The Surface Water and Ocean Topography (SWOT) mission is a swath mapping radar interferometer that would provide new measurements of inland water surface elevation (WSE) for rivers, lakes, wetlands, and reservoirs. SWOT WSE estimates would provide a source of information for characterizing streamflow globally and would complement existing in situ gage networks. In this paper, we evaluate the accuracy of river discharge estimates that would be obtained from SWOT measurements over the Ohio river and eleven of its major tributaries within the context of a virtual mission (VM). SWOT VM measurements are obtained by using an instrument measurement model coupled to simulated WSE from the hydrodynamic model LISFLOOD-FP, using USGS streamflow gages as boundary conditions and validation data. Most model pixels were estimated two or three times per 22-day orbit period. These measurements are then input into an algorithm to obtain estimates of river depth and discharge. The algorithm is based on Manning's equation, in which river width and slope are obtained from SWOT, and roughness is estimated a priori. SWOT discharge estimates are compared to the discharge simulated by LISFLOOD-FP. Instantaneous discharge estimates over the one-year evaluation period had median normalized root mean square error of 10.9%, and 86% of all instantaneous errors are less than 25%.