A simple model for the operation of the Hall current plasma accelerator, a crossed field discharge device that accelerates a flow of quasi-neutral plasma, is used to calculate the performance of an actual device at various configurations and operating conditions. The solutions demonstrate that the performance, characterized by the ionized fraction of the flow, the mass-averaged exit flow velocity and the total efficiency, improves as the flow rate or the accelerator length are increased at a given discharge voltage, trends that were also observed experimentally. Nevertheless, the calculated values for the longer lengths, especially the total efficiencies, are significantly higher than the measured ones, indicating the importance of an accurate solution of the electron energy equation and the need to include in the model plasma-wall interactions.