The velocity and temperature distributions in turbulent buoyant induced by a line source or point source of heat are calculated by assuming the eddy viscosity and eddy diffusivity to be constant in any cross section of the plume. Two solutions in closed forms are obtained for the two‐dimensional plume, corresponding to turbulent Prandtl number &sgr; equal to 2/3 and 2. Two such solutions are also obtained for the round plume, corresponding to &sgr; equal to 1.1 and 2. The solution for &sgr;=2/3 is compared with previous measurements for two‐dimensional plumes, and the solution for &sgr;=1.1 is compared with previous measurements for the axisymmetric plume. The analytical and experimental results agree well in the two‐dimensional case, and satisfactorily in the axisymmetric case.