A device for pressurizing a turbomachine downstream enclosure, the device being fed by means of a pressurizing air flow and including: a first shaft portion, a second shaft portion coupled to the first shaft portion via internal splines and external splines and extending, at a distance, inside the first shaft portion. The device includes at least a first passage made through the splines, and at least one orifice passing right through the second shaft portion, the orifice being arranged upstream of the first passage, in fluidic communication with the first passage, and opening out inside the second shaft portion so as to allow the pressurizing air flow to circulate from the first passage, between the first and second shaft portions, towards the downstream enclosure.