Electrical power generation employing pressure-driven flows is a fundamental problem in microfluidics. In the present work, analytical and numerical analyses are performed to study the interplaying effects of electrolyte motion with the associated electrical current in a flat microchannel with and without fluid reservoirs. The modified Navier–Stokes equations as well as a Poisson equation for the distribution of electric potential and the Nernst–Planck equations for the distribution of charge densities are solved for the steady flow of a Newtonian liquid. The results show that for a pressure-driven flow, an electric potential is induced due to the motion of charged particles, which increases linearly along the microchannel. This streaming potential generates an opposing conduction current in the core region of the channel as well as in the immediate vicinity of the walls, where the streaming current is negligible. The streaming potential varies in a nonlinear manner with the zeta potential at the walls such that a maximum potential exists at a certain zeta potential. The maximum potential is also observed to increase with both the applied pressure difference and the electric double layer thickness in the range studied. The presence of reservoirs adds significant complexity to this electrokinetic flow.