![]() The performance of a head-type flow meter installation is a function of the precision of the flow element and of the accuracy of the d/p cell. The user can simply enter the application data and automatically find the recommended size, although these results should be checked for reasonableness by hand calculation. Some include data on the physical properties of many common fluids. ![]() These programs include the required data from graphs, charts, and tables as well as empirical equations for flow coefficients and correction factors. ![]() Today, many engineering societies and organizations and most primary element manufacturers offer software packages for sizing d/p flow elements. As shown in Figure 2, the transition between laminar and turbulent flows can cover a wide range of Reynolds numbers the relationship with the discharge coefficient is a function of the particular primary element. At high Reynolds numbers (well over Re = 3,000), the flow becomes fully turbulent, and the resulting mixing action produces a uniform axial velocity across the pipe. Where ID is the inside diameter of the pipe in inches, Q is the volumetric liquid flow in gallons/minute, SG is the fluid specific gravity at 60oF, and µ is the viscosity in centipoises.Īt low Reynolds numbers (generally under Re = 2,000), the flow is laminar, and the velocity profile is parabolic. The relationship between flow and pressure drop varies with the velocity profile, which can be laminar or turbulent (Figure 1) as a function of the Reynolds number (Re), which for liquid flows can be calculated using the relationship: In-place calibration is required if testing laboratories are not available or if better accuracy is desired than that provided by the uncertainty range noted above. By using such published discharge coefficients, it is possible to obtain reasonably accurate flow measurements without in-place calibration. ![]() The uncertainties of these published values vary from 0.5% to 3%. Published values represent, generally, the average value for that geometry over a minimum of 30 calibration runs. The discharge coefficients of primary elements are determined by laboratory tests that reproduce the geometry of the installation. These parameters can be computed from equations or read from graphs and tables available from the American National Standards Institute (ANSI), the American Petroleum Institute (API), the American Society of Mechanical Engineers (ASME), and the American Gas Association (AGA). The discharge coefficient k is influenced by the Reynolds number (refer to Figure 2) and by the “beta ratio”, the ratio between the bore diameter of the flow restriction and the inside diameter of the pipe.įigure 2: Effect of Reynolds Numbers on Various Flow MetersĪdditional parameters or correction factors can be used in the derivation of k, depending on the type of flow element used. K is the discharge coefficient of the element (which also reflects the units of measurement), A is the cross-sectional area of the pipe’s opening, and D is the density of the flowing fluid. The pressure differential (h) developed by the flow element is measured, and the velocity (V), the volumetric flow (Q), and the mass flow (W) can all be calculated using the following generalized formulas: Part of the pressure drop is recovered as the flow returns to the unrestricted pipe.įigure 1: Orifice Plate Pressure Drop Recovery Consequently, the line pressure drops at the point of constriction (Figure 1). As a fluid passes through a restriction, it accelerates, and the energy for this acceleration is obtained from the fluid’s static pressure. In the 18th century, Daniel Bernoulli, a Swiss mathematician and physicist, established “Bernoulli’s Equation” – which explains the relationship between static and kinetic energy in a flowing stream. ![]() Table 1: Orientation Table for Flow Sensors Primary Element Options Variations on the theme of differential pressure (d/p) flow measurement include: The pressure drops generated by a wide variety of geometrical restrictions have been well characterized over the years, and, as compared in Table 1, these primary or “head” flow elements come in a wide variety of configurations, each with specific application strengths and weaknesses. Using the Bernoulli Equation, which states that as the speed of the flow of a fluid increases its pressure decreases, these types of flow meters have no moving parts and measure the difference between a primary and secondary measurement – one on either side of the restriction. Differential pressure flow meters calculate fluid flow by reading pressure loss across a pipe restriction. ![]()
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