For high Reynolds number flows the total pressure remains constant along stream lines. At low Reynolds numbers the total pressure decreases in a global sense due to the actions of viscosity, but it may increase locally in regions such as stagnation points. Previous studies have considered the case of constant viscosity flow. However, gradients in the effective viscosity can occur normal to the wall for the flow of lubricating oils, and for turbulent flows calculated using an eddy viscosity model. In this paper the effect of these viscosity gradients on the stagnation point pressure are examined.