The electrohydrodynamic flow in the system “needle–two wires” has been investigated using the Shadow method with simultaneous recording of the transversal pumping intensity. An unstable electrohydrodynamic flow appears as a fluctuation of the central jet (flow from the blade) between the electrodes, which results in decreasing of the efficiency of the three-electrode system. The possibility of electrohydrodynamic flow stabilization by means of decreasing the interelectrode gap and using an additional, fourth electrode, which is situated behind the first two electrodes, is shown. A theoretical model of the pumping process considering the flow as a diffuser flow from the blade limited by two lateral eddies near the upper electrode collectors is proposed. As the electrohydrodynamic flow develops, the average speed of the diffuser flow, as well as the eddy dimensions, is increasing. These two factors influence the maximum flow rate of the electrohydrodynamic pump. The maximum flow rate was found theoretically, and the optimum parameters of the electrohydrodynamic pump were established.