Energy Dissipation in Gradually Expanding Channel by Free Overfall Flow through Weir

Abstract

This study intends to derive the theory of energy dissipation in gradually expanding channel and to investigate its characteristic parameters including the conjugate depth ratio, the relative energy loss, and the energy dissipation efficiency of hydraulic jump. The study has proved that the theoretical formula of the energy dissipation efficiency of hydraulic jump, which is affected by the change of height, width, and discharge of weir. The sensitive analysis shows the correlation between the hydraulic parameters. The analysis and comparison of gradually expanding channel with different forms of cross-section channels explore the hydraulic jump, the efficiency of energy dissipation, and the characteristics of hydraulic jump upon which a better design is proposed. The results showed the efficient of energy dissipation of the gradually expanding channel is better as compared with that of the prismatic channel. The experiments indicated of the relationship between the side-pressure correction factor and pre-jump and post-jump cross-sectional width ratio, a highly sensitively and positive correlation. Moreover, the theoretical analysis showed the average relation error of the energy dissipation efficiency of the hydraulic jump is 5.53 percent and this parameter is very beneficial to the design profession of weirs.

本研究推導堰壩投潭於漸擴形渠道之消能理論，探討其特性參數，包含共軛水深比ϕ、相對能量損失∆E/E_i及投潭水躍消能效率η。文中藉由定量清水流經投潭作用，藉由改變堰壩高度(H_d=40.5~52.5 cm)與堰壩寬度(b=18.2~8.8 cm），以及配合不同流量（Q=0.0036~0.0088 cms）進行堰壩投潭水渠槽試驗，利用理論解析以驗證投潭水對下游漸擴形渠床進行水流沖擊研究之能量消減，進一步以敏感度分析各項水力參數間相關性。藉著推理、分析及比較漸擴形渠道與不同斷面形式渠道，探究因受堰壩投潭作用而產生水躍現象、水躍特性、行為與消能功效等，可作為傳統式靜水池設計上另一進俾方案，並發展出漸擴形渠道之堰壩投潭水躍消能效率近似模式，提供堰壩下游估算或預測用。 研究結果發現，漸擴形渠道之堰壩投潭特性比定型渠道(prismatic channel)者有較佳的消能效果；經由渠槽試驗結果顯示側壓力修正係數C_p相對於水躍前後渠道寬度比μ，屬高敏感度且正相關性。另外與理論解析比較，漸擴形渠道之消能效率η平均相對誤差δ ¯為-5.53％，對於堰壩投潭水相關設計參數推估，可提供便利應用方法。