A rotary machine includes a stationary housing, a rotor, a shaft, a bearing unit, and a sealing arrangement to seal the bearing unit with respect to the rotor. The sealing arrangement includes a stationary sealing element surrounding the shaft. The sealing arrangement includes a rotor ring to prevent an axial flow along the shaft to the rotor and a cover plate, the rotor ring rotationally fixedly connected to the rotor and arranged axially adjacent to the sealing element, the rotor ring including a radially outer edge extending in the axial direction and surrounding the sealing element. The cover plate is fixed with respect to the housing and surrounding the rotor ring, and has an outer rim, a drain chamber formed between the outer edge of the rotor ring and the outer rim of the cover plate, and a discharge passage to discharge the drain chamber.