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In response to there being an increased need for accurate flow measurements ofviscous fluids through various types of differential pressure flow meters, computersimulations were conducted as part of this research to more accurately define thecharacteristics of the discharge coefficient, (C) at small Reynolds numbers. Theheavyoil industry has found that with rising oil prices it has become more economicalforcompanies to pursue the extraction of extremely viscous oils, which results in smallReynolds numbers flowing through the pipe and consequently the meters (GOA, 2009).Accurate flow measurement is one of the greatest concerns among many industries,because uncertainties in product flows can cost companies considerable profits.Currently there is little known about the C values at small Reynolds (Re) numbers for themeters in this report (Miller, 1996), since calibrations for these meters are generallyperformed in a laboratory using cold water. Differential pressure meters are popular forthese applications because they are relatively inexpensive and produce reliableresults.Four different types of differential pressure flow meters were studied which

include: Venturi, standard concentric orifice plate, V-cone, and wedge flow metersshown in Fig. 1. The Venturi flow meter obtains a pressure differential by constrictingthe flow area and therefore increasing the velocity at the constriction, which creates alower pressure according to Bernoullis Theorem. The concentric orifice plate flowmeter reduces the pressure by forcing the fluid through a thin plated circular openingsmaller than the pipe diameter. The V-cone flow meter has a cone shaped obstruction inthe middle the pipe, which forces the flow around the outside of the cone creating a

2pressure differential. The wedge flow meter has a wedge shaped obstruction located inthe upper portion of the pipe, which reduces pressure on the downstream side ofthewedge. Fig. 1 shows sketches of the different types of meters investigated.The viscosity of a fluid is inversely proportional to the Reynolds number for aspecific flow, so increasing the viscosity of the fluid results in a smaller Reynoldsnumber for a viscous fluid. With an increased accuracy in numerical modeling over theyears, it is now plausible to use it for flow conditions where experimental procedures

may be inadequate. Viscous fluids with very small Reynolds numbers cannot accuratelybe tested in the laboratory with water because the pressure differences are toosmall toaccurately measure. Therefore, computer modeling simulations can be used tocharacterize the discharge coefficients over very small Reynolds numbers. All ofthecomputer model simulations were verified by comparing them to lab data or previousfindings where the discharge coefficients were well known. Once the numerical mo

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delswere verified they were taken to more viscous regions where experimental data withwater would have a high degree of uncertainty.