Experiments on Standard Spillway Flow (Including Appendix).

Hager, W.H.

doi:10.1680/iicep.1991.15622

Cited by 19 publications

(17 citation statements)

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“…The present study aims at filling this knowledge gap and providing a complete description of the discharge characteristics of trapezoidal-shaped weirs, including the salient features of the 2D weir flows. The results of previous investigations on flow over various weir shapes show that the weir geometry, especially the upstream and downstream weir face slopes, significantly affects the free-flow discharge coefficient (see, e.g., [23][24][25][26][27]). As is generally known, a variation in the downstream-face slope leads to a change in the degree of the streamline curvature over the weir crest and hence, a modification of the discharge coefficient.…”

Section: Introductionmentioning

confidence: 99%

Free Flow and Discharge Characteristics of Trapezoidal-Shaped Weirs

Zerihun¹

2020

Fluids

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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.

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Section: Introductionmentioning

confidence: 99%

Free Flow and Discharge Characteristics of Trapezoidal-Shaped Weirs

Zerihun¹

2020

Fluids

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“…In addition of USBR (1987) equation, there are other formula for the design of ogee profile. For example Hager (1991) presented the following equation for design of ogee profile in dam spillways. Equation ( 10) is valid for 0:498 , x=H d , 0:484.…”

Section: Ethical Approvalmentioning

confidence: 99%

Discharge coefficients for ogee spillways

Salmasi

Abraham

2022

Water Supply

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Discharge over an ogee weir is related to the length of weir, upstream total head above the weir crest and the discharge coefficient. The discharge coefficient is influenced by several factors; in this study, some parameters that influence discharge coefficients of ogee weirs are investigated. These factors include: the weir upstream slope, apron elevation, and downstream submergence. In this regard, ogee weir physical models were fabricated. These models comprise: an ogee weir with a vertical upstream face, ogee weirs with inclined upstream faces (18, 33, and 45 degrees), ogee weirs with downstream apron thicknesses of 3, 5, 7, and 10 cm in free flow and an ogee weir with a vertical upstream slope under submerged flow conditions. Results show that for all ogee weirs, the discharge coefficient (C) increases with increasing P/He, and then remains constant (P is the spillway height and He is the head above the weir crest). The value of the discharge coefficient decreases from 2.25 in free flow conditions to 2.15 with submerged flow conditions. For a constant head over the ogee weirs (He), the discharge coefficient decreases with increasing downstream apron elevation and submergence. The relative discharge coefficient shows a constant trend initially, with increasing hd/He, then later shows a decreasing tendency (hd is the difference between the downstream head and the ogee spillway crest). The threshold value for submergence ratio (hd/He), is 0.75 in the ogee weir in this study. With increasing submergence ratio from 0.75 to 1, the relative discharge coefficient (Cs/C0) decreases from 0.88 to 0.24.

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“…4a). It was successfully used at spillway crests [38][39][40]. It is illustrative to compare this iteration cycle with the germane step of the Picard iteration in Cartesian coordinates, whose irrotational flow condition is…”

Section: First Iteration Cyclementioning

confidence: 99%

Dressler’s theory for curved topography flows: iterative derivation, transcritical flow solutions and higher-order wave-type equations

Castro-Orgaz

Hager

2015

Environ Fluid Mech

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The Dressler equations are a system of two non-linear partial differential equations for shallow fluid flows over curved topography. The theory originated from an asymptotic stretching method formulating the equations of motion in terrain-fitted curvilinear coordinates. Apparently, these equations failed to produce a transcritical flow profile changing from sub-to supercritical flow conditions. Further, wave-like motions over a flat bottom are excluded because the bed-normal velocity component is not accounted for. However, the theory was found relevant for several environmental flow problems including density currents over mountains and valleys, seepage flow in hillslope hydrology, the development of antidunes, the formation of geological deposits from hyper-concentrated flows, and shallow-water flow modeling in hydraulics. In this work, Dressler's theory is developed in an alternative way by a systematic iteration of the stream and potential functions in terrain-fitted coordinates. The first iteration was found to be the former Dressler's theory, whereas a second iteration of the governing equations results in velocity components generalizing Dressler's theory to wave-like motion. Dressler's first-order theory produces a transcritical flow solution over topography only if the total head is fixed by a minimum value of the specific energy at the transition point. However, the theory deviates from measurements under subcritical flow conditions, given that the bed-normal velocity component is significant. A second iteration to the velocity field was used to produce a second-order differential equation that resembles the cnoidal-wave theory. It accurately produces flow over an obstacle including the critical point and the minimum specific energy as part of the numerical solution. The new cnoidal-wave model compares well with the theory of a Cosserat surface for directed fluid sheets, whereas the SaintVenant theory appears to be poor.

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Experiments on Standard Spillway Flow (Including Appendix).

Cited by 19 publications

References 0 publications

Free Flow and Discharge Characteristics of Trapezoidal-Shaped Weirs

Free Flow and Discharge Characteristics of Trapezoidal-Shaped Weirs

Discharge coefficients for ogee spillways

Dressler’s theory for curved topography flows: iterative derivation, transcritical flow solutions and higher-order wave-type equations

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