Recent investigations have shown that electrohydrodynamic (EHD) flows caused by the field-enhanced dissociation can emerge near solid insulation elements, which makes it possible to create a fundamentally new scheme of an EHD pump, where the key elements of the design are those of solid insulation rather than electrodes. The present work tests this new way of pumping and explores its performance capabilities in a system consisting of two parallel plane electrodes and a dielectric barrier between them with a small non-symmetrical hole. With the help of the software complex Comsol Multiphysics, the distributions of physical quantities in this system were computed and analyzed, and the pump performance curves were calculated. The system is capable of generating pressure head of the order of 1 kPa and shows the prospects for optimization.