Free Flow and Discharge Characteristics of Trapezoidal-Shaped Weirs

Abstract

A number of studies have considered the effects of weir design variations on the free- and submerged-flow characteristics of trapezoidal broad-crested weirs. It appears that the hydraulics of short-crested weir flows have received little attention; thus, the current knowledge is incomplete. By systematically analyzing a large set of experimental data, the present study aims to fill in this knowledge gap and to provide a complete description of the discharge characteristics of trapezoidal-shaped weirs, including the salient features of two-dimensional weir flows. The analysis of the axial free-surface profiles for short-crested weir flows attested that the location of the nearest station for the correct measurement of the overflow depth under free-flow conditions is at η0 from the heel of the weir, where η0 is the upstream free-surface elevation. Additionally, an empirical equation for the free-flow discharge coefficient is proposed as being valid for a trapezoidal-shaped weir with varying upstream- and downstream-face slopes. The results of this investigation reveal that the streamline curvature and the slopes of the upstream and downstream weir faces significantly affect the streamwise flow patterns and, hence, the free-flow discharge.

On the Hydraulic Characteristics of Submerged Flow over Trapezoidal-Shaped Weirs

“…8). Compared to this, the bed-pressure profile of a short-crested weir under free-flow conditions has one absolute minimum pressure near the downstream edge of the weir crest due to the effects of the sharp curvature of the streamline (Zerihun 2020). The result of this analysis confirmed that the bed-pressure profiles exhibit self-similarity only over the upstream face of the weir (see Fig.…”

“…6a). In contrast, the free-flow discharge of a similar short-crested weir significantly increases as the slope of the downstream face increases (Zerihun 2020).…”

“…For a deeply submerged-flow situation, the weir flow becomes a hydrostatic free-surface flow with Ω(X) 1.0. In contrast to the above flow profile characteristics, the free overflow profiles of a trapezoidal short-crested weir show self-similarity throughout the sub-and super-critical flow regimes, as demonstrated by Zerihun (2020). For the flow region downstream from the axis of symmetry of the crest, the normalized free-surface profile is approximately represented by Ω(X) = 1.0 − 0.093 exp(−0.155X), X ≥ 1.5.…”

“…Its value decreases with increasing roughnesses of the weir surface and approach channel (Kindsvater 1964) and increases as the downstream-face slope flattens (Thomas 1966). The influence of the latter factor is the result of the highly dependent of the dynamic characteristics of the overflow on the slope of the downstream weir face (Zerihun 2020). It is apparent that a variation of the relative overflow head ζ (= H 0 /L, where H 0 is the upstream crest-referenced energy head of a modular flow, and L is the crest length in a streamwise direction) results in a change in the degree of the curvature of the overflow and thus a modification of the modular limit characteristics.…”

Discharge Coefficients of Standard Spillways at High Altitudes

“…The results show a good fit with the experimental data for ratios 𝐻𝐻 ⁄ between 0 and 5. Moreover, different studies have been carried out in the last five years regarding the analysis of discharge coefficients over particular spillway types, such as: the studies to increase the discharge coefficient in lateral triangular labyrinth weirs by implementing antivortices [36]; the effects of geometric parameters in trapezoidal-triangular labyrinth weirs [37]; the behavior in horizontal crested weirs under free-flow conditions [38]; the variation with respect to discharge coefficients in round-crested weirs [39]; the impact of upstream orientation angle on the discharge coefficient in wide-crested trapezoidal weirs [40]; or, the appropriate use of modeling approaches for the determination of discharge coefficients in lateral rectangular weirs [41] and predictive models [42]. Nevertheless, neither the past or the recent empirical investigation has been studied at high-altitudes, as Condorama.…”