Solutions for the point mean flow field properties in the turbulent core for suspension flow in a vertical circular tube have been developed for the fully developed flow condition. For uniform particle density flows, the suspension velocity distribution is logarithmic and is given in terms of parameters which must be determined by experiment, but the paper shows that all flows which satisfy the conditions of the model should follow the same universal law. Analytic expressions for the gas velocity and the slip velocity are also presented. The purpose of the analysis was to produce solutions of practical utility and to provide a basis for the extrapolation and interpretation of experimental results which are presented in another paper.