ESDU 97029 derives a mean-value set for representation of a non-uniform flow of a thermally-perfect gas at a duct section. A thermodynamically-rigorous, uniform reference-mean flow is derived by extending the stagnation reservoir concept for total-state conditions in uniform flow to non-uniform flow and requiring equality of the sectional mass flow and entropy between the non-uniform flow and a uniform reference-mean flow, leading to rational definitions of the mean pressure, temperature and density. Conventional "variable-c sub p" uniform flow relationships can then be applied for other properties of the reference-mean flow. Rationally-defined profile factors are used to relate other sectional properties of the real flow to the reference-mean flow. This new method allows for the simultaneous variation of total and static temperature and pressure across a duct section and enables the use of temperature-entropy and Mollier diagrams. It provides a correct allocation of work and irreversibilities among components of a multi-component system so that artificial losses are not attributed upstream or downstream of the duct section. Consistent comparison with other averaging methods is possible. Several examples illustrate analytically the use of the model.