This purge device comprises a connection element comprising a plurality of fluid flow channels which each comprise a proximal end, intended to be connected fluidically to a respective fluid flow conduit of a flow tube, and a distal end opposite the respective proximal end, and a plurality of fluid flow openings which are each connected fluidically to a respective fluid flow channel; a closure element comprising a fluid evacuation opening and a closure part, the closure element being mounted movably with respect to the connection element and being configured to occupy a plurality of closure positions, in each of which the closure part closes the distal end of a fluid flow channel and the fluid evacuation opening is connected fluidically to the fluid flow opening associated with the fluid flow channel, of which the distal end is closed by the closure part; and a connection nozzle intended to be connected to a catheter.