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Free over-fall in exponential channel cross-sections based on free vortex theory in supercritical flow regimes

机译：基于自由涡理论的超临界流态中指数通道截面的自由落体

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Free over-fall can be used as a flow metering hydraulic structure by a single measurement of an end depth. Many theoretical and experimental researches carried out on free over-fall with various approaches for different cross-sectional shapes. This paper presents a theoretical method to compute the end depth ratio (EDR) and the end depth discharge (EDD) relationships in steep sloping channel for the exponential cross-section. The exponential cross-section is a general section which can reduce to rectangular, wide rectangular, parabolic, semi-parabolic, triangular, and semi-triangular channels. Applying the momentum equation based on the free vortex theory, a theoretical approach is presented to obtain the EDR for the exponential channel cross-section in supercritical flow regime. Experimental and theoretical studies are then utilized to verify the proposed EDR and EDD relationships. The computed results are in acceptable agreement with the relevant experimental and theoretical studies. Direct solutions of the discharge for the known end depth for each cross-section are provided in tabular forms where two empirical discharge expressions with their relevant range of applications for each channel cross-section are detailed as the main outcome of this study. (C) 2016 Elsevier Ltd. All rights reserved.
机译：通过单次测量端部深度，可以将自由落下用作流量计量液压结构。许多关于自由落体的理论和实验研究都针对不同的横截面形状采用了各种方法。本文提出了一种理论方法来计算陡峭倾斜通道中指数剖面的端深比（EDR）和端深放电（EDD）关系。指数横截面是一般截面，可以缩小为矩形，宽矩形，抛物线形，半抛物线形，三角形和半三角形通道。应用基于自由涡理论的动量方程，提出了一种理论方法来获得超临界流态下指数通道截面的EDR。然后利用实验和理论研究来验证提议的EDR和EDD关系。计算结果与相关的实验和理论研究相吻合。以表格形式提供了每个横截面的已知端部深度的流量的直接解，其中详细列出了两个经验性的流量表达式以及每个通道横截面的相关应用范围，作为本研究的主要结果。 （C）2016 Elsevier Ltd.保留所有权利。

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