Abstract A side orifice is an important type of hydraulic structure which is used widely in irrigation and waste management systems to divert desired discharges from a main channel or to distribute the flow within the basins. Circular pipes flowing partially full are often used in these systems, but existing predictive relations developed for rectangular channels result in significant error. In the present study, the flow through a side orifice in a circular open-channel is numerically simulated and validated to test the effect of different parameters on the discharge coefficient and propose an appropriate predictive equation. To minimize the number of required simulations and validations, a Response Surface Method-Central Composite Design (RSM-CCD) is employed. Results showed that the discharge coefficient is inversely related to the Froude number (Fr) and the ratio of the side orifice length to the approaching flow water depth. However, any increase in either the ratio of the orifice length to the main channel diameter or the ratio of the lower crest level to the orifice length will increase the discharge coefficient. A new equation is presented to determine the discharge coefficient of side orifice in a circular open-channel using RSM-CCD. The sensitivity analysis showed that all linear terms must considered in the equation but that the interaction terms can be dropped. The maximum error of the equation to predict the training and validation data are 1% and 2% respectively.

中文翻译：

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响应面法对圆形明渠中自由流过侧孔板的数值模拟

摘要 侧孔口是一种重要的水工结构，广泛用于灌溉和废物管理系统，以从主渠道转移所需的排放或在盆地内分配流量。在这些系统中经常使用部分充满流动的圆形管道，但是为矩形通道开发的现有预测关系会导致显着错误。在本研究中，通过圆形明渠侧孔口的流量进行了数值模拟和验证，以测试不同参数对流量系数的影响并提出适当的预测方程。为了最大限度地减少所需的模拟和验证次数，采用了响应面方法-中心复合设计 (RSM-CCD)。结果表明，流量系数与弗劳德数(Fr)和侧孔口长度与接近水深的比值成反比。然而，任何增加的孔口长度与主通道直径的比率或下峰水平与孔口长度的比率都会增加流量系数。提出了利用RSM-CCD确定圆形明渠侧孔口流量系数的新方程。敏感性分析表明，方程中必须考虑所有线性项，但可以删除交互项。预测训练和验证数据的方程的最大误差分别为 1% 和 2%。任何增加的孔口长度与主通道直径的比值或降低波峰高度与孔口长度的比值都会增加流量系数。提出了利用RSM-CCD确定圆形明渠侧孔口流量系数的新方程。敏感性分析表明，方程中必须考虑所有线性项，但可以删除交互项。预测训练和验证数据的方程的最大误差分别为 1% 和 2%。任何增加的孔口长度与主通道直径的比值或降低波峰高度与孔口长度的比值都会增加流量系数。提出了利用RSM-CCD确定圆形明渠侧孔口流量系数的新方程。敏感性分析表明，方程中必须考虑所有线性项，但可以删除交互项。预测训练和验证数据的方程的最大误差分别为 1% 和 2%。敏感性分析表明，方程中必须考虑所有线性项，但可以删除交互项。预测训练和验证数据的方程的最大误差分别为 1% 和 2%。敏感性分析表明，方程中必须考虑所有线性项，但可以删除交互项。预测训练和验证数据的方程的最大误差分别为 1% 和 2%。