In this work a simplified model based on the Lubrication Theory and on the equivalent viscosity is presented to study the drilling fluid flow dynamics through an eccentric annular space with rotation of the drilling column. As a result of the non-Newtonian behavior of the fluid, the rotation of the column has a significant impact on the pressure drop since the viscosity of the fluids is a function of the strain rate applied. A complete analysis of this problem requires a tridimensional solution of the equation of momentum conservation, which makes the solution computationally expensive. For such, simplified accurate models that describe the main phenomena observed have to be developed. On the proposed model, the flow dynamics equations are simplified by the Lubrication Theory in cylindrical coordinates. Therefore, the tridimensional flow is described by one single two dimensional equation for the pressure field. The mechanical behaviour of the fluid is evaluated through the Equivalent Newtonian Viscosity method. The proposed model, as well as the accuracy of the simplifications used, was validated by comparison with numerical solutions of the complete set of equations available on the literature. The results show the range in which the proposed simplified model is accurate and presents the effects of the fluids properties, well geometry and column rotation on the pressure loss.