A spinneret assembly for spinning polymeric fibers, including: (a) a cap provided with an inlet port and a flared lower surface that flares outwardly from the inlet port in the direction of flow; (b) a spinneret having numerous spinning flow channels through its thickness; (c) a filter freely resting on the spinneret; and (d) a flow guide with a tapered geometry mounted in a cavity defined by the cap and the spinneret. The flow guide has an apex facing the inlet port, a base facing the filter, and one or more side surfaces tapering up to the apex. A diverging flow passage is defined by the tapering side surface(s) of the flow guide and the cap's flared lower surface. The base of the flow guide is spaced apart from an upper surface of the spinneret, creating a space that is in fluid communication with the divergent flow passage.