General Free-Flow Discharge Equation for Parshall Flumes

Author(s)

Ali R. Vatankhah, PhD

Abstract

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%.

Keywords

fluid mechanics hydraulics & hydrodynamics waterways & canals
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