Elbow flowmeters

Post-Oil Energy Technology After the Age of Fossil Fuels 

Elbow taps develop relatively low differential pressures. For this reason, they cannot be used for measurement of low-velocity streams. Typically, water flowing at an average velocity of 1.5 m/s (5 ft/s) through a short-radius elbow with a centerline radius equal to the pipe diameter develops about 2.5 kPa (10 in. H20) water differential pressure. This is approximately the minimum full-scale pressure drop that is needed for reliable measurement. If the elbow is installed with 25 diameter upstream and 10 diameter downstream straight pipe runs, the measurement error will be under 10% FS over a 3 1 range. 

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FIGURE 18.9 Differential pressure flowmeters (a) Venturi flowmeter, (b) orifice flowmeter, (c) nozzle flowmeter, (d) pipebend (elbow) flowmeter, (e) pitot static flowmeter. 

To avoid swirl, elbows should be well separated and have large radii of curvature. If this is not possible then the flowmeter should be sited at least 40 pipe diameters downstream of fittings causing asymmetric flow only and a minimum of 100 pipe diameters downstream when swirl is likely to occur0 S). There should also be at least 10 pipe diameters allowed downstream of the meter free of any obstruction or fitting. If the flow is laminar then these distances should be doubled. 

Meters that measure differential pressures over the flowmeter and such pressure changes that can be interpreted as flowrates. Such flowmeters with a large number of designs include orifices, venturi tubes, pitot tubes, elbow taps, etc. Fluids that result in changes of the cross-sectional area due to erosion, corrosion, or deposition of solids obviously change the calibrations. These meters tend to be relatively cheap but are often not very accurate. 

The flow of a fluid through an elbow resembles free vortex motion, the product of the local flow velocity, bend radius remains constant, and there is a well-defined pressure gradient along the radius of curvature of the elbow. One can relate these pressure gradients to the flowrate through the elbow, and the measurement of the pressure difference between the inside and the outside of the elbow can be used to determine the volumetric flow rate of a fluid through the elbow. The first use of elbow as flowmeter was reported by Jacobs and Sooy [15]. They found that the inner and outer pressure difference (Ah) was related to the average velocity as... 

Yamell and Nagler [17] reported the flow of water through elbows and observed that the average velocity varied with VAh. However, Lansford [18] observed that the velocity/head relationship varied between Equation 22 and 23. Addison reviewed all the published literature on the use of rectangular and circular cross section duct bends as flowmeter [19]. He modelled the flow around the bend as a free vortex and obtained the following relationship... 

He also noted that a minimum velocity of approximately 2 m/s was necessary for proper flow rate measurement. Spink [20], Murdock et al. [21], Kittredge [22], Hauptmann [23], Polentz [24] and Morrison et al. [25] have reviewed the use of elbow as flowmeter for single phase liquid. Most experimental data were obtained for steam or water. Hauptmann suggested that the elbow flow meter could be used for slurry, but no data concerning this application were presented in his work [23]. Brook [26] and Morrison et al. [25] used elbow as slurry flow meter. 

Finally, Rivkin et al. (1986) also used the capillary flow technique to measure the viscosity of aqueous boron solutions, at temperatures up to 623 K and at pressures up to 30 MPa. In this case they employed a platinum capillary of 500 nun length and 0.3 nun ID, placed in a liquid thermostat in which temperature was controlled with an uncertainty of 0.03 K. A prunp-flowmeter was used to measure the volume of the fluid flowing through the capillary tube at each given temperatme and pressure. The pressure drop across the capillary ends was measmed with a compensation-type differential mercmy pressure gauge with a movable elbow. The details of the experimental apparatus and measurement procedme are given in Rivkin et al. (1979). 

Elbow Axial Flow Transverse Momentum Flowmeter. If Eq. (8.18) is... 

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