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A detailed, step-by-step derivation of the above equation is given in the book
"Fundamentals of Stack Gas Dispersion" which can be ordered from this website.

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Or click on one of these Feature Technical Articles:

Error Propagation in Air Dispersion Modeling

Calculating Accidental Release Rates From Pressurized Gas Systems

Source Terms For Accidental Discharge Flow Rates

Logic Diagram For Using Briggs' Plume Rise Equations

Air Dispersion Modeling Conversions and Formulas