Newtonian and non-Newtonian laminar fluid flow has been simulated using Computational Fluid Dynamics for a cylindrical vessel stirred by a helical screw agitator. Simulations have been performed for a vessel geometry with and without a draft tube. Simulated flow patterns in the vessel have been examined and compared with the experimental work of previous authors. The power number and the circulation number have been evaluated, and interpreted in a similar manner to other works. The P-O Re constant, A, has been determined to be 295 for the geometry with the draft tube and 150 for that without the draft tube. These results are in the same range as previously reported values. The Metzner and Otto constant, k, has been evaluated to be 16.23 which is in excellent agreement with experimental results reported in the literature.