Numerical solutions were obtained for the field of velocity in angular forced flow through the annulus between two concentric cylinders of large and infinite aspect ratio with a gap-to-inner radius ratio of 0.05 using a finite-element representation and the FIDAP code. For an infinite aspect ratio, velocity vectors reveal a purely angular motion below a critical Dean number of 37.31 and a secondary motion in the form of pairs of counterrotating vortices above that value. The wavelength of these vortices and the friction factor ave correlated in terms of the Dean number. For large but finite aspect ratios a weak secondary motion around the periphery is found to occur below the critical Dean number, while for greater values the vortex at each end of the channel is greatly extended. The computed patterns of flow are in good agreement with prior experimental visualizations as well as with those carried out as part of this investigation, The computed characteristics are also in good agreement with prior theoretical results for limiting cases. The adaptation of the results for flow through an Archimedean spiral is described.