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Logic Diagram For Using The Briggs Equations
To Calculate The Rise of Bent-over Buoyant Plumes

Milton R. Beychok, Consulting Engineer
Newport Beach, California, USA

Gary A. Briggs published his first plume rise model observations and comparisons in 1965.1  In 1968, at a symposium sponsored by CONCAWE (a Dutch organization), he compared many of the plume rise models then available in the literature.2  In that same year, Briggs also wrote the section of the publication edited by Slade 3 dealing with the comparative analyses of plume rise models.  That was followed in 1969 by his classical critical review of the entire plume rise literature 4, in which he proposed a set of of plume rise equations which have since become widely known as "the Briggs equations".  Subsequently, Briggs modified his 1969 plume rise equations in 1971 and in 1972.5, 6

Briggs divided air pollution plumes into these four general categories:

  (1)  Cold jet plumes in calm ambient air conditions
  (2)  Cold jet plumes in windy ambient air conditions
  (3)  Hot, buoyant plumes in calm ambient air conditions
  (4)  Hot, buoyant plumes in windy ambient air conditions

Briggs considered the trajectory of cold jet plumes to be dominated by their initial velocity momentum ... and the trajectory of hot, buoyant plumes to be dominated by their buoyant momentum to the extent that their initial velocity momentum was relatively unimportant.  Although Briggs proposed plume rise equations 4 for each of the above plume categories, it is important to emphasize that "the Briggs equations" which have become widely known and widely used are those that he proposed for bent-over, hot buoyant plumes.

In general, Briggs' equations for bent-over, hot buoyant plumes are based on observations and data involving plumes from typical combustion sources such as the flue gas stacks from steam-generating boilers burning fossil fuels in large power plants.  We can therefore assume the stack exit velocities were in the range of 20 to 100 ft/sec ( i.e., 6 to 30 m/sec ) with exit temperatures in the range of 250 to 500 °F ( i.e., 120 to 260 °C ).

A logic diagram for using the Briggs equations to obtain the plume rise trajectory of bent-over buoyant plumes is presented below:

How to calculate the terms used in the logic diagram is discussed in Beychok's book. 7


(1)   Briggs, G.A., "A plume rise model compared with observations", JAPCA, 15:433-438, 1965

(2)   Briggs, G.A., "CONCAWE meeting: discussion of the comparative consequences of different plume rise formulas", Atmos. Envir., 2:228-232, 1968

(3)   Slade, D.H. (editor), "Meteorology and atomic energy 1968", Air Resources Laboratory, U.S. Dept. of Commerce, 1968

(4)   Briggs, G.A., "Plume Rise", USAEC Critical Review Series, 1969

(5)   Briggs, G.A., "Some recent analyses of plume rise observation", Proc. Second Internat'l. Clean Air Congress, Academic Press, New York, 1971

(6)   Briggs, G.A., "Discussion: chimney plumes in neutral and stable surroundings", Atmos. Envir., 6:507-510, 1972

(7)   Beychok, M.R., "Fundamentals Of Stack Gas Dispersion", published by the author, Irvine, CA, Fourth Edition, 2005.

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