Comparison of Different Discharge Calculation Equations for Large Canal Radial Gates

Abstract

【Objective】 The purpose of this paper is to compare different equations for calculating discharge through large canal radial gates. 【Method】 We took the Yanlinghe Radial Gate at the Middle Route of the South-to-North Water Diversion Project as an example, collecting 18 000 field-measured datasets and analyzing the characteristics of its orifice flow using seven equations available in the literatures. 【Result】 The Froude number at the vena contracta was in the range of 0.152~0.985, exceeding the limits that the NHRI empirical equation applies. The critical ratio of orifice flow to weir flow was near 0.991, rendering the WHUEE empirical equation inapplicable. The R2 of CAP equation, the dimensionless equation, and three other quadratic empirical equations were 0.989, 0.996, 0.809, 0.822 and 0.832, and their associated mean absolute errors were 2.25%, 2.65%, 4.11%, 4.08% and 3.98%, respectively. Under low-moderate submergence flow conditions (Xr≤0.9), the maximum absolute errors (|E|max) of all equations were less than 10%, When Xr exceeded 0.9, |E|max increased significantly, reaching 18% for the CAP equation, 25% for the dimensionless equation, and 36% for other three quadratic empirical equations. 【Conclusion】 The large radial gate we studied was out of the range that the NHRI empirical equation and the WHUEE empirical equation apply. For other five equations, their |E|max was less than 10% under low-moderate flow conditions, but increased when Xr exceeded 0.9. Overall, CAP and the dimensionless equation worked better among all seven equations we compared.

Keywords

• hydraulics
• large arch canal gate
• south-to-north water diversion project
• submerged orifice flow