Flow visualization experiments have been used to characterize the fluid dynamics of a thermotropic liquid crystalline polymer, Vectra A, in the barrel and conical entry of a capillary rheometer. The displacement profiles indicate shear-thinning in the straight section, with a power law index much lower than that measured rheometrically. The contraction flow is complex and three-dimensional. There are asymmetrical vortices and signs of macroscopic structural changes. For flow in a corner, the profiles display patterns that cannot be predicted by the shear-thinning effects alone. These characteristics are in striking contrast to the results on lyotropic solutions in thin slit geometries (see J.N. Baleo and P. Navard, J. Rheol., 38 (1994) 1641-1655, and B.D. Bedford and W.R. Burghardt, J. Rheol., 38 (1994) 1657-1679).