A single-lumen, multi-stage cannula particularly adapted for venous drainage during cardiac surgery includes a first stage comprising a longitudinal tubular tip having a first plurality of fenestrations to provide an axial flow at a proximal end of the tip. A second stage coaxial with the first stage comprises a nozzle section having an outer lumen wall and an inner annular wall. A central passage disposed within the inner annular wall continues the axial flow from the first stage. A plurality of outer passages is disposed between the outer lumen wall and the inner annular wall so that the inner annular wall isolates the central passage from the outer passages. The outer lumen wall includes a plurality of second fenestrations, wherein each second fenestration supplies fluid from a second region outside the cannula to a respective outer passage. The outer passages have respective outlets arranged to provide an injected flow substantially parallel to the axial flow. At least an initial portion of the central lumen of a proximal tube has an inside diameter greater than a diameter of the central passage. The central lumen continues the axial flow and receives the injected flow annularly injected around and substantially parallel with the axial flow.