An affine transformation model is used to calculate the macroscopic stress tensor for uniaxial liquid crystals. In the special case of constant degrees of alignment, it is shown to be of the form occurring in the Ericksen-Leslie director theory for nematic liquid crystals, resolving an apparent discrepancy on the form of the stress tenser. The corresponding Leslie and Miesowicz viscosities are calculated in terms of the alignment order parameters ant those of the affine model. These results improve the approximate calculations of Ehrentraut and Hess [Phys. Rev. E 51, 2203 (1995)] based on a hindered rotation assumption. It is further shown that the calculated orientation-dependence of the viscosities based on the affine model is the same as that resulting from calculations based on an alternative Fokker-Planck equation for the one particle orientational distribution function.