So far, electrohydrodynamic (EHD) pumps based on the injection or the field-enhanced dissociation (the Wien effect) at the surface of metal electrodes have been studied. This paper proposes and studies both numerically and experimentally a fundamentally new pump scheme, namely, the EHD pump operating due to the Wien effect in a conical hole located in the solid insulation barrier. An experimental setup of the pump has been created, and performance (pressure vs flow rate) characteristics have been measured that satisfactorily agree with the results of computer simulation. With the size of the hole being a fraction of a millimeter, the proposed system performance is comparable to that of the previously studied EHD pumps.