Accurate determination of hydraulic parameters such as pressure losses, equivalent circulation density (ECD), etc. plays profound roles in drilling, cementing and other well operations. Hydraulics characterization requires that all factors are considered as the neglect of any could become potential sources of errors that would be detrimental to the overall well operation. Drilling Hydraulics has been extensively treated in the literature. However, these works almost entirely rely on the assumption that the drill string lies perfectly at the center of the annulus-the so-called "concentric annulus". In reality, concentricity is almost never achieved even when centralizers are used. This is because of high well inclination angles and different string geometries. Thus, eccentricity exists in practical oil and gas wells especially horizontal and extended reach wells (ERWs) and must be accounted for. The prevalence of drillstring (DS) eccentricity in the annulus calls for a re-evaluation of existing hydraulic models. This study evaluates the effect of drilling fluid rheology types and DS eccentricity on the entire drilling hydraulics. Three non-Newtonian fluid models were analyzed, viz: Herschel Bulkley, power law and Bingham plastic models. From the results, it was observed that while power law and Bingham plastic models gave the upper and lower hydraulic values, Herschel Bulkley fluid model gave annular pressure loss (APL) and ECD values that fall between the upper and lower values and provide a better fit to the hydraulic data than power law and Bingham plastic fluids. Furthermore, analysis of annular eccentricity reveals that APLs and ECD decrease with an increase in DS eccentricity. Pressure loss reduction of more than 50% was predicted for the fully eccentric case for Herschel Bulkley fluids. Thus, DS eccentricity must be fully considered during well planning and hydraulics designs.