Discussion of “Supercritical Flow Measurement Using a Large Parshall Flume” by Amanda L. Cox, Christopher I. Thornton, and Steven R. Abt

Abstract

The discusser would like to thank the authors for proposing a rating equation that is applicable to large Parshall flumes. The discusser, however, would like to add a few points. The authors have compared the resulting 1.5-m (5-ft) Parshall flume data to existing rating equations for predicting discharge in small Parshall flumes with subcritical and supercritical flow regimes. The original Parshall flume equation is modified to incorporate crest width, channel slope, channel roughness, and convergence in the prediction algorithm. Based on the proposed prediction models by the authors (Table 2 of the original paper), the mean absolute percent error for 1.5-m (5-ft) Parshall flume data is 3.1%, and for the small Parshall flumes are 4.4 and 4.8%, respectively, for subcritical and supercritical flow regimes. The authors consider channel slope and channel roughness to be independent variables in the proposed regression equations. As will be shown, channel slope and channel roughness can be eliminated from the proposed stage-discharge equations without any reduction of accuracy. The data reported in the original paper are shown in Table 1 and Fig. 1 of this discussion. In Fig. 1, W is the throat width of the Parshall flume, Wr is the width ratio (1⁄4 We=W, in which We is the entrance width of the Parshall flume); h is the dimensionless flow depth (1⁄4 ha=W, in which ha is the flow depth measured upstream from the crest/throat of the flume at a distance of twothirds of the converging section length); and Q 1⁄4 Fr is the dimensionless discharge or Froude number {1⁄4 Q=1⁄2WhaðghaÞ ,