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%.
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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)
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Acknowledgements
The first author would like to express his gratitude to the Ministry of Human Resource Development, Govt. of India for granting research scholarship.
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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
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DOI: https://doi.org/10.1007/s40999-021-00607-x