The ability to numerically simulate the flow in baffled, stirred vessels is fast becoming vital io their optimal design, Most of the past attempts have adopted a black box treatment to the impeller swept region, requiring experimentally-based input. More recent effects are based on the computation of the full time varying flow held within and outside the impeller swept region. An intermediate approach has been developed here, in which a quasi-steady flow is computed for any momentary impeller position, The method proposed here raptures almost all the significant details of the now both within and outside the impeller without requiring any empirical input/adjustable parameter. The method was applied to the flow generated by an axial impeller which is the most widely used impeller in the process industries. The case of a fully baffled vessel with standard pitched blade turbine was simulated using a FLUENT code. The time-averaged momentum transport equations were solved along with a turbulence model. The time derivative terms in the full transport equations were formulated in terms of spatial derivatives for the impeller swept region. The impeller rotation tvas simulated in terms uf appropriate source terms at the blade surfaces, The model predictions were compared with the published experimental data obtained using the laser Doppler anemometer. It must be emphasized here again that all the predictions were obtained by specifying just an impeller geometry, location and tip speed without requiring ally boundary conditions near the impeller, The influence of impeller clearance on the generated flow was also correctly simulated. The approach presented here can be used as a general purpose design tool for screening various mixer configurations and to evolve an optimum stirred vessel design.