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Discharge Coefficient Calibrations of Normal and Oblique Circular-Crested Weirs Under Incremental Flow Conditions

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Abstract

Circular-crested weirs have gained recognition for their high discharge coefficients in recent times. This study focuses on the experimental investigation of circular-crested weirs, specifically normal (ε = 0°) and oblique (ε = 30°) weirs, in a rectangular flume. The experiments were conducted under nine different flow conditions with progressively increasing discharge. Two distinct approaches were proposed to calculate the discharge coefficients for normal and oblique weirs during the gradual increase of flow discharge. In the flume, a flow with varying discharge rates was generated, and multiple discharge coefficients were considered at regular intervals. The first approach aimed to determine the instantaneous discharge coefficient of circular-crested weirs, while the second approach calculated the calibrated discharge coefficient for each flow condition. A comparative analysis of the findings from both approaches, conducted for each weir and flow condition, revealed that the average discharge coefficients obtained using the instantaneous method closely aligned with those derived from the calibrated method. Importantly, the discharge coefficients were determined without assuming dCd/dt = 0, thereby reducing inaccuracies compared to previous studies. The results indicated that increasing the weir angle in the channel, at a constant upstream flow depth, led to higher flow rates. Furthermore, this experimental study involved the calibration of the discharge coefficient for a 30º oblique crested weir, yielding a range of values between 0.52 and 1.07. Similarly, the discharge coefficient was calibrated for a normal crested weir, resulting in values ranging from 0.57 to 1.09.

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Abbreviations

b :

Weir width (m)

g :

Gravity acceleration (m2/s)

H :

Height over the weir (m)

h :

Upstream water height (m)

P :

Weir height (m)

R :

Weir radius (m)

L :

Weir length (m)

Q :

Flow discharge (m3/s)

C d :

Discharge coefficient of oblique weir

C D :

Discharge coefficient of normal weir

Ɛ:

Weir angle in the channel (o)

α :

The angle of the upstream side of the weir with respect to the vertical direction (o)

β :

The angle of the downstream side of the weir with respect to the vertical direction (o)

References

  • Abhash A, Pandey KK (2021) Numerical study of discharge-head relationship of piano key weirs for low heads. Water Resour 48(2):235–244

    Google Scholar 

  • Aichel OG (1953) Discharge ratio for oblique weirs. Z Ver Dtsch Ing 95(1):26–27 ([in German])

    Google Scholar 

  • Al-Naely H, Al-Khafaji Z, Khassaf S (2018) Effect of opening holes on the hydraulic performance for crump weir. Int J Eng 31(12):2022–2027

    Google Scholar 

  • Aydin I, Altan-Sakarya A, Sisman C (2011) Discharge formula for rectangular sharp-crested weirs. Flow Meas Instrum 22(2):144–151

    Google Scholar 

  • Bagheri S, Heidarpour M (2010) Overflow characteristics of circular-crested weirs. J Hydraul Res 48(4):515–520

    Google Scholar 

  • Baiamonte G (2021) Complex rating curves for sharp crested orifices and rectangular or triangular weirs under unsteady flow conditions. J Hydrol Eng 26(4):04021005

    Google Scholar 

  • Bautista-Capetillo C, Robles O, Júnez-Ferreira H, Playán E (2014) Discharge coefficient analysis for triangular sharp-crested weirs using low-speed photographic technique. J Irrig Drain Eng 140(3):06013005

    Google Scholar 

  • Bazaz A (2008) Discharge coefficient of weirs in unsteady flow. M. Sc. thesis. Graduate School of the University of Tehran

  • Bijankhan M, Di Stefano C, Ferro V (2018) Generalised stage–discharge relationship for rectangular weirs. Proc Inst Civ Eng Water Manag 171(3):125–133

    Google Scholar 

  • Borghei SM, Vatannia Z, Ghodsian M, Jalili MR (2003) Oblique rectangular sharp-crested weir. Proc Inst Civ Eng Water Maritime Eng 156(2):185–191

    Google Scholar 

  • Bortoni EC, Rocha MS, Rodrigues MA, Laurindo BC (2017) Calibration of weirs using unsteady flow. Flow Meas Instrum 57:73–77

    Google Scholar 

  • Brakeni A, Filippov E, Meridja M (2019) Flow through Crump Weir. Larhyss J 2521–9782(38):93–102

    Google Scholar 

  • Chanson H, Wang H (2013) Unsteady discharge calibration of a large V-notch weir. Flow Meas Instrum 29:19–24

    Google Scholar 

  • Chanson H, Aoki S, Maruyama M (2002) Unsteady two-dimensional orifice flow: a large-size experimental investigation. J Hydraul Res 40(1):63–71

    Google Scholar 

  • Crookston BM, Tullis B (2010)‏ Labyrinth weirs. Hydraul Struct 59

  • Darvas LA (1971) Discussion of ‘Performance and design of labyrinth weirs.’ J Hydraul Div 97(8):1246–1251

    Google Scholar 

  • DeCoursey DG, Blanchard BJ (1970) Flow analysis of large triangular weir. J Hydraul Div 96(7):1435–1454

    Google Scholar 

  • Dias F, Keller JB, Vanden-Broeck JM (1988) Flows over rectangular weirs. Phys Fluids 31(8):2071–2076

    Google Scholar 

  • Ferro V (2006) La sistemazione dei bacini idrografici-seconda edizione. MILANO, McGraw-Hill 1:1–848

    Google Scholar 

  • Ghaderi A, Daneshfaraz R, Abbasi S, Abraham J (2020) Numerical analysis of the hydraulic characteristics of modified labyrinth weirs. Int J Energy Water Resourc 4(4):425–436

    Google Scholar 

  • Ghasemzadeh F, Kouchakzadeh S, Belaud G (2020) Unsteady stage-discharge relationships for sharp-crested weirs. J Irrig Drain Eng 146(6):04020009

    Google Scholar 

  • Hager WH (1985) Critical flow condition in open channel hydraulics. Acta Mech 54(3):157–179

    Google Scholar 

  • Haghiabi AH (2012) Hydraulic characteristics of circular-crested weir based on dressler theory. Biosys Eng 112(4):328–334

    Google Scholar 

  • Haghiabi AH, Mohammadzadeh-Habili J, Parsaie A (2018) Development of an evaluation method for velocity distribution over cylindrical weirs using doublet concept. Flow Meas Instrum 61:79–83

    Google Scholar 

  • Haun S, Olsen NRB, Feurich R (2011) Numerical modeling of flow over trapezoidal broad-crested weir. Eng Appl Comput Fluid Mech 5(3):397–405

    Google Scholar 

  • Hay N, Taylor G (1970) Performance and design of labyrinth weirs. J Hydraul Div 96(11):2337–2357

    Google Scholar 

  • Hussien NJ (2014) Experimental study of height and surface roughness effects of crump weirs on over flow characteristics. J Univ Babylon 22(4):845–859

    Google Scholar 

  • Izadinia E, Rismani N, Kabiri Samani AR (2017) Investigation on discharge coefficient of circular-crested weir using numerical modeling. J Hydraul 12(3):53–60

    Google Scholar 

  • Kabiri Samani AR, Bagheri S (2014) Design of channels and water conveyance structures. Arkan-Danesh Publishing Co., Isfahan

    Google Scholar 

  • Keller RJ (1989) Slo** crest crump weir. J Irrig Drain Eng 115(2):231–238

    MathSciNet  Google Scholar 

  • Khalil MF (2020) Quasi-steady state method for unsteady flow calibration of triangular weir. Alex Eng J 59(6):4139–4146

    Google Scholar 

  • Kumar S, Ahmad Z, Mansoor T (2011) A new approach to improve the discharging capacity of sharp-crested triangular plan form weirs. Flow Meas Instrum 22(3):175–180

    Google Scholar 

  • Kumar B, Kadia S, Ahmad Z (2019) Evaluation of discharge equations of the piano key weirs. Flow Meas Instrum 68:101577

    Google Scholar 

  • Li S, Li G, Jiang D, Ning J (2020) Influence of auxiliary geometric parameters on discharge capacity of piano key weirs. Flow Meas Instrum 72:101719

    Google Scholar 

  • Machiels O, Pirotton M, Pierre A, Dewals B, Erpicum S (2014) Experimental parametric study and design of piano key weirs. J Hydraul Res 52(3):326–335

    Google Scholar 

  • Mohammadzadeh-Habili J, Heidarpour M, Afzalimehr H (2013) Hydraulic characteristics of a new weir entitled of quarter-circular-crested weir. Flow Meas Instrum 33:168–178

    Google Scholar 

  • Niazkar M, Afzali SH (2018) Application of new hybrid method in develo** a new semicircular-weir discharge model. Alex Eng J 57(3):1741–1747

    Google Scholar 

  • Parsaie A, Haghiabi AH (2019) The hydraulic investigation of circular-crested stepped spillway. Flow Meas Instrum 70:101624

    Google Scholar 

  • Parsaie A, Haghiabi AH (2021) Uncertainty analysis of discharge coefficient of circular-crested weirs. Appl Water Sci 11:1–6

    Google Scholar 

  • Parsaie A, Azamathulla HM, Haghiabi AH (2018) Prediction of discharge coefficient of cylindrical weir–gate using GMDH-PSO. ISH J Hydraul Eng 24(2):116–123

    Google Scholar 

  • Ramamurthy AS, Vo N (1993) Characteristics of circular-crested weir. J Hydraul Eng 119(9):1055–1062

    Google Scholar 

  • Sangsefidi Y, MacVicar B, Ghodsian M, Mehraein M, Torabi M, Savage BM (2019) Evaluation of flow characteristics in labyrinth weirs using response surface methodology. Flow Meas Instrum 69:101617

    Google Scholar 

  • Sangsefidi Y, Tavakol-Davani H, Ghodsian M, Mehraein M, Zarei R (2021) Hydrodynamics and free-flow characteristics of piano key weirs with different plan shapes. Water 13(15):2108

    Google Scholar 

  • Schmocker L, Halldórsdóttir BR, Hager WH (2011) Effect of weir face angles on circular-crested weir flow. J Hydraul Eng 137(6):637–643

    Google Scholar 

  • Shamsi Z, Parsaie A, Haghiabi AH (2022) Optimum hydraulic design of cylindrical weirs. ISH J Hydraul Eng 28(sup1):86–90

    Google Scholar 

  • Soulis KX, Dercas N (2012) Field calibration of weirs using partial volumetric flow measurements. J Irrig Drain Eng 138(5):481–484

    Google Scholar 

  • Soydan Oksal NG, Akoz MS, Simsek O (2020) Numerical modelling of trapezoidal weir flow with RANS. LES DES Models Sādhanā 45(1):1–18

    Google Scholar 

  • Vatankhah A, Khamisabadi M (2019) Stage-discharge relationship for triangular and curved-edge triangular weirs. Flow Meas Instrum 69:101609

    Google Scholar 

  • Zerihun YT (2020) Free flow and discharge characteristics of trapezoidal-shaped weirs. Fluids 5(4):238

    Google Scholar 

  • Zounemat-Kermani M, Ramezani-Charmahineh A, Kermani SG (2021) Studying the relationship between the hydraulic and geometry characteristics of labyrinth weirs based on the historical memory of reported data. Flow Meas Instrum 82:102079

    Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Civil Engineering, Isfahan (Khorasgan) Branch, Islamic Azad University, Isfahan, Iran

    Sayed Mojtaba Mahdavi

  2. Department of Civil Engineering, Shahid Ashrafi Esfahani University, Isfahan, Iran

    Elham Izadinia

  3. Water Studies Research Center, Isfahan (Khorasgan) Branch, Islamic Azad University, Isfahan, Iran

    Ali Khoshfetrat

Authors
  1. Sayed Mojtaba Mahdavi
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  2. Elham Izadinia
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  3. Ali Khoshfetrat
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Contributions

SMM helped in data curation, methodology, writing—original draft preparation. EI was involved in conceptualization, investigation, visualization, writing—review & editing, and supervision. AK helped in investigation, visualization, writing—review & editing.

Corresponding author

Correspondence to Elham Izadinia.

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The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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Mahdavi, S.M., Izadinia, E. & Khoshfetrat, A. Discharge Coefficient Calibrations of Normal and Oblique Circular-Crested Weirs Under Incremental Flow Conditions. Iran J Sci Technol Trans Civ Eng 48, 2679–2689 (2024). https://doi.org/10.1007/s40996-023-01277-6

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  • DOI: https://doi.org/10.1007/s40996-023-01277-6

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