Dimensional analysis and stage-discharge relationship for weirs: a review

Bijankhan, M.; Ferro, Vito

doi:10.4081/jae.2017.575

Cited by 51 publications

(16 citation statements)

References 31 publications

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“…According to Ferro () and Bijankhan and Ferro (), for a sharp‐crested rectangular weir y c / P is a function of h / P . For a sharp‐crested power‐law weir, the exponent n is also an effective variable, thus:

\frac{y_{normalc}}{P} = G_{4} ((),, \frac{h}{P}, n)

where G 4 is a functional symbol.…”

Section: Deducing Stage–discharge Relationship Of Power‐law Weirmentioning

confidence: 99%

“…By determining this relation, and by substituting y c in terms of h into Equation (32), the general stage-discharge relationship for power-law weirs will be obtained. Dimensional analysis for deducing critical flow equation of Model II According to Ferro (2012) and Bijankhan and Ferro (2017), for a sharp-crested rectangular weir y c /P is a function of h/P. For a sharp-crested power-law weir, the exponent n is also an effective variable, thus:…”

Section: Critical Flow Theory (Model Ii)mentioning

confidence: 99%

“…The sharp‐crested rectangular weir under free‐flow conditions is well known for its simple structure and simple governing equation (Chaudhry, ; Herschy, ; Qu et al, ). Although there have been many experimental and analytical studies for normal sharp‐crested weirs of different shapes (Swamee, ; Bos, ; Balachandar et al, ; Johnson, ; Baddour, ; Vatankhah and Kouchakzadeh, ; Vatankhah, ; Vatankhah, ; Bautista‐Capetillo et al, ; Cox et al, ; Vatankhah and Khalili, ; Bijankhan and Ferro, ), there is no investigation available in the literature for the general sharp‐crested power‐law weir. With the development of computer numerical control (CNC) technologies, construction of weirs of any shape has become easier.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

General Stage–discharge Relationship for Sharp‐crested Power‐law Weirs: Analytical and Experimental Study

Vatankhah

Khamisabadi

2019

Irrigation and Drainage

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The efficient use of water for irrigation and agriculture projects depends mainly on measurement of water. Weirs are widely used in irrigation networks to measure flow discharge. Flow estimation through weirs of different shapes is very important in irrigation engineering. Weirs are characterized by a relation between the water head and discharge, which mainly depends on the shape and dimensions of the weir. A power‐law weir is very versatile and allows modelling of weirs with different shapes. The generic results of the power‐law weir can also be applied to its special forms such as triangular, semi‐cubic, parabolic, cubic and rectangular weirs. Up to now, the hydraulic behaviour of a general power‐law weir has not been studied. In this study, sharp‐crested power‐law weirs were studied experimentally and theoretically. For this, weir (Model I) and critical flow (Model II) theories along with Buckingham's theorem of dimensional analysis were used to deduce the stage–discharge relationship of power‐law weirs. A series of laboratory experiments (502 runs) were performed to calibrate the deduced theoretical stage–discharge relationships under free‐flow conditions. The proposed general stage–discharge relationships have an average error less than 1.7%; thus, actual discharge through the channel can be simply and reliably estimated. © 2019 John Wiley & Sons, Ltd.

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\frac{y_{normalc}}{P} = G_{4} ((),, \frac{h}{P}, n)

where G 4 is a functional symbol.…”

Section: Deducing Stage–discharge Relationship Of Power‐law Weirmentioning

confidence: 99%

Section: Critical Flow Theory (Model Ii)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

General Stage–discharge Relationship for Sharp‐crested Power‐law Weirs: Analytical and Experimental Study

Vatankhah

Khamisabadi

2019

Irrigation and Drainage

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“…For H/P≤4 the head-measurement section is located (2↔8)*Hmax upstream of the weir, where Hmax is the maximum upstream head. In this paper tilted thin-plate weir is being examined, referred to as inclined or pivot weir as well [3][4][5]. The inclination angle θ is measured in degrees from the bottom of the channel on the downstream side of the weir, while α=90-θ is measured from the vertical.…”

Section: Kindsvater-carter Rehbockmentioning

confidence: 99%

Nova Metoda Za Utvrđivanje Proticaja Na Nesuženom, Nagnutom, Oštroivičnom Prelivu

Hovanj¹

2019

Zbornik GFS

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The aim of this paper is to determine the possibility of measuring the discharge of a modular flow of water over a full-width, tilted thin-plate weir, referred to as inclined or pivot weir as well. The results of the previous analyses: deal only with ventilated discharge. Within the scope of the research of the possibility of measuring runoff hydrograph using thin-plate weir under modular flow, of the tested solutions, the one recommended for practical use is the full-width, tilted weir. Based on the measurements conducted at the Faculty of Civil Engineering in Subotica (Serbia), in this paper, the limits between ventilated and unventilated flows are specified, and proposals are made for the measurement of the entire range of discharge (ventilated and unventilated) of modular flow over a full-width, tilted thin-plate weir.

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“…Ferro and collaborators presented numerous papers in which the Buckingham theorem and dimensional analysis were repeatedly applied for a multitude of shapes of the crested weirs (labyrinth, parabolic, circular, radial, elliptical, W-weirs, etc. ), however not frequently used in practice; some of these were also summarized in a review paper [33].…”

Section: Introductionmentioning

confidence: 99%

Dimensionless Stage-Discharge Relationship for a Non-Linear Water Reservoir: Theory and Experiments

Baiamonte

2020

Hydrology

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In the field of hydrology, stage–discharge relationships are commonly used to estimate the discharge at the basin outlet or by experimental plots. Many experimental efforts have been made in order to derive stage–discharge relationships, according to the Buckingham theorem and dimensional analysis, for a multiplicity of gauge geometry. However, these relationships require experimental and physical meaningless numerical coefficients, thus they need extended calibration. The latter issue merits attention, since the empirical coefficients can be applied when the experimental conditions are strictly reproduced in the field. The aim of this paper is to derive a theoretically based stage–discharge relationship of a non-linear water reservoir that requires limited calibration, by using the continuity equation and the principle of conservation of energy. An analysis was performed using a rectangular water tank with a hole at the bottom. However, the suggested approach can be similarly used for tank geometries that differ from the example used in this study. Since the proposed approach is purely hydraulic, only limited calibration of the physical meaningful discharge coefficient characteristic of the hole is needed. A tank design procedure is suggested, and different theoretical and experimental applications of the proposed methodology are performed and discussed. For the considered cases, the mass water balance was also checked.

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Dimensional analysis and stage-discharge relationship for weirs: a review

Cited by 51 publications

References 31 publications

General Stage–discharge Relationship for Sharp‐crested Power‐law Weirs: Analytical and Experimental Study

General Stage–discharge Relationship for Sharp‐crested Power‐law Weirs: Analytical and Experimental Study

Nova Metoda Za Utvrđivanje Proticaja Na Nesuženom, Nagnutom, Oštroivičnom Prelivu

Dimensionless Stage-Discharge Relationship for a Non-Linear Water Reservoir: Theory and Experiments

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