paraphrase:

The relation between the Reynolds number and differential producer discharge coefficient was obtained through solutions to the steady, Reynolds-averaged Navier-Stokes equations. Discharge coefficients were also obtained experimentally for the purpose of validating the numerical results. The focus of the study was directed toward low Reynolds numbers commonly associated with pipeline transportation of viscous fluids, however high Reynolds number were also considered. The study indicates that, at low Reynolds numbers, the discharge coefficients decrease rapidly with decreasing Reynolds number for Venturi, V-cone, and wedge flow meters. The orifice plate meter did not follow the general trends of the other meters, but rather as the Reynolds number decreased, the discharge coefficient increased to a maximum before sharply dropping off with further decrease in the Reynolds number. The results presented herein provide an improved understanding of differential flow meters operating at low Reynolds numbers, and demonstrate the usefulness of computational fluid dynamics in predicting discharge coefficient trends at very low Reynolds numbers.