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Algorithms III · stack testing

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:

h_e=h_s+1.60 [(F_b x²)^1/3/u_s]      (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:

h_e=h_s+[3F_mx/(bet_j²u_s²)]^1/3      (22)

where x is the downwind distance, with a maximum value x_max:

x_max=4d_s(v_s+3u_s)/(v_su_s)   for F_b=0                 (23)

x_max=49 F_b^5/8             for 0 < F_b < 55 m²s³      (24)

x_max=119 F_b^2/5            for F_b > 55 m²s³         (25)

b) stable conditions:

h_e=h_s+(3F_m)^1/3{sin[x s^1/2/u_s]}^1/3[bet_j²u_ss^1/2]^-1/3   (26)

where x is the downwind distance, with a maximum value x_max:

x_max=0.5 pi u_s/s^1/2            (27)

The jet entrainment coefficient, bet_j, is given by,

bet_j=(1/3)+(u_s/v_s)       (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 sig_y and sig_z (in meters) for the rural mode. The equations used to calculate sig_y are of the form:

sig_y=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 sig_z is of the form:

sig_z=ax^b    (31)

where the downwind distance x is in kilometers and sig_z 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 s_ze is calculated as follows:

sig_ze=[sig_z² +(Dh/3.5)]^1/2        (32)

where sig_z is the vertical dispersion due to ambient turbulence and Dh is the plume rise due to momentum or buoyancy. The lateral plume spread is:

sig_ye=[sig_y² +(Dh/3.5)]^1/2        (33)

where sig_y 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.