A pressure-actuated shaft seal assembly and associated method for controlling the flow of fluid adjacent a rotatable shaft are provided. The seal assembly includes one or more seal members that can be adjusted between open and closed positions, for example, according to the rotational speed of the shaft. For example, the seal member can be configured to be adjusted according to a radial pressure differential in a fluid that varies with the rotational speed of the shaft. In addition, in the closed position, each seal member can contact a rotatable member connected to the shaft to form a seal with the rotatable member and prevent fluid from flowing through the assembly. Thus, the seal can be closed at low speeds of operation and opened at high speeds of operation, thereby reducing the heat and wear in the seal assembly while maintaining a sufficient seal during all speeds of operation
