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A mathematical model was developed for predicting the downward descending behavior of the buoyant smoke layer under sprinkler spray. The behavior of the smoke layer was determined by considering the interaction between the drag force of the sprinkler spray and the buoyancy force of the hot smoke layer itself in the spray region. The smoke layer may be pulled down with its thickness increased at the center of the spray region due to the cooling and drag effects of the sprinkler spray, thus to form a downward "smoke logging" plume. In the mathematical model developed in this paper, the critical condition under which the smoke layer lost its stability, as a serious concern, was predicted. Additionally, the length of the downward plume, which was rarely investigated before, was also further calculated.

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