A study on the derivation of a mean velocity formula from Chiu's velocity formula and bottom shear stress

Abstract

Abstract. This study proposed a new discharge estimation method using a mean velocity formula derived from Chiu's 2D velocity formula of probabilistic entropy concept and the river bed shear stress of channel. In particular, we could calculate the mean velocity, which is hardly measurable in flooding natural rivers, in consideration of several factors reflecting basic hydraulic characteristics such as river bed slope, wetted perimeter, width, and water level that are easily obtainable from rivers. In order to test the proposed method, we used highly reliable flow rate data measured in the field and published in SCI theses, estimated entropy M from the results of the mean velocity formula and, at the same time, calculated the maximum velocity. In particular, we obtained phi(M) expressing the overall equilibrium state of river through regression analysis between the maximum velocity and the mean velocity, and estimated the flow rate from the newly proposed mean velocity formula. The relation between estimated and measured discharge was analyzed through the discrepancy ratio, and the result showed that the estimate value was quite close to the measured data.

Estimating the Average River Cross‐Section Velocity by Observing Only One Surface Velocity Value and Calibrating the Entropic Parameter

“…Also, Φ ( M ) = 0.88 (Hii River data of Shinohara and Tsubaki (1959)) and Φ ( M ) = 0.91 (Leo‐River data of Leopold (1969)) were reported by Choo et al. (2011). The entropy parameter depends on both the suspended sediment rate and aspect ratio (flow width/flow depth).…”

“…The magnitudes of Φ(M) for the present study were in agreement with the data reported for small rivers for example, 0.66 < Φ(M) < 0.80 for natural channels in the United States (Chiu et al, 2000), 0.6 < Φ(M) < 0.68 for Tiber River in Italy (Moramarco et al, 2019), 0.63 < Φ(M) < 0.69 for Godavari and Ulhas Rivers in India (Vyas et al, 2021), and for large rivers for example, 0.4 < Φ(M) < 0.61 for Amazon River in Brazil (Bahmanpouri et al, 2022). Also, Φ(M) = 0.88 (Hii River data of Shinohara and Tsubaki (1959)) and Φ(M) = 0.91 (Leo-River data of Leopold (1969)) were reported by Choo et al (2011). The entropy parameter depends on both the suspended sediment rate and aspect ratio (flow width/flow depth).…”