A mathematical model of a turbulent diffusion buoyant flame based on a number of simplifying assumptions is presented. The model predicts the general characteristics of a free-burning fire in both the region where combustion is occurring and the hot gas plume formed above the combustion section. The solution yields the mass-flow rate as a function of height which can be directly related to the excess air. It was found that the height at which 400% excess air has been entrained corresponds to the visible flame height according to data taken in our laboratory as well as that presented by a number of other workers.