New Theoretical Solution of Stage-Discharge Relationship for Slit Weirs

Abstract

In this paper, the flow-process of a slit weir was analyzed on the basis of a theorem of dimensional analysis and incomplete self-similarity theory. The theoretically deduced stage-discharge formula then was calibrated using experimental data obtained for a ratio between the weir and the channel width, ranging from .5 to .25. The deduced stage-discharge relationship allowed measuring discharge values characterized by errors that, for 98% of the measured values, were less than or equal to ±5%. The performance of the proposed theoretical stage-discharge formula also was improved by introducing the Reynolds number (for 98.5% of the measured values the error was less than or equal to ±5%, and the error for 74% of the measured values was less than or equal to ±2%).