A lyotropic solution of hydroxypropylcellulose in m-cresol has been studied in a nonhomogeneous shear (plane Poiseuille) flow, and in a set of flows with mixed shear and extension (slit contractions). The average molecular orientation is measured using flow birefringence, while laser-Doppler velocimetry is used to characterize extensional kinematics in the slit-contraction flows. In slit flow, we observe very similar behavior to recently published observations in another model lyotropic, PEG in m-cresol [B. D. Bedford and W. R. Burghardt, J. Rheol. 38, 1657 (1994)]. Steady flow at low rates gives way to an instability characterized by large scale structural heterogeneities and time-dependent birefringence at higher rates. Throughout the entire flow rate range, however, average birefringence measured in slit flow may be quantitatively predicted from simple shear flow data, assuming that the locally averaged rheological and structural properties in the slit flow are equivalent to those occurring in simple shear flow at identical stress levels. In slit-contraction flows we have observed substantial enhancements in molecular orientation in the vicinity of the contraction, resulting from extensional velocity gradients. Orientation is studied in a variety of geometries in which contraction ratio and shape are varied to change the relative balance of shear and extension. We attribute the increased alignment to a transition from tumbling to flow-aligning dynamics due to the presence of extension in the contraction region.