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All Conditions - Distance Less Than Distance to Final Rise.
Where gradual rise is to be estimated for unstable, neutral, or stable conditions, if the distance downwind from source to receptor, x, is less than the distance to final rise:
he=hs+1.60 [(Fb x2)1/3/us] (21)
This height will be used only for buoyancy dominated conditions; should it exceed the final rise for the appropriate condition. For momentum dominated conditions, the following equations are used to calculate a distance dependent momentum plume rise:
a) unstable conditions:
he=hs+[3Fmx/(betj2us2)]1/3 (22)
where x is the downwind distance, with a maximum value xmax:
xmax=4ds(vs+3us)/(vsus) for Fb=0 (23)
xmax=49 Fb5/8 for 0 < Fb < 55 m2s3 (24)
xmax=119 Fb2/5 for Fb > 55 m2s3 (25)
b) stable conditions:
he=hs+(3Fm)1/3{sin[x s1/2/us]}1/3[betj2uss1/2]-1/3 (26)
where x is the downwind distance, with a maximum value xmax:
xmax=0.5 pi us/s1/2 (27)
The jet entrainment coefficient, betj, is given by,
betj=(1/3)+(us/vs) (28)
If the distance-dependent momentum rise exceeds the final rise for the appropriate condition, then the final rise is substituted instead.
The Dispersion Parameters
Point Source Dispersion Parameters:
Equations that approximately fit the Pasquill-Gifford curves are used to calculate sigy and sigz (in meters) for the rural mode. The equations used to calculate sigy are of the form:
sigy=465.11628 x tan (TH) (29)
where:
TH=0.017453293[c - d ln(x)] (30)
In both Equations the downwind distance x is in kilometers. The equation used to calculate sigz is of the form:
sigz=axb (31)
where the downwind distance x is in kilometers and sigz is in meters.
Procedures Used to Account for Buoyancy-Induced Dispersion.
The method of Pasquill is used to account for the initial dispersion of plumes. With this method, the effective vertical dispersion sze is calculated as follows:
sigze=[sigz2 +(Dh/3.5)]1/2 (32)
where sigz is the vertical dispersion due to ambient turbulence and Dh is the plume rise due to momentum or buoyancy. The lateral plume spread is:
sigye=[sigy2 +(Dh/3.5)]1/2 (33)
where sigy is the lateral dispersion due to ambient turbulence. It should be noted that Dh is the distance-dependent plume rise if the receptor is located between the source and the distance to final rise, and final plume rise if the receptor is located beyond the distance to final rise.
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Canarina Algoritmos Numéricos, S.L.
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