Fire Technology

, Volume 53, Issue 3, pp 1479–1484 | Cite as

A Simple Solution of the Smoke Filling Equation

  • Yan ZhouEmail author
  • Qian Meng
Short Communication


Thirty four years after the enclosure smoke filling equation was first published by Zukoski, Novozhilov found an exact analytical solution for the case of constant fire heat release rate (HRR). This exact solution is fundamentally important in theory, but quite complicated. In this note, a simple solution is reported for the same case. Because of its simple visual appearance, the formula of this solution can be easily calculated on a hand calculator or on a spreadsheet. Comparing with the exact solution, the relative error of this simple solution is from −5 to 5% in the range where the non-dimensional HRR is larger than 0.001 or the non-dimensional smoke layer height is larger than 0.2. This range covers most practical cases.


Enclosure Smoke filling Fire dynamics Simple solution 



A Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD).


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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Key Laboratory of Gas and Fire Control for Coal Mines (CUMT)Ministry of EducationXuzhouChina
  2. 2.School of Computer Science and TechnologyJiangsu Normal UniversityXuzhouChina

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