A high pressure centrifugal pump has an impeller assembly including two mating impeller sections which are each constituted by a shroud with fixed geometry blades. The impeller sections are fixedly mounted upon a rotatable shaft and are of a construction which permits the pressure between the impeller sections to engender flexure of the sections away from each other so as to vary the breadth of the impeller assembly. A servo control device is adapted to control the pressure behind the shrouds such that the pump delivers a constant flow at varying back pressures.