This paper aims to assess the influence of the momentum flux correction coefficient in the coupled 2D-1D simulations. The study presents analytical solutions for the momentum correction coefficient in both steady and unsteady time-periodic scenarios. In the case of steady flow, an analytically precise value is determined for incompressible flow in a 2D planar channel and 3D tube. Additionally, a simple 2D-1D coupled model is introduced to capture some essential features of oscillatory air flow. This model combines the flow of incompressible viscous fluid in a 2D rigid channel, solved using a simple finite-difference method and immersed boundary setting, with a simplified 1D FSI model considering channel with elastic walls. Using this coupled model, the influence of both time-dependent and constant values of the momentum flux correction coefficient in the unsteady time-periodic case are examined. The results indicate that this coefficient, has only minor importance in the considered case. These findings contribute to a better understanding of this coefficient role within 1D models applicable to respiratory system simulations.