Abstract In this study, the flow through a simple low-cost flume constructed using two semi-cylinder contractions on either side of a rectangular channel was experimentally investigated. In practice, these flumes may operate under free- or submerged-flow conditions depending on the downstream flow depth. To reliably estimate the flume discharge, free- and submerged-flow conditions should be accurately distinguished. At present, there is no equation to estimate the submergence threshold. This study investigates the possibilities of using these flumes under submerged-flow conditions. The discharge of the submerged flume may be calculated on the basis of the free-flow discharge equation. Thus, two new free-flow discharge equations were deduced: a general equation by considering the contraction ratio with an average error of 2.25%, and another one by neglecting it with an average error of 4.88%. Compared with the existing discharge equations, the proposed free-flow equations are the best ones. Under submerged-flow conditions, the submergence ratio affects the flow discharge. Using the measurements carried out in this study, the submergence threshold ratio and submerged-flow discharge were formulated and calibrated with the average errors of 2.96% and 3.80%, respectively. The equation to distinguish the free- and submerged-flow conditions was also deduced by equating the submerged- and free-flow discharge equations yielding a novel real solution.

中文翻译：

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具有两个半圆柱收缩（自由流和淹没流）的水槽的实验建模

摘要 在这项研究中，通过在矩形通道两侧使用两个半圆柱收缩构造的简单低成本水槽的流动进行了实验研究。在实践中，这些水槽可以在自由流动或潜流条件下运行，具体取决于下游流动深度。为了可靠地估计水槽流量，应准确地区分自由流动和浸没流动条件。目前，还没有公式来估计淹没阈值。本研究调查了在潜流条件下使用这些水槽的可能性。淹没水槽的流量可以根据自由流动的流量方程计算。因此，推导出了两个新的自由流排放方程：考虑收缩率的一般方程，平均误差为 2.25%，另一个忽略它，平均误差为 4.88%。与现有的流量方程相比，所提出的自由流动方程是最好的。在淹没流条件下，淹没比影响流量。使用本研究中进行的测量，淹没阈值比和淹没流排放被制定和校准，平均误差分别为 2.96% 和 3.80%。区分自由流动和淹没流动条件的方程也可以通过使淹没和自由流动的排放方程相等来推导出一个新的实数解。使用本研究中进行的测量，淹没阈值比和淹没流排放被制定和校准，平均误差分别为 2.96% 和 3.80%。区分自由流动和浸没流动条件的方程也通过使淹没和自由流动的排放方程相等来推导出一个新的实数解。使用本研究中进行的测量，淹没阈值比和淹没流排放被制定和校准，平均误差分别为 2.96% 和 3.80%。区分自由流动和浸没流动条件的方程也通过使淹没和自由流动的排放方程相等来推导出一个新的实数解。