A Simple Solution of the Smoke Filling Equation

Abstract

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.