An integral model of the behaviour of a single horizontally discharged buoyant flow in a coflowing ambient fluid is presented. The usual integral equations for the conservation of mass, momentum and buoyancy flux are used. However, the model differs from those presented previously by using the spread assumption rather than the more usual entrainment assumption and by explicitly forcing the initially gaussian velocity distribution to become a thermal distribution. The position and the form of this transition is determined from laboratory data (Brown [1984], Knudsen [1988]) and field data (Lee and Neville-Jones [1987]).