A rotary fluid handling device, such as a hydraulic pump, comprising a housing defining a cylindrical chamber, a shaft journalled in the housing and coaxial with the chamber, a cylindrical cam eccentrically mounted on said shaft within the chamber, a cylindrical sleeve rotatably surrounding said cam, the chamber space around said sleeve being divided into a plurality of similar compartments by radial blades or partition members slidable in slots of the housing and urged against the sleeve. Rotation of the cam produces cyclic decrease and increase of the volume of the compartments in succession to provide for the pumping effect in the case of a pump. Each compartment has its own inlet and outlet port. Each outlet port has a check valve. The inlet ports are arranged along a circle coaxial with the shaft. A valve member is keyed on the shaft and provides an inlet port closing surface extending through half a circle to therefore close half the inlet ports at the same time and to successively open the inlet ports with rotation of the shaft. The pump can be easily converted into a hydraulic motor. Means are provided to angularly shift the valve member for the inlet ports with respect to the top dead center position of the cam, in order to retard or advance the admission of fluid into the compartments, resulting in a variable flow pump or motor. A new centrifugal type governor system, in the form of a pump acting as a turbine, produces increase of the fluid pressure in a cylinder which acts on the piston to move the same axially of the shaft, to thereby produce angular shifting of the valve member with respect to the shaft. The hydraulic type governor system can be applied to other uses.