<p>Intricate flow dynamics under blockage effects, such as narrow and shallow channels, considerably influence the efficacy of hydrokinetic turbines. Mathematical models have been developed to capture these effects; however, most existing approaches primarily emphasize the correction of experimental data for blockage, rather than the prediction and optimization of turbine performance under such constrained flow conditions. This study addresses this gap by formulating novel mathematical models specifically tailored for horizontal-axis turbines operating in blockage environments. The models expand upon the momentum framework initially developed by Jamieson (2008), modifying it for situations when blockage significantly affects flow. The initial phase utilizes a modified inviscid thrust-based momentum model, enhanced with empirically obtained boundary constraints to more accurately represent realistic flow under blockage conditions. In the subsequent stage, this formulation is assimilated into the Blade Element Momentum (BEM) framework, facilitating the integration of rotor-specific aerodynamic characteristics. Validation is performed using published datasets and the authors’ CFD simulations, proving precision and reliability across various blockage conditions. The resultant framework offers a predictive instrument for turbine design, performance estimation, and blade optimization under blockage flow circumstances. The models provide a computationally efficient alternative to comprehensive CFD simulations or expensive experimental testing, improving predictive capability for hydrokinetic turbine applications.</p>