The relationship between the Reynolds number (Re) and discharge coefficients (C) was investigated through differential pressure flow meters. The focus of the study was directed toward very small Reynolds numbers commonly associated with pipeline transportation of viscous fluids. There is currently a relatively small amount of research that has been performed in this area for the Venturi, standard orifice plate, V-cone, and wedge flow meters. The Computational Fluid Dynamics (CFD) program FLUENT© was used to perform the research, while GAMBIT© was used as the preprocessing tool for the flow meter models created. Heavy oil and water were used separately as the two flowing fluids to obtain a wide range of Reynolds numbers with high precision. Multiple models were used with varying characteristics, such as pipe size and meter geometry, to obtain a better understanding of the C vs. Re relationship. All of the simulated numerical models were compared to physical data to determine the accuracy of the models. The study indicates that the various discharge coefficients decrease rapidly as the Reynolds number approaches 1 for each of the flow meters; however, the Reynolds number range in which the discharge coefficients were constant varied with meter design. The standard orifice plate does not follow the general trend in the discharge coefficient curve that the other flow meters do; instead as the Re decreases, the C value increases to a maximum before sharply dropping off. Several graphs demonstrating the varying relationships and outcomes are presented. The primary focus of this research was to obtain further understanding of discharge coefficient performance versus Reynolds number for differential producing flow meters at very small Reynolds numbers.