A mathematical model is introduced estimating the frictional pressure losses of Newtonian fluids flowing through a concentric annulus. A computer code is developed for the proposed model. Also, extensive experiments with water have been conducted at Middle East Technical University, Petroleum and Natural Gas Engineering Department Flow Loop and recorded pressure drop within the test section for various flow rates. The performance of the proposed model is compared with computational fluid dynamics (CFD) software simulated annulus flow section and various criteria such as crittendon, hydraulic diameter and slot flow approximation as well as experimental data. The results showed that the proposed model and experimental results are in good agreement for almost all cases when compared with the other criteria and CFD software. Also, the proposed model could estimate the frictional pressure losses for both laminar and turbulent flow regimes within an error range of +/- 10%.