A hydrodynamic model for the electrorheological effect in a polymeric nematic confined in a rectangular cell is studied. The competition between a constant electric and a uniform shear flow is explicitly considered. For the final stationary state where the induced reorientation of the director has already occurred, we show that the averaged viscosity is enhanced. For this same state several rheological properties such as the first normal stress difference and the force between the cell plates are also analytically calculated as a function of position, the applied field, and Reynolds' number. These results are compared with those obtained previously for a pressure driven flow. The scope and limitations of the model and methods employed are discussed.