Discharge Coefficients of Standard Spillways at High Altitudes
Abstract
:1. Introduction and Objective
Previous Studies
2. Materials and Methods
2.1. Experimental Facility
2.2. Instrumentation
2.3. Operating Conditions
2.4. Methodology
3. Results
3.1. Data Processing
3.2. Spillway
3.3. P/Hd Aggregated Analysis
4. Discussion
5. Conclusions
- -
- The experimental results were compared with previous research. At altitudes above 4000 m a.s.l., the discharge coefficients show substantial differences, with consistently lower values than those obtained to date in previous works conducted at lower altitudes above sea level.
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- Particularly, the discharge coefficient Co of Equation (5) when H/Hd ≈ 1 at Condoroma seems to tend towards a value slightly lower than 2.1, lower than the 2.17 proposed by USBR [4].
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- The P/Hd ratio influences the discharge coefficients in Condoroma, and P/Hd ≥ 1 values are recommended for the design of the spillway profile. The authors observed more stable and predictable flow behavior for higher P/Hd ratios.
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- Although the results obtained for P/Hd ≥ 1 at Condoroma show significantly lower values than those obtained in previous experience at much lower altitudes, it can be seen that the tests for P/Hd < 1 the discharge coefficients, although still significantly lower, are more similar to the results obtained by other authors.
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- The equations to determine the discharge coefficients (Equations (10) and (11)) for Condoroma could be used in areas at similar altitudes in the absence of experimental data.
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Author | Width (m) | Hd (m) | P/Hd | Q (L/s) | Elevation m a.s.l. |
---|---|---|---|---|---|
Dillman [12] | - | 0.05 | - | - | 520 |
Cassidy [24] | - | - | 2; 2.5; 3.7; 6.6 | - | 210 |
Rouse [48] | 0.500 | - | - | 62 | 115 |
Murphy [26] | 0.732 | 0.305 | 3.5; 7.0 | 560 | 38 |
Maynord [28] | 0.762 | 0.249 | 0.25; 0.5; 1.0; 2.0 | 385 | 38 |
Hager [29] | 0.500 | 0.20/0.1 | 3.5/7.0 | 375 | 495 |
Erpicum [31] | 0.200 | 0.10/0.15 | - | 358 | 240 |
Condoroma dam | 0.915 | 0.20/0.175 | 0.25; 0.5; 1; 1.5/2 | 415 | 4075 |
P (m) | P/Hd | Q (L/s) | Stage (m) | Fr | yb (m) | Frb |
---|---|---|---|---|---|---|
(1) | (2) | (3) | (4) | (5) | (6) | (7) |
0.35 | 2.0 | 53–363 | 0.45–0.634 | 0.062–0.25 | 0.073–0.21 | 0.96–1.28 |
0.30 | 1.5 | 49–400 | 0.40–0.607 | 0.068–0.31 | 0.074–0.24 | 0.85–1.18 |
0.20 | 1.0 | 52–415 | 0.30–0.492 | 0.11–0.42 | 0.074–0.23 | 0.89–1.29 |
0.10 | 0.50 | 56–391 | 0.20–0.368 | 0.22–0.62 | 0.086–0.21 | 0.78–1.40 |
0.05 | 0.25 | 61–345 | 0.15–0.280 | 0.37–0.93 | 0.100–0.22 | 0.63–1.15 |
P/Hd | Data | m0 | n | R2 |
---|---|---|---|---|
2.0 | Condoroma | 0.467 | 0.184 | 0.962 |
2.0 | Maynord [28] | 0.494 | 0.157 | 0.984 |
2.0 | Cassidy [24] | 0.518 | 0.186 | 0.993 |
2.5 | Murphy [26] | 0.503 | 0.139 | 0.974 |
3.5 | Hager [29] | 0.493 | 0.122 | 0.988 |
1.5 | Condoroma | 0.470 | 0.172 | 0.969 |
1 | Condoroma | 0.472 | 0.158 | 0.974 |
1 | Maynord [28] | 0.490 | 0.129 | 0.989 |
0.5 | Condoroma | 0.480 | 0.098 | 0.82 |
0.5 | Maynord [28] | 0.487 | 0.099 | 0.849 |
0.25 | Condoroma | 0.465 | 0.085 | 0.807 |
0.25 | Maynord [28] | 0.468 | 0.063 | 0.489 |
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© 2024 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
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Rendón, V.; Sánchez-Juny, M.; Estrella, S.; Sanz-Ramos, M.; Rucano, P.; Huarca Pulcha, A. Discharge Coefficients of Standard Spillways at High Altitudes. Designs 2024, 8, 22. https://doi.org/10.3390/designs8020022
Rendón V, Sánchez-Juny M, Estrella S, Sanz-Ramos M, Rucano P, Huarca Pulcha A. Discharge Coefficients of Standard Spillways at High Altitudes. Designs. 2024; 8(2):22. https://doi.org/10.3390/designs8020022
Chicago/Turabian StyleRendón, Víctor, Martí Sánchez-Juny, Soledad Estrella, Marcos Sanz-Ramos, Percy Rucano, and Alan Huarca Pulcha. 2024. "Discharge Coefficients of Standard Spillways at High Altitudes" Designs 8, no. 2: 22. https://doi.org/10.3390/designs8020022