This paper provides the results of numerical calculations of pressure drops and centerline velocities for laminar fully-developed flows of non-Newtonian fluids in circular ducts. The particular non-Newtonian fluid model considered is the Cross model, which has shown the ability to model the behavior of time-independent purely-viscous fluids over a wide range of shear rates. It is shown that the Cross model is equivalent to the more recently proposed extended modified power law (EMPL) model, and an alternative formulation of the nondimensional parameters arising from the use of these models is explored. Results are presented for friction factors and nondimensional centerline velocities over a wide range of fluid and flow conditions, and it is shown that simpler constitutive models can be used in cases where the ratios of the limiting Newtonian viscosities are extreme. The implications of the results to the design and analysis of piping systems is considered, and simple and accurate correlations are provided for engineering calculations.