Compared with conventional channels, experiments of microchannel often exhibit some controversial findings and sometimes even opposite trends, most notably the effects of the Reynolds number and the scaled channel height on the Poiseuille number. The experimental method has still been constrained by two key facts, firstly the current ability to machine microstructures and secondly the limitation of measurement of parameters related to the Poiseuille number. As a consequence, numerical method was adopted in this study in order to analyze a flow in two-dimensional rectangular microchannels using water as working fluid. Results are obtained by the solution of the steady laminar incompressible Navier-Stokes equations using control volume finite element method (CVFEM) without pressure correction. The computation was made for channel height ranging from 50μm to 4.58μm and Reynolds number varying from 0.4 to 1600. The effect of Reynolds number and channel heights on flow characteristics was investigated. The results showed that the Poiseuille numbers agree fairly well with the experimental measurements proving that there is no scale effect at small channel height. This scaling effect has been confirmed by two additional simulations being carried out at channel heights of 2.5μm and 0.5μm, respectively and the range of Reynolds number was extended from 0.01 up to 1600. This study confirm that the conventional analysis approach can be employed with confidence for predicting flow behavior in microchannels when coupled with carefully matched entrance and boundary conditions in the dimensional range considered here.