A rotary pump-flowmeter comprises a body including a cylindrical cavity and a rotor assembly including at least one flange disposed within the cylindrical cavity in a rotatable arrangement about an axis of rotation parallel to and offset from the central axis of the cylindrical cavity and a plurality of flaps having a round first edge and a crescent second edge disposed about the axis of rotation and supported by the flange, wherein each of the plurality of flaps is pivotable about an axis of pivot parallel to and offset from the axis of the rotation and coinciding with the center of the radius defining the round first edge of the flap. Each individual flap includes at least one cam roller anchored to one end face of the flap in a rotatable arrangement about an axis parallel to and offset from the axis of the pivot of the flap. A cam guide groove included in a rotary member rotatable about an axis parallel to and offset from the axis of rotation of the rotor assembly guides the orbiting motions of the cam rollers about the axis of rotation in such a way that a clearance of small tolerance is maintained between the extremities of the crescent edges of the flaps and the inner cylindrical surface of the cylindrical cavity, wherein the rotary member is rotated by the rotating motion of the rotor assembly positively or frictionally.