A sealing device for sealing a leakage flow on a machine element, which is circular in cross section, of a working machine includes a housing, which has an upstream end and a downstream end and through which the machine element extends, an upstream pressure chamber which is arranged at the upstream end of the housing, a downstream pressure chamber which is arranged at the downstream end of the housing, and a sealing element which is arranged between the upstream pressure chamber and the downstream pressure chamber. The sealing element is mounted within the housing and rests sealingly against the machine element. A bypass line runs around the sealing element and fluidly connects the upstream pressure chamber to the downstream pressure chamber. A throttle element designed to reduce the pressure of a flowing leakage fluid by a predetermined pressure difference is arranged in the bypass line.