Orifice plate flow meter still plays significant role in industrial process flow measurements and has many variations in shapes and dimensions. Each orifice type has different performances such as coefficient of discharge and permanent pressure loss. The value of the coefficient of discharge of the orifice is significantly affected by its geometry, ratio of diameter (β) and flow Reynolds number (Re). In this study, the flow characteristics in the orifices were studied numerically using Ansys Fluent 6.3.26 CFD software. A Gambit software is used to create geometry and meshing of the flow domain for 3D models of the orifices. Two different types of orifice are studied: square edge and quadrant edge orifices with diameter ratios (β) of 0.5 and 0.7. The study was performed at Re = 5 × 103 and 5 × 104 using the standard k-epsilon turbulent model. The main parameters to be evaluated in this study include the orifice discharge coefficient (Cd) and permanent pressure loss. The results of the study indicate that the quadrant edge orifice has better performance than the square edge orifice. At given values of Re and β, Cd of the quadrant edge orifice remains constant at approximately of 0.746 for β = 0.5 and of 0.765 for β = 0.7. Next, the square edge orifice shows decreasing in Cd between 0.644 and 0.628 for β = 0.5, and between 0.693 and 0.646 for β = 0.7 as Re increases. Quadrant edge orifice has a lower permanent pressure loss of approximately 3.25% than that for square edge orifice.