In this work, axisymmetric, viscous, steady, incompressible and laminar flow through square-edged orifices has been studied. A numerical solution of the steady-state vorticity transport equation has been obtained from the two-dimensional Navier-Stokes equations. Finally, streamline patterns, vortex formations and separated flow regions have been predicted. The effects of orifice plate thickness and Reynolds number on the flow characteristics have been investigated numerically and experimentally. The Navier-Stokes equations have also been integrated in order to compute the pressure distributions through the orifice. From these results, the orifice discharge coefficient has been computed and examined as the Reynolds number and the orifice plate thickness were varied. A comparison has been made between the experimental results, the numerical predictions and available experimental results. The predicted flow discharge coefficient values agreed closely with the experimental results.