Orifice flowmeters are widely used in industries to measure the flowrate in pipelines. The flowrate inside the pipe can be calculated using the relationship between the flow velocity and the pressure drop across the orifice plate. In the present study, numerical simulations have been carried out using three-dimensional Reynolds-averaged Navier–Stokes (RANS) equations combined with the k–ω shear-stress transport (SST) turbulence model to thoroughly investigate the turbulent flow through a circular square-edged orifice with various orifice plate thicknesses and orifice diameters inside a pipe at different Reynolds numbers ranging from 2500 to 40,000. The orifice thickness to pipe diameter ratio (t) varies between 0.125 and 2, and the orifice diameter to pipe diameter (β) varies between 0.25 and 0.75. The resulting centerline profiles of the streamwise velocity and pressure of the present study are compared with the previous published numerical results and experimental data as the validation study. The effects of Reynolds numbers and orifice geometries on the pressure, the flow velocity, and vorticity distribution in the orifice are discussed in detail. It is found that for the fixed β, the discharge coefficient increases with the increasing t, and the vortical structure inside the orifice is separated into two regions located at the two edges of the orifice. For the fixed t, the size of the large recirculation motions behind the plate increases, and the vorticity around the plate becomes stronger with the decreasing β.