Flow Characteristics and Energy Dissipation Over Single Step Broad – Crested Weirs

Abstract

The main purpose of traditional broad -crested weir is to rise and control upstream (U/S) water level. In this study a new performance was added to this weir, by making it as an energy dissipater. In order to study the energy dissipation percent (E%), the downstream (D/S) height of the weir (12 cms U/S height) was reduced four times as 9.8,8,6and3.8cms.Thirty experiments were performed in a laboratory horizontal channel of 12 m length, 0.5 m width and 0.45 m depth for a wide range of discharge. A mathematical model to compute theoretical coefficient of discharge (Cdth) was modified depending upon momentum equations. Experimental results gave a high validity to the computed values of the proposed model. On the other hand, three empirical non dimensional relations were obtained. The first is liner relation to estimate the ratio for D/S water head to U/S weir height (h/P1) in terms of the ratio for U/S water head to U/S weir height (H/P1). The second relation is nonlinear relation to estimate the discharge coefficient (Cd) in terms of H/P1 and the ratio of D/S weir height to U/S weir height (P2/P1). While the third relation is to estimate E% in terms of h/P1and P2/P1 with high correlation coefficients. The experimental results of the study showed that E% increased up to 46%. Furthermore, Cd was improved and gets higher values in comparison with traditional weirs. ‫ﺍﻟﻬﺩﺍﺭﺍﺕ‬ ‫ﻓﻭﻕ‬ ‫ﺍﻟﻁﺎﻗﺔ‬ ‫ﻭﺘﺒﺩﻴﺩ‬ ‫ﺍﻟﺠﺭﻴﺎﻥ‬ ‫ﺨﺼﺎﺌﺹ‬ ‫ﻤﻔﺭﺩﺓ‬ ‫ﺍﻟﺩﺭﺠﺔ‬ ‫ﺍﻟﻌﺭﻴﻀﺔ‬ ‫ﺍﻟﻘﻤﺔ‬ ‫ﺫﺍﺕ‬ ‫ﺍل‬ ‫ﺸﺭﻴﻑ‬ ‫ﺴﻠﻴﻤﺎﻥ‬ ‫ﺠﻌﻔﺭ‬ ‫ﺼﺎﻟﺢ‬ ‫ﺠﻤﻌﻪ‬ ‫ﻗﺎﺴﻡ‬ ‫ﻋﻠﻲ‬ ‫ﺇﻨﻌﺎﻡ‬ ‫ﺤﺴﻴﻥ‬ ‫ﺤﻤﻭﺩ‬ ‫ﺤﺎﻤﺩ‬ ‫ﺩﻜﺘﻭﺭ‬ ‫ﺍ‬ ‫ﺍﻟﺘﻘﻨﻴﺔ‬ ‫ﻟﻜﻠﻴﺔ‬ / ‫ﺍﻟﻤﻭﺼل‬ ‫ﺍﻟ‬ ‫ﻜﻠﻴﺔ‬ ‫ﻬﻨﺩﺴﺔ‬ / ‫ﺍﻟﻤﻭﺼل‬ ‫ﺠﺎﻤﻌﺔ‬ ‫ﺍﻟﺘﻘﻨﻴﺔ‬ ‫ﺍﻟﻜﻠﻴﺔ‬ / ‫ﺍﻟﻤﻭﺼل‬ ‫ﻤﻠﺨـــﺹ‬ ‫ﺭ‬ ‫ﺍ‬ ‫ﺩ‬ ‫ﻬ‬ ‫ﻟ‬ ‫ﺍ‬ ‫ﻡ‬ ‫ﺩ‬ ‫ﻘ‬ ‫ﻤ‬ ‫ﻲ‬ ‫ﻓ‬ ‫ﻪ‬ ‫ﻴ‬ ‫ﻠ‬ ‫ﻋ‬ ‫ﺓ‬ ‫ﺭ‬ ‫ﻁ‬ ‫ﻴ‬ ‫ﺴ‬ ‫ﻟ‬ ‫ﺍ‬ ‫ﻭ‬ ‫ﺀ‬ ‫ﺎ‬ ‫ﻤ‬ ‫ﻟ‬ ‫ﺍ‬ ‫ﻯ‬ ‫ﻭ‬ ‫ﺘ‬ ‫ﺴ‬ ‫ﻤ‬ ‫ﻊ‬ ‫ﻓ‬ ‫ﺭ‬ ‫ﻭ‬ ‫ﻫ‬ ‫ﻱ‬ ‫ﺩ‬ ‫ﻴ‬ ‫ﻠ‬ ‫ﻘ‬ ‫ﺘ‬ ‫ﻟ‬ ‫ﺍ‬ ‫ﺔ‬ ‫ﻀ‬ ‫ﻴ‬ ‫ﺭ‬ ‫ﻌ‬ ‫ﻟ‬ ‫ﺍ‬ ‫ﺔ‬ ‫ﻤ‬ ‫ﻘ‬ ‫ﻟ‬ ‫ﺍ‬ ‫ﻭ‬ ‫ﺫ‬ ‫ﺭ‬ ‫ﺍ‬ ‫ﺩ‬ ‫ﻬ‬ ‫ﻟ‬ ‫ﺍ‬ ‫ﻥ‬ ‫ﻤ‬ ‫ﻲ‬ ‫ﺴ‬ ‫ﻴ‬ ‫ﺌ‬ ‫ﺭ‬ ‫ﻟ‬ ‫ﺍ‬ ‫ﺽ‬ ‫ﺭ‬ ‫ﻐ‬ ‫ﻟ‬ ‫ﺍ‬ ‫ﻥ‬ ‫ﺇ‬ . ‫ﻫﺫﻩ‬ ‫ﻓﻲ‬ ‫ﺘﺒﺩ‬ ‫ﺨﻼل‬ ‫ﻤﻥ‬ ‫ﺍﻟﻬﺩﺍﺭ‬ ‫ﻟﻬﺫﺍ‬ ‫ﺠﺩﻴﺩ‬ ‫ﺃﺩﺍﺀ‬ ‫ﺃﻀﺎﻓﺔ‬ ‫ﺘﻡ‬ ‫ﺍﻟﺩﺭﺍﺴﺔ‬ ‫ﺀ‬ ‫ﺎ‬ ‫ﻤ‬ ‫ﻟ‬ ‫ﺍ‬ ‫ﻥ‬ ‫ﺎ‬ ‫ﻴ‬ ‫ﺭ‬ ‫ﺠ‬ ‫ﺔ‬ ‫ﻗ‬ ‫ﺎ‬ ‫ﻁ‬ ‫ﻟ‬ ‫ﻩ‬ ‫ﺩ‬ ‫ﻴ‬ . ‫ﻥ‬ ‫ﺎ‬ ‫ﻴ‬ ‫ﺭ‬ ‫ﺠ‬ ‫ﻟ‬ ‫ﺍ‬ ‫ﺔ‬ ‫ﻗ‬ ‫ﺎ‬ ‫ﻁ‬ ‫ﺩ‬ ‫ﻴ‬ ‫ﺩ‬ ‫ﺒ‬ ‫ﺘ‬ ‫ﺔ‬ ‫ﺒ‬ ‫ﺴ‬ ‫ﻨ‬ ‫ﺔ‬ ‫ﺴ‬ ‫ﺍ‬ ‫ﺭ‬ ‫ﺩ‬ ‫ﻟ‬ ‫ﻭ‬) E% (‫ﺘﺨﻔﻴﺽ‬ ‫ﺘﻡ‬ ‫ﺍﻟﻬﺩﺍﺭ‬ ‫ﺴﻁﺢ‬ ‫ﻤﺅﺨﺭ‬ ‫ﻤﻨﺴﻭﺏ‬) ‫ﺍﻟﻤﻘﺩﻡ‬ ‫ﻓﻲ‬ ‫ﺍﺭﺘﻔﺎﻋﻪ‬ ‫ﻭﺍﻟﺫﻱ‬ 12 ‫ﺴﻡ‬ (‫ﺏ‬ ‫ﻴ‬ ‫ﺴ‬ ‫ﺎ‬ ‫ﻨ‬ ‫ﻤ‬ ‫ﺒ‬ ‫ﻭ‬ ‫ﺕ‬ ‫ﺍ‬ ‫ﺭ‬ ‫ﻤ‬ ‫ﺔ‬ ‫ﻌ‬ ‫ﺒ‬ ‫ﺭ‬ ‫ﺃ‬ 3.8,6,8,9.8 ‫ﺴﻡ‬ . ‫ﻲ‬ ‫ﻓ‬ ‫ﺔ‬ ‫ﺒ‬ ‫ﺭ‬ ‫ﺠ‬ ‫ﺘ‬ ‫ﻥ‬ ‫ﻴ‬ ‫ﺜ‬ ‫ﻼ‬ ‫ﺜ‬ ‫ﺭ‬ ‫ﺎ‬ ‫ﺒ‬ ‫ﺘ‬ ‫ﺨ‬ ‫ﺍ‬ ‫ﻡ‬ ‫ﺘ‬ ‫ل‬ ‫ﻭ‬ ‫ﻁ‬ ‫ﺕ‬ ‫ﺍ‬ ‫ﺫ‬ ‫ﺔ‬ ‫ﻴ‬ ‫ﻘ‬ ‫ﻓ‬ ‫ﺍ‬ ‫ﺔ‬ ‫ﻴ‬ ‫ﺭ‬ ‫ﺒ‬ ‫ﺘ‬ ‫ﺨ‬ ‫ﻤ‬ ‫ﺓ‬ ‫ﺎ‬ ‫ﻨ‬ ‫ﻗ‬ 12 ‫ﺽ‬ ‫ﺭ‬ ‫ﻋ‬ ‫ﻭ‬ ‫ﻡ‬ 0.5 ‫ﻕ‬ ‫ﻤ‬ ‫ﻋ‬ ‫ﻭ‬ ‫ﻡ‬ 0.45 ‫ﺭ‬ ‫ﺎ‬ ‫ﺼ‬ ‫ﺘ‬ ‫ﻟ‬ ‫ﺍ‬ ‫ﻥ‬ ‫ﻤ‬ ‫ﻊ‬ ‫ﺴ‬ ‫ﺍ‬ ‫ﻭ‬ ‫ﻯ‬ ‫ﺩ‬ ‫ﻤ‬ ‫ﻟ‬ ‫ﻭ‬ ‫ﻡ‬ ‫ﻴﻑ‬ . ‫ﺏ‬ ‫ﺎ‬ ‫ﺴ‬ ‫ﺤ‬ ‫ﻟ‬ ‫ﺔ‬ ‫ﻴ‬ ‫ﻀ‬ ‫ﺎ‬ ‫ﻴ‬ ‫ﺭ‬ ‫ﺔ‬ ‫ﻗ‬ ‫ﻼ‬ ‫ﻋ‬ ‫ﻕ‬ ‫ﺎ‬ ‫ﻘ‬ ‫ﺘ‬ ‫ﺸ‬ ‫ﺍ‬ ‫ﻡ‬ ‫ﺘ‬ ‫ﻱ‬ ‫ﺭ‬ ‫ﻅ‬ ‫ﻨ‬ ‫ﻟ‬ ‫ﺍ‬ ‫ﻑ‬ ‫ﻴ‬ ‫ﺭ‬ ‫ﺼ‬ ‫ﺘ‬ ‫ﻟ‬ ‫ﺍ‬ ‫ل‬ ‫ﻤ‬ ‫ﺎ‬ ‫ﻌ‬ ‫ﻤ‬) Cdth (‫ﺔ‬ ‫ﻴ‬ ‫ﺭ‬ ‫ﺒ‬ ‫ﺘ‬ ‫ﺨ‬ ‫ﻤ‬ ‫ﻟ‬ ‫ﺍ‬ ‫ﺞ‬ ‫ﺌ‬ ‫ﺎ‬ ‫ﺘ‬ ‫ﻨ‬ ‫ﻟ‬ ‫ﺍ‬ ‫ﺕ‬ ‫ﻁ‬ ‫ﻋ‬ ‫ﺃ‬ ‫ﻭ‬ ، ‫ﺔ‬ ‫ﻗ‬ ‫ﺎ‬ ‫ﻁ‬ ‫ﻟ‬ ‫ﺍ‬ ‫ﻡ‬ ‫ﺨ‬ ‫ﺯ‬ ‫ﺕ‬ ‫ﻻ‬ ‫ﺩ‬ ‫ﺎ‬ ‫ﻌ‬ ‫ﻤ‬ ‫ﻰ‬ ‫ﻠ‬ ‫ﻋ‬ ‫ﺩ‬ ‫ﺎ‬ ‫ﻤ‬ ‫ﺘ‬ ‫ﻋ‬ ‫ﻻ‬ ‫ﺎ‬ ‫ﺒ‬ ‫ﺘ‬ ‫ﻴ‬ ‫ﺠ‬ ‫ﻕ‬ ‫ﺒ‬ ‫ﺎ‬ ‫ﻁ‬ ‫ﺩ‬ ‫ﺔ‬ ‫ﺒ‬ ‫ﻭ‬ ‫ﺴ‬ ‫ﺤ‬ ‫ﻤ‬ ‫ﻟ‬ ‫ﺍ‬ ‫ﻡ‬ ‫ﻴ‬ ‫ﻘ‬ ‫ﻟ‬ ‫ﺍ‬ ‫ﻊ‬ ‫ﻤ‬ ‫ﺍﻟﻤﻌﺎﺩﻟﺔ‬ ‫ﺒﻬﺫﻩ‬ . ‫ﻻﺒﻌﺩﻴﺔ‬ ‫ﻭﻀﻌﻴﺔ‬ ‫ﻋﻼﻗﺎﺕ‬ ‫ﺜﻼﺙ‬ ‫ﺃﺴﺘﻨﺒﺎﻁ‬ ‫ﺘﻡ‬ ‫ﺃﺨﺭ‬ ‫ﺠﺎﻨﺏ‬ ‫ﻤﻥ‬ . ‫ﻟﺤﺴﺎﺏ‬ ‫ﺨﻁﻴﺔ‬ ‫ﻋﻼﻗﺔ‬ ‫ﺍﻷﻭﻟﻰ‬) h/P1 (‫ﺔ‬ ‫ﻟ‬ ‫ﻻ‬ ‫ﺩ‬ ‫ﺒ‬) H/P1 .(‫ﺎ‬ ‫ﻤ‬ ‫ﺃ‬ ‫ﻟﺤﺴﺎﺏ‬ ‫ﺨﻁﻴﺔ‬ ‫ﻏﻴﺭ‬ ‫ﻓﻜﺎﻨﺕ‬ ‫ﺍﻟﺜﺎﻨﻴﺔ‬ ‫ﺍﻟﻌﻼﻗﺔ‬ Cd ‫ﻡ‬ ‫ﺩ‬ ‫ﻘ‬ ‫ﻤ‬ ‫ﻟ‬ ‫ﺍ‬ ‫ﻲ‬ ‫ﻓ‬ ‫ﺭ‬ ‫ﺍ‬ ‫ﺩ‬ ‫ﻬ‬ ‫ﻟ‬ ‫ﺍ‬ ‫ﻉ‬ ‫ﺎ‬ ‫ﻔ‬ ‫ﺘ‬ ‫ﺭ‬ ‫ﺍ‬ ‫ﻰ‬ ‫ﻟ‬ ‫ﺍ‬ ‫ﺭ‬ ‫ﺍ‬ ‫ﺩ‬ ‫ﻬ‬ ‫ﻟ‬ ‫ﺍ‬ ‫ﻡ‬ ‫ﺩ‬ ‫ﻘ‬ ‫ﻤ‬ ‫ﺀ‬ ‫ﺎ‬ ‫ﻤ‬ ‫ﻟ‬ ‫ﺍ‬ ‫ﻕ‬ ‫ﻤ‬ ‫ﻋ‬ ‫ﺔ‬ ‫ﺒ‬ ‫ﺴ‬ ‫ﻨ‬ ‫ﺔ‬ ‫ﻟ‬ ‫ﻻ‬ ‫ﺩ‬ ‫ﺒ‬) H/P1 (‫ﺔ‬ ‫ﺒ‬ ‫ﺴ‬ ‫ﻨ‬ ‫ﻭ‬ ‫ﺍﻟﻤﻘﺩﻡ‬ ‫ﻓﻲ‬ ‫ﺍﻟﻬﺩﺍﺭ‬ ‫ﺍﺭﺘﻔﺎﻉ‬ ‫ﺍﻟﻰ‬ ‫ﺍﻟﻬﺩﺍﺭ‬ ‫ﻤﺅﺨﺭ‬ ‫ﺍﺭﺘﻔﺎﻉ‬) P2/P1 .(‫ﻟﺤﺴﺎﺏ‬ ‫ﺃﻴﻀﺎ‬ ‫ﺨﻁﻴﻪ‬ ‫ﻏﻴﺭ‬ ‫ﺍﻟﺜﺎﻟﺜﺔ‬ ‫ﺍﻟﻌﻼﻗﺔ‬ ‫ﻜﺎﻨﺕ‬ ‫ﻭ‬ E% ‫ﻋﻤﻕ‬ ‫ﻨﺴﺒﺔ‬ ‫ﺒﺩﻻﻟﺔ‬ ‫ﺀ‬ ‫ﺎ‬ ‫ﻤ‬ ‫ﻟ‬ ‫ﺍ‬ ‫ﻡ‬ ‫ﺩ‬ ‫ﻘ‬ ‫ﻤ‬ ‫ﻟ‬ ‫ﺍ‬ ‫ﻲ‬ ‫ﻓ‬ ‫ﺭ‬ ‫ﺍ‬ ‫ﺩ‬ ‫ﻬ‬ ‫ﻟ‬ ‫ﺍ‬ ‫ﻉ‬ ‫ﺎ‬ ‫ﻔ‬ ‫ﺘ‬ ‫ﺭ‬ ‫ﺍ‬ ‫ﻰ‬ ‫ﻟ‬ ‫ﺍ‬ ‫ﺭ‬ ‫ﺍ‬ ‫ﺩ‬ ‫ﻬ‬ ‫ﻟ‬ ‫ﺍ‬ ‫ﺭ‬ ‫ﺨ‬ ‫ﺅ‬ ‫ﻤ‬) h/P1 (‫ﻡ‬ ‫ﺩ‬ ‫ﻘ‬ ‫ﻤ‬ ‫ﻟ‬ ‫ﺍ‬ ‫ﻲ‬ ‫ﻓ‬ ‫ﺭ‬ ‫ﺍ‬ ‫ﺩ‬ ‫ﻬ‬ ‫ﻟ‬ ‫ﺍ‬ ‫ﻉ‬ ‫ﺎ‬ ‫ﻔ‬ ‫ﺘ‬ ‫ﺭ‬ ‫ﺍ‬ ‫ﻰ‬ ‫ﻟ‬ ‫ﺍ‬ ‫ﺭ‬ ‫ﺍ‬ ‫ﺩ‬ ‫ﻬ‬ ‫ﻟ‬ ‫ﺍ‬ ‫ﺭ‬ ‫ﺨ‬ ‫ﺅ‬ ‫ﻤ‬ ‫ﻉ‬ ‫ﺎ‬ ‫ﻔ‬ ‫ﺘ‬ ‫ﺭ‬ ‫ﺍ‬ ‫ﺔ‬ ‫ﺒ‬ ‫ﺴ‬ ‫ﻨ‬ ‫ﻭ‬) P2/P1 (‫ﻋﺎﻟﻴﺔ‬ ‫ﺍﺭﺘﺒﺎﻁ‬ ‫ﻭﺒﻤﻌﺎﻤﻼﺕ‬ . ‫ﺒﺄﻥ‬ ‫ﺍﻟﺩﺭﺍﺴﺔ‬ ‫ﻟﻬﺫﻩ‬ ‫ﺍﻟﻤﺨﺘﺒﺭﻴﺔ‬ ‫ﺍﻟﻨﺘﺎﺌﺞ‬ ‫ﺃﻅﻬﺭﺕ‬ E% ‫ﺒﻨﺴﺒﺔ‬ ‫ﺃﺯﺩﺍﺩﺕ‬ 46 . % ‫ﻫﺫﺍ‬ ‫ﺃﺩﺍﺀ‬ ‫ﺘﺤﺴﻥ‬ ‫ﺫﻟﻙ‬ ‫ﺍﻟﻰ‬ ‫ﺒﺎﻻﻀﺎﻓﺔ‬ ‫ﺃﺯ‬ ‫ﺤﻴﺙ‬ ‫ﺍﻟﻬﺩﺍﺭﺍﺕ‬ ‫ﻤﻥ‬ ‫ﺍﻟﻨﻭﻉ‬ ‫ﺍﻟﺘﺼﺭﻴﻑ‬ ‫ﻤﻌﺎﻤل‬ ‫ﻗﻴﻡ‬ ‫ﺩﺍﺩﺕ‬ Cd ‫ﺍﻟﺘﻘﻠﻴﺩﻱ‬ ‫ﺍﻟﻌﺭﻴﻀﺔ‬ ‫ﺍﻟﻘﻤﺔ‬ ‫ﺫﻭ‬ ‫ﺍﻟﻬﺩﺍﺭ‬ ‫ﻤﻊ‬ ‫ﻤﻘﺎﺭﻨﺔ‬ . The following symbols are used in this research: B = channel width, Cd= weir discharge coefficient, E%= energy dissipation ratio, Fτ o = boundary shear force, see figure (1), g = acceleration due to gravity, H = U/S water head above the crest, h = D/s water head, L = length of the weir, L 2 = length of D/S step, P 1 = U/S weir height, P 2 = D/S weir height, q = discharge over the weir per unit width, Q = Flow discharge, R = radius of U/S corner of the weir, Rn = Reynolds number V 1 = velocity at sec.1, V 2 = velocity at sec.2, τ o = boundary shear stress, υ = kinematics viscosity of water. µ = dynamic viscosity,