A semianalytical solution for a power-law fluid flowing through a conical annulus was derived to estimate the velocity profile in the axial direction, the shear rate and the elongation rate within a spinneret during the spinning of hollow fiber membranes. The angle coefficient was introduced as a new parameter to account for the effect of radial flow and to modify the governing equation, which initially neglected the effect of radial flow. The results estimated from this semianalytical solution agreed more closely with computational fluid dynamics simulation results than those obtained from the approximate analytical solution in our previous study. By accurately predicting the velocity profile in the axial direction and the shear and elongation rates in a conical annulus, the solution derived in this study is expected to provide a reliable criterion for spinneret design to achieve a specified membrane morphology with a desired performance. (c) 2015 American Institute of Chemical Engineers AIChE J, 61: 3489-3499, 2015