Measurements of mean axial velocity, and the corresponding normal stress are reported for the isothermal flow of air and for a combusting mixture of natural gas in an axisymmetric furnace enclosure with a coaxial burner. Temperature and wall heat flux measurements were also obtained for the combusting flow. The swirl number of the flow was 0.5. The measurements are compared with the results of a calculation procedure incorporating a two equation turbulence model and a one step reaction model. The combustion model allowed fuel and oxygen to coexist at the same place but not at the same time. The comparison indicates that the calculation procedure qualitatively represents the measurements but that quantitative differences exist. The argument is sufficiently close, however, to justify the use of the method for some design purposes.