Performance of models to determine flow rate using orifice plates

Abstract

This study aimed to evaluate three methodologies for orifice-plate water-flow estimation by quantifying errors in the flow determinations to propose an appropriate measurement range for each evaluated condition. Two orifice-plate models (nominal diameters of 100 and 150 mm) with 50% restriction in the flow section were evaluated. In the theoretical equations, the discharge coefficient was obtained using the Reader-Harris/Gallagher equation (Method 1) and approximated from experimental data using the angular coefficient of a zero-intercept straight line (Method 2). The recommended measurement ranges for errors that were lower than 5% for the 100 and 150 mm plates were 30 to 65 m3 h-1 and 70 to 130 m3 h-1 using the theoretical equation and 20 to 65 m3 h-1 and 40 to 130 m3 h-1 using the empirical equation, respectively. The Reader-Harris/Gallagher equation (Method 1) adequately estimated the discharge coefficient of the orifice plates; however, the use of empirical equations (Method 3) demonstrated smaller measurement errors and greater rangeability of the evaluated flow meters.

Indicators for evaluation of model performance: irrigation hydraulics applications

“…The 1:1 graph showed that the methodology of ISO 5167-2 (2003) overestimates 47.5% of the data by 8.0 ± 0.2% and underestimates 52.5% of the data by 3.1 ± 0.1% in relation to the values observed experimentally (Figure 3a). Even more precisely, 95.2 and 73.0% of the predictions made by the equations of Cano et al (2021) andISO 5167-2 (2003), respectively, had a relative error of up to 5% (Figure 3b). Thus, this graph shows us how far those points outside the 1:1 line in Figure 3a can be accepted.…”

“…Datasets from three typical problems of irrigation hydraulics were used as case studies to assess the indicators. Methodologies and particularities from each case study are fully described in Pimenta et al (2018), Katsurayama et al (2020), andCano et al (2021). Pimenta et al (2018) used the Colebrook and White (1937) equation (Equation 1) to obtained reference values of the friction factor (f) for pressurized conduits and compared these reference values with values predicted by the equations of Swamee and Jain (1976 -Equation 2) and Shaikh, Massan, and Wagan (2015 -Equation 3) for turbulent flow conditions (4000 ≤ R e ≤ 10 8 ).…”

“…The last case evaluated was based on the study carried out by Cano et al (2021) in the modeling of corner taps' orifice plates to determine the flow rate in pipes. Based on experimental data, the authors adjusted an empirical equation for orifice plates with an internal diameter of 150 mm (Equation 6).…”

“…In this way, datasets of 480, 615, and 2,000 records from Pimenta et al (2018), Katsurayama et al (2020), and Cano et al (2021), respectively, were used to test the statistical indicators described above. Both indicators were calculated using an electronic spreadsheet following the equations of the respective indices.…”