For rheometry and polymer processing applications, it is important to correlate fluid material properties with extrusion parameters like pressure buildup and revolutions per minute. Previous attempts to obtain such correlations have resorted to numerical techniques or approximate relationships. Here we show that upon a suitable rotation of coordinate axes, analysis of the metering zone in closed-discharge single-screw extrusion is simplified. Taking advantage of such simplification, we have derived an analytic, self-consistent relation between fluid properties and extrusion parameters, where the power-law model is used throughout the analysis.