The effect of the dielectric walls of a channel on the electrohydrodynamic flows in it is considered. The effect in question is analyzed on the basis of numerically simulating a complete set of equations that includes Poisson’s, Navier-Stokes, and Nernst-Planck equations. This led to solutions for models with narrow and wide arrangements of channel walls. The width of the profile of a liquid in the gap between electrodes in a free space is chosen as a parameter of comparison. The distributions of the electric-charge velocities and density are presented for resulting solutions. The channel-width dependences of the efficiency and flow rate are constructed.