The effective viscosity of a polar fluid is a measure of the amount of traditional shear viscosity the polar fluid will appear to possess in a particular flow situation. Four classical flow configurations are considered here; Couette flow, plane Poiseuille flow, pipe flow, and flow between concentric rotating cylinders. The principal non-Newtonian characteristic of polar fluids in these flow configurations is an increased effective viscosity which is dependent upon the relative size and configuration of the flow situation. It is shown that the non-Newtonian characteristics of polar fluids are more pronounced, and thus probably more easily measured, in pipe flow than in any of the other flow configurations considered here.