Skip to main content
SpringerLink
Log in

Discharge Characteristics of Piano Key Weirs with and Without Upstream Siltation

  • Research paper
  • Published:
International Journal of Civil Engineering Aims and scope Submit manuscript

Abstract

The application of a piano key (PK) weir in a channel may lead to changes in the flow characteristics, upstream siltation conditions, and bed elevation. In this study, laboratory-based Type-A PK weir models with noses below the upstream apexes were studied under different flow and siltation conditions. A total of 342 datasets were collected from the three models. Upstream siltation had no impact on the discharge efficiency of submerged PK weirs, but under the free-flow condition, there was a maximum reduction of 4% in the coefficient of discharge. Planners and designers must consider such variations in channels with a high sediment load. However, at high H/P (where H is the head over the weir crest and P is the weir height), the siltation effect starts to decrease, possibly due to the alternation in the flow condition caused by tailwater submergence. The modular submergence was found to be approximately 0.5, which is close to the values available in the literature. The proposed equations for free-flowing PK weirs performed very well with a maximum error of approximately 7% and a mean absolute percentage error (MAPE) of approximately 2.5%. Furthermore, approximately 60% of the data lie within the ± 3% error bands, and almost all data lie within the ± 6% error bands. The equations proposed for submerged PK weirs also efficiently estimated the coefficient of discharge with a maximum error ranging from 9.0 to 11.32% and an MAPE varying from 2.94 to 4.27%.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

Abbreviations

a :

Inlet key width (m)

b :

Outlet key width (m)

B :

Sidewall overflowing crest length (m)

B b :

Base length of the PK weir (m)

B i :

Overhang length for the inlet key (m)

B o :

Overhang length for the outlet key (m)

C PK :

Coefficient of discharge for a PK weir with no siltation on the upstream side (–)

C PKs :

Coefficient of discharge of a submerged PK weir (–)

C PK′ :

Coefficient of discharge for a PK weir with upstream siltation (–)

h :

Flow depth over the crest (m)

h v :

Velocity head (m)

H :

Total upstream head over the crest (m)

H d :

Total downstream hydraulic head (m)

L :

Total crest length of the weir (m)

P :

Height of inlet (Pi) and outlet keys (Po) (m)

P′:

Incoming flow depth below the inlet key sill (m)

Q :

Discharge capacity of a PK weir (m3/s)

Q s :

Discharge passing under the submerged condition (m3/s)

T s :

Wall thickness (m)

W :

Width of the weir (m)

y :

Total upstream flow depth (m)

S w :

Submergence of a PK weir (–)

σ :

Surface tension (N/m)

μ :

Viscosity (Pa s)

References

  1. Leite RM, Pfister M, Schleiss AJ, Boillat JL (2012) Hydraulic design of a-type piano key weirs. J Hydraul Res 50(4):400–408

    Article  Google Scholar 

  2. Lempérière F, Ouamane A (2003) The piano keys weir: a new cost-effective solution for spillways. Int J Hydropower Dams 10(5):144–149

    Google Scholar 

  3. Leite RM, Bieri M, Boillat JL, Schleiss AJ, Singhal G, Sharma N (2012) Discharge capacity of piano key weirs. J Hydraul Eng 138(2):199–203

    Article  Google Scholar 

  4. Singhal GD, Sharma N (2011) Rehabilitation of Sawara Kuddu Hydroelectric Project—model studies of piano key weir in India. In: Proceedings of the international conference on labyrinth and piano key weirs—PKW 2011, Liege, Belgium. CRC Press, London, pp 241–250

  5. Noseda M, Stojnic I, Pfister M, Schleiss AJ (2019) Upstream erosion and sediment passage at piano key weirs. J Hydraul Eng 145(8):04019029

    Article  Google Scholar 

  6. Laugier F (2007) Design and construction of the first piano key weir spillway at Goulours dam. Int J Hydropower Dams 14(5):94–101

    Google Scholar 

  7. Erpicum S, Archambeau P, Dewals B, Pirotton M (2017) Hydraulics of piano key weirs: a review. In: Proceedings of the 3rd international workshop on labyrinth and piano key weirs (PKW 2017), Qui Nhon, Vietnam. CRC Press, London, pp 27–36

  8. Crookston BM, Erpicum S, Tullis BP, Laugier F (2019) Hydraulics of labyrinth and piano key weirs: 100 years of prototype structures, advancements, and future research needs. J Hydraul Eng 145(12):02519004

    Article  Google Scholar 

  9. Lempérière F, Vigny JP, Ouamane A (2011) General comments on labyrinths and piano keyweirs: the past and present. In: Proceedings of the international conference on labyrinth and piano key weirs—PKW 2011, Liege, Belgium. CRC Press, London, pp 17–24

  10. Kabiri-Samani A, Javaheri A (2012) Discharge coefficients for free and submerged flow over Piano Key weirs. J Hydraul Res 50(1):114–120

    Article  Google Scholar 

  11. Oertel M (2018) Piano key weir research: state-of-the-art and future challenges. In: 7th IAHR international symposium on hydraulic structures, Aachen, Germany. Utah State University, pp 474–481

  12. Anderson RM, Tullis BP (2013) Piano key weir hydraulics and labyrinth weir comparison. J Irrig Drain Eng 139(3):246–253

    Article  Google Scholar 

  13. Anderson RM, Tullis BP (2012) Comparison of piano key and rectangular labyrinth weir hydraulics. J Hydraul Eng 138(4):358–361

    Article  Google Scholar 

  14. Belaabed F, Ouamane A (2013) Submerged flow regimes of piano key weir. In: Proceedings of the second international workshop on labyrinth and piano key weirs—PKW 2013, Paris, France. CRC Press, London, pp 85–92

  15. Cicero GM, Delisle JR (2013) Discharge characteristics of piano key weirs under submerged flow. In: Proceedings of the second international workshop on labyrinth and piano key weirs—PKW 2013, Paris, France. CRC Press, London, pp 101–109

  16. Crookston BM, Anderson RM, Tullis BP (2018) Free-flow discharge estimation method for piano key weir geometries. J Hydro-environ Res 19:160–167

    Article  Google Scholar 

  17. Karimi CM, Nazari S, Shooshtari MM (2019) Investigating the effect of a parapet wall on the hydraulic performance of an arced piano key weir. J Hydraul Res 58(2):274–282

    Article  Google Scholar 

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

    Article  Google Scholar 

  19. Laugier F, Pralong J, Blancher B (2011) Influence of structural thickness of sidewalls on PKW spillway discharge capacity. In: Proceedings of the international conference on labyrinth and piano key weirs—PKW 2011, Liege, Belgium. CRC Press, London, pp 159–165

  20. Lempérière F (2009) New labyrinth weirs triple spillways discharge, dams, piano keys weirs, tidal energy and energy storage. http://www.hydrocoop.org. Accessed 13 June 2019

  21. Li G, Li S, Hu Y (2019) The effect of the inlet/outlet width ratio on the discharge of piano key weirs. J Hydraul Res 58(4):594–604

    Article  Google Scholar 

  22. Machiels O, Erpicum S, Archambeau P, Dewals B, Pirotton M (2011) Piano key weir preliminary design method: application to a new dam project. In: Proceedings of the international conference on labyrinth and piano key weirs—PKW 2011, Liege, Belgium. CRC Press, London, pp 199–206

  23. Machiels O, Erpicum S, Archambeau P, Dewals B, Pirotton M (2013) Parapet wall effect on piano key weir efficiency. J Irrig Drain Eng 139(6):506–511

    Article  Google Scholar 

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

    Article  Google Scholar 

  25. Pfister M, Schleiss AJ (2013) Effect of driftwood on hydraulic head of piano key weirs. In: Proceedings of the second international workshop on labyrinth and piano key weirs—PKW 2013, Paris, France. CRC Press, London, pp 255–264

  26. Dabling MR, Tullis BP (2012) Piano key weir submergence in channel applications. J Hydraul Eng 138(7):661–666

    Article  Google Scholar 

  27. Tullis BP, Young JC, Chandler MA (2007) Head-discharge relationships for submerged labyrinth weirs. J Hydraul Eng 133(3):248–254

    Article  Google Scholar 

  28. Kabiri-Samani A, Ansari A, Borghei SM (2010) Hydraulic behaviour of flow over an oblique weir. J Hydraul Res 48(5):669–673

    Article  Google Scholar 

  29. Villemonte JR (1947) Submerged weir discharge studies. Eng News Rec 139(26):54–57

    Google Scholar 

  30. Erpicum S, Tullis BP, Lodomez M, Archambeau P, Dewals BJ, Pirotton M (2016) Scale effects in physical piano key weirs models. J Hydraul Res 54(6):692–698

    Article  Google Scholar 

  31. Tullis BP, Crookston BM, Young N (2020) Scale effects in free-flow nonlinear weir head-discharge relationships. J Hydraul Eng 146(2):04019056

    Article  Google Scholar 

  32. Novak P, Cabelka J (1981) Models in hydraulic engineering: physical principles and design applications. Pitman Publishing Ltd, Boston

    Google Scholar 

  33. Henderson FM (1966) Open channel flow. Macmillan, New York

    Google Scholar 

  34. Jüstrich S, Pfister M, Schleiss AJ (2016) Mobile riverbed scour downstream of a piano key weir. J Hydraul Eng 142(11):04016043

    Article  Google Scholar 

Download references

Acknowledgements

The first author would like to express his gratitude to the Ministry of Human Resource Development, Govt. of India for granting research scholarship.

Author information

Authors and Affiliations

  1. Department of Civil Engineering, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand, 247667, India

    Binit Kumar & Zulfequar Ahmad

  2. Department of Civil and Environmental Engineering, Norwegian University of Science and Technology, 7491, Trondheim, Norway

    Subhojit Kadia

  3. Department of Water Resources Development and Management, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand, 247667, India

    Subhojit Kadia

Authors
  1. Binit Kumar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Subhojit Kadia
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zulfequar Ahmad
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zulfequar Ahmad.

Ethics declarations

Conflict of interest

The authors hereby declare that they do not have any conflicts of interest.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kumar, B., Kadia, S. & Ahmad, Z. Discharge Characteristics of Piano Key Weirs with and Without Upstream Siltation. Int J Civ Eng 19, 1043–1054 (2021). https://doi.org/10.1007/s40999-021-00607-x

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40999-021-00607-x

Keywords

Search

Navigation