The invention relates to a pressurized-air supply unit for an air-jet cooling device cooling an outer casing of a turbomachine turbine. This unit is notable in that it is monobloc, in that it comprises: —a body which has an interior wall provided with air-ejection perforations, an exterior wall and outlet ducts which are configured to be coupled to cooling lines of the cooling device, —an elbowed air-conveying pipe coupled by its outlet opening to said exterior wall of the body, and in that said unit comprises at least one air-distribution partition, arranged in the outlet opening and connecting the internal face of the portion of the air-conveying pipe that is situated facing the body to the internal face of the opposite portion of the air-conveying pipe.