This article aims to introducenumerical study of two different incompressible Newtonian fluid flows. The first type of flow is through the straight channel, while the second flow is enclosed within a square cavity and the fluid is moved by the upper plate at a specific velocity. Numerically, a Taylor-Galerkin\ pressure-correction finite element method (TGPCFEM) is chosen to address the relevant governing equations. The Naiver-Stoke partial differential equations are usually used to describe the activity of fluids. These equations consist of the continuity equation (conservation of mass) and the time-dependent conservation of momentum, which are preserved in Cartesian coordinates. In this study, the effect of Reynolds number (Re) variation is presented for both problems. Here, the influence of Re on the convergence rate and solution behavior is provided. Findings display that, there is a significant impact of Re upon the temporal convergence rates of velocity and pressure. As well, the rate of convergence increases as the values of Re are risen. For the cavity problem, one can infer that, as the Reynolds number rises, the size of the vortex is reduced.
