Standard Parshall flumes are widely used as in-line flow measurement structures in open channels and irrigation projects. The calibration of flow measurement structures is an important issue in practical applications. At present, free-flow Parshall flumes have separate empirical discharge equations for each nominal flume size, ranging from 1 inch to 50 ft (0.0254–15.24 m). In this study, using dimensional analysis and 420 data points generated from the original rating equations of 21 standard Parshall flume sizes, different dimensionally homogeneous equations were developed to calculate discharge values in Parshall flumes. The results showed that the throat width, the contraction ratio and the Reynolds number are key parameters for deducing a generic discharge equation. A general calibration discharge equation was developed for free-flow conditions for any Parshall flume in the range of 21 standard sizes and a specified contraction ratio of 0.15–0.82 according to the original design criteria. The proposed equation also enables computation of the discharge of Parshall flumes with custom and intermediate sizes. Compared with the original values, the average error in the discharges estimated using the proposed unified discharge equation for all flume sizes was found to be 0.95%.

中文翻译：

---

Parshall 水槽的一般自由流动排放方程

标准 Parshall 水槽广泛用作明渠和灌溉项目中的在线流量测量结构。流量测量结构的校准是实际应用中的一个重要问题。目前，自由流动的 Parshall 水槽对于每个标称水槽尺寸都有单独的经验流量方程，范围从 1 英寸到 50 英尺（0.0254-15.24 m）。在这项研究中，使用维度分析和从 21 个标准 Parshall 水槽尺寸的原始评级方程生成的 420 个数据点，开发了不同的维度齐次方程来计算 Parshall 水槽中的流量值。结果表明，喉道宽度、收缩率和雷诺数是推导通用流量方程的关键参数。根据原始设计标准，为任何 Parshall 水槽的自由流动条件开发了一个通用校准排放方程，该水槽有 21 种标准尺寸和 0.15-0.82 的指定收缩率。所提出的方程还可以计算具有自定义和中间尺寸的 Parshall 水槽的排放量。与原始值相比，使用所提出的统一流量方程估算的所有水槽尺寸的流量平均误差为 0.95%。