Bernoulli Theorem, Minimum Specific Energy, and Water Wave Celerity in Open-Channel Flow |
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Authors: | Oscar Castro-Orgaz Hubert Chanson |
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Affiliation: | 1Research Engineer, Dept. of Agronomy, Univ. of Cordoba, c/Fernando Colón no1, 3 izq., E-14002 Cordoba, Spain. E-mail: oscar@tecagsl.com 2Professor in Hydraulic Engineering, School of Civil Engineering, Univ. of Queensland, Brisbane, Queensland 4072, Australia. E-mail: h.chanson@uq.edu.au
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Abstract: | One basic principle of fluid mechanics used to resolve practical problems in hydraulic engineering is the Bernoulli theorem along a streamline, deduced from the work-energy form of the Euler equation along a streamline. Some confusion exists about the applicability of the Bernoulli theorem and its generalization to open-channel hydraulics. In the present work, a detailed analysis of the Bernoulli theorem and its extension to flow in open channels are developed. The generalized depth-averaged Bernoulli theorem is proposed and it has been proved that the depth-averaged specific energy reaches a minimum in converging accelerating free surface flow over weirs and flumes. Further, in general, a channel control with minimum specific energy in curvilinear flow is not isolated from water waves, as customary state in open-channel hydraulics. |
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Keywords: | Open channel flow Critical flow Weirs Flumes Water waves |
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