situations, the value of the Briggs buoyancy flux parameter, Fb (m4/s3), is needed

Fb=gvsds2(DT/4Ts)    (7)

where DT = Ts - Ta, Ts is stack gas temperature (K), and Ta is ambient air temperature (K).

For determining plume rise, the momentum flux parameter, Fm (m4/s2), is calculated based on the following formula:

Fm=gvs2ds2(Ta/4Ts)    (8)

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Canarina DISPER software · air pollution mapping

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