This paper presents an analytical solution to periodical streaming potential, flow-induced electric field and velocity of periodical pressure-driven flows in two-dimensional uniform microchannel based on the Poisson-Boltzmann equations for electric double layer and Navier-Stokes equation for liquid flow. Dimensional analysis indicates that electric-viscous force depends on three factors: (1) Electric-viscous number representing a ratio between maximum of electric-viscous force and pressure gradient in a steady state, (2) profile function describing the distribution profile of electro-viscous force in channel section, and (3) coupling coefficient reflecting behavior of amplitude damping and phase offset of electro-viscous force. Analytical results indicate that flow-induced electric field and flow velocity depend on frequency Reynolds number (R_e = wh²/v). Flow-induced electric field varies very slowly with R_e when R_e < 1 , and rapidly decreases when R_e<1. Electro-viscous effect on flow-induced electric field and flow velocity are very significant when the rate of the channel width to the thickness of electric double layer is small.