Refined Energy Correction for Calibration of Submerged Radial Gates

Abstract

The energy-momentum ͑E-M͒ method for calibrating submerged radial gates was refined using a large laboratory data set collected at the Bureau of Reclamation hydraulics laboratory in the 1970s. The original E-M method was accurate in free flow, and when the gate significantly controls submerged flow, but for large gate openings with low head loss through the gate, discharge prediction errors were sometimes large ͑approaching 70%͒. Several empirical factors were investigated with the laboratory data, including the combined upstream energy loss and velocity distribution factor and the submerged flow energy correction. The utility of the existing upstream energy loss and velocity distribution factor relation was extended to larger Reynolds numbers. The relation between the relative energy correction and the relative submergence of the vena contracta was shown to be sensitive to the relative jet thickness. A refined energy correction model was developed, which significantly improved the accuracy of submerged flow discharge predictions. Although the focus of this work was radial gates, the energy correction concept and these refinements potentially have application to all submerged sluice gates.

New equation for estimation of radial gate discharge

“…The developed equations were then compared with the methods of Buyalski (1983), Clemmens et al (2003), Wahl (2005) and Shahrokhnia and Javan (2006). Maximum error (ME), root mean square error (RMSE), modelling efficiency (EF), coefficient of residual mass (CRM) and mean absolute error (MAE) were used to compare the observed and simulated values.…”

“…This may be due to variation of geometric characteristics of the radial gate, in particular variation of P h , which was not considered in the methods of Shahrokhnia and Javan (2006) and Buyalski (1983). The methods proposed by Clemmens et al (2003) and Wahl (2005) show adequate accuracy, but application of these methods is very difficult. High EF values and low RMSE, CRM, ME and MAE values show that Equations 32 and 33 are capable of estimating flow discharge with sufficient accuracy and could be used for free flow radial gates.…”

“…Figure 5 shows a comparison of values computed from Equations 32 and 33 and field data for radial gates under free flow conditions. Table 7 and Figure 6 indicate that all the proposed equations are accurate for practical applications; however, the method of Buyalski (1983) is very difficult to use because it is based on several complicated equations and the methods proposed by Clemmens et al (2003) and Wahl (2005) are iterative. The method of Shahrokhnia and Javan (2006) 0 .…”

“…The other parameters in Equations 7 and 8 are defined for the free flow condition. Wahl (2005) where…”

“…The methods proposed by Clemmens et al (2003) and Wahl (2005) require iterative solutions, while the method of Buyalski (1983) is based on several equations. Other methods (e.g.…”