Citation

Thomas PH. Fire Safety J. 2000; 34(1): 47-53.

Copyright

(Copyright © 2000, Elsevier Publishing)

DOI

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PMID

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Abstract

The Lee and Emmons [1] model of a two-dimensional plume from an infinitely long horizontal strip source in a uniform atmosphere is the basis of one current design method [2] of smoke control in buildings. Lee and Emmons approximated the density in the expressions for mass and momentum flows by [rho]A, the uniform density of the surroundings, and they assumed the upward velocity 'w' and the density deficiency [Delta][rho] were distributed across the plume by Gaussian profiles. Hansell and Morgan [2] transformed the Lee and Emmons solution for [Delta][rho]C/[rho]A into [Delta]TC/(TA+[Delta]TC) where TA is the temperature of the surroundings and [Delta]TC the local excess temperature, the suffix 'c' denoting the central axis value. In view of the original approximation that [rho]C=[rho]A there is no justification in theory for this complication which is the result of decoupling a coupling already made. It is shown here that one need not make the approximation [rho]C=[rho]A to develop a solution little more complicated than the Lee and Emmons solution. The form of Lee and Emmons solutions, including a relevant integral, can be used with an effective mean densitywhere [lambda] is a constant, the ratio of the width of the profile of density deficiency to that of the velocity. Lee and Emmons found [lambda] to be 0.9 in their experiments, i.e.[rho]eff=[rho]A-0.78[Delta][rho]cor for [lambda]=1 (similar Gaussian profiles for velocity and density deficiency)[rho]eff=[rho]A-0.82[Delta][rho]c.These are nearer to [rho]A-[Delta][rho]C=[rho]C than to [rho]A, so the simple [Delta]Tc/TA is more accurate and less complicated than the form used by Hansell and Morgan [2] and repeated in a recently published book [3].