Briggs Fundamental Model

 
The commonest plume rise model in use is that of Briggs (1975) which applies to plumes which largely rise through buoyancy. The models presented by Masters are based on his work and that of the USEPA.
Briggs calculated the plume rise z as a function of downwind distance x.
Where Fo is the initial buoyancy flux, defined as

Where most of the symbols have the meanings defined above and where g is the acceleration due to gravity (m/s2) and wo is the initial plume vertical speed (m/s) usually taken as the efflux velocity Vs as above.

The coefficient 1.6 in the equation to calculate z is reported by Briggs to be accurate to + or - 40% with variations due to downwash and local terrain. This would seem to represent the accuracy of this plume rise model and it is instructive to look at the effect of this on predictions made by any models being used.

Under Stable Conditions

The final plume rise is given by:
Where S is the ambient stability parameter (units of s-2) defined as:

Note that is the adiabatic lapse rate (0.01C/m) and that dTa /dz is the actual rate of temperature change with altitude.

Note that a +ve value means temperature is increasing with altitude.

If you do not know this value but are sure conditions are stable use a value of about 2 oC/km.

In the case of calm winds a buoyant plume will rise vertically until

Note that this formula implies that a "virtual source" exists 3 stack diameters below the stack outlet.

Other Conditions

Briggs recommends the following formula for neutral conditions:
But the parameter uf, the friction velocity is not easy to obtain and the following procedure recommended by Masters and by the USEPA can be used for neutral or unstable conditions:
u = Wind speed. m/s
xf = Distance downwind to point of final plume rise.
Calculation of xf depends on buoyancy flux:
If F is not less than 55 use:
 

Task 4:

Using the following data calculate the plume rise using (Briggs model) for the following meteorological conditions:

a) Slightly Unstable Conditions.

b) Stable Conditions with temperature rising at 2oC per km.

In both cases assume the average wind speed over the plume rise altitude range is 5m/s.

STACK DATA

Stack Diameter 4m
Stack Gas Temperature 413K
Ambient Temperature 298K
Exit velocity of stack gases 15m/s