A detailed understanding of the hydrodynamics of a tidal current turbine is paramount to the further development and adaptation of tidal current energy. Hydrodynamic modelling of such systems assists with reducing the cost of energy through accurate performance prediction enabling design refinement. Blade element momentum theory offers an efficient modelling technique to compute the hydrodynamic performance of a tidal current turbine. In this work, a corrected mathematical model, based on unsteady blade element momentum theory, for the application of tidal current turbines is presented. The mathematical model is compared with experimental data found in the literature, showing excellent agreement. Particular attention is given to the hydrodynamic performance of a tidal current turbine subjected to tidal current shear and yaw misalignment. The results of this study indicate that tidal current shear and yaw misalignment have a significant impact on the hydrodynamic performance of a tidal current turbine. Importantly, the hydrodynamic model presented can be used as an efficient design and optimisation tool for tidal current turbine blades. Moreover, the mathematical model presented can be combined with an economic model to assess the techno-economic performance of a tidal current turbine operating in actual site conditions.