Apparatus and method for separating flowing immiscible fluid phases of different specific gravities includes an elongate conduit having an inlet for receiving incoming fluids, an outlet for discharging separated fluids, a first end and an open second end. The outlet is formed by the open second end. The inlet is longitudinally spaced away from the outlet on the elongate conduit. A flow assembly is provided for creating cyclonic flow of the fluid from the inlet through the outlet of the elongate conduit in order to centrifugally separate the fluids so that that the separated fluids flow concentrically through the outlet. The separator can include an outer tank surrounding the elongate conduit.