A seal assembly for a rotary machine, such as a turbine engine, may include one or more seal segments that respectively include a seal housing defining a seal chamber and one or more fluid supply apertures that pass through the seal housing, and a seal body defining a seal face and one or more fluid conduits that pass through the seal body to the seal face. The seal chamber may receive at least a portion of the seal body, and the seal body may move within the seal chamber along a radial axis of a rotor of the rotary engine. The fluid supply apertures may fluidly communicate with the fluid conduits, and the fluid conduits may fluidly communicate with a fluid-bearing gap defined between the seal face and a rotor face of the rotor.