Characterization of the Erosion Basin Shaped by the Jet Flow of Sky-Jump Spillways
Abstract
:1. Introduction
2. Materials and Methods
2.1. General Approach
2.2. Relevant Parameters
2.3. Physical Modeling
2.3.1. Experimental Set-Up
2.3.2. Test Procedure
2.3.3. Test Program
3. Results and Discussion
3.1. Erosion Depth
3.1.1. Estimation of Erosion Depth
3.1.2. Influence of the Flip Bucket Radius
3.1.3. Influence of the Flip Angle
3.2. Position of the Point of Maximum Erosion Depth
3.3. Length of the Erosion Basin
3.4. Erosion Basin Shape
3.5. Procedure for Estimating the Location, the Size, and the Shape of the Erosion Basin
3.6. Limitations of the Present Study
- -
- The height of the spillway is constant, so it has not allowed us to obtain a formula in order to estimate the depth of erosion depending on the flow and the geometric characteristics of the spillway; one of the formulas provided by any other author can be used for this purpose;
- -
- The spillway width is constant, so it has not allowed us to provide a direct formula for the estimation of the total width of the limit scour hole;
- -
- A wider test channel would reduce the effect of the walls, which are most likely the reason for the deviations observed in the limit scour hole.
4. Conclusions
- -
- Increasing the radius of the flip bucket allows a reduction in the depth of the scour hole. Although the cost of the structure is higher for a greater radius, this extra cost might in some cases be justified for the extra safety level achieved.
- -
- The greater the flip angle is, in the range of tested angles, 15° to 45°, the greater the depth of erosion is.
- -
- Scour hole is longer in the riverbed direction and less deep for low flip angles.
- -
- For the length of flip bucket tested, the scour hole is quasi-circular for a flip angle of 45° and more elongated for lower angles. However, the influence of the lip length is evident, so a different shape should be expected for different lip lengths.
- -
- The plan position of the point where the depth erosion is maximum moves away from the flip bucket with increasing flip angles between 0° and 30°. However, it is nearer the structure for a flip angle of 45°. Two opposite effects might explain this fact: increasing the angle increases the launch scope, up to 45°, but a greater angle of incidence makes the erosion more vertical, so the scour hole develops less in the direction of the riverbed and more in depth.
- -
- Empirical formulas were derived from the experimental data to estimate the position, size and shape of the scour hole. However, it should be noted that a different width, and so shape, should be expected for different lengths of the flip bucket lip, which is a parameter not considered in this experimental research. More tests are needed with different lip lengths.
- -
- A methodology is proposed, using the above mentioned formulas, to estimate position, size, and shape of the scour hole, which was fitted to a combination of two semi-ellipses.
- -
- The proposed methodology was used with success to determine whether the scour hole is likely to affect the flip bucket structure, comparing the length of the scour hole upstream of the point where the depth is maximum with the distance from that point to the flip bucket. If the scour hole overlaps with the structure, affection is likely to occur.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
A | total length of the limit scour hole in the river longitudinal direction |
A/B | circularity index |
A1 | semi-axis length in the direction of flow from the maximum scour point to the furthest downstream point |
A2 | semi-axis length in the direction of flow from the maximum scour point to the furthest upstream point |
AR | absolute error |
B | total width of the limit scour hole |
B1 | semi-axis length in the transverse direction to the flow from the maximum scour point towards the furthest point towards the hydraulic right |
B2 | semi-axis length in the transverse direction to the flow from the maximum scour point towards the furthest point towards the hydraulic left |
D | total scour depth |
Dexp | experimental total scour depth |
Dcal | calculated total scour depth |
d50 | grain diameter at 50% of weight |
d90 | grain diameter at 90% of weight |
H | total head (distance between upstream and downstream water level) |
h2 | tailwater depth (downstream water level) |
Lc | distance of maximum scour from bucket lip |
MAE | mean absolute error |
MRE | mean relative error |
Q | flow rate |
q | unit flow rate |
R | radius of flip bucket |
RE | relative error |
T | scour depth |
z1 | distance from the flip bucket’s lip to the downstream water level |
zo | distance between flip bucket’s lip and upstream water level |
zp | distance from the flip bucket’s lip to the ground |
α | flip angle |
θ | impingement jet angle |
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Authors | Erosion Depth (m) | |
---|---|---|
Veronese B | [3] | |
Damle A | [12] | |
Damle B | [12] | |
Damle C | [12] | |
INCYTH | [30] | |
Schoklitsch | [2] | |
Veronese A | [3] | |
Eggenberger | [31] | |
Hartung | [32] | |
Franke | [33] | |
Mikhalev | [23] | |
Mirtskhulava | [15] | |
Chee and Kung | [24] | |
Yildiz and Üzücek | [5] | |
Martins A | [34] | |
Chian Min Wu | [23] | |
Martins B | [35] | |
Taraimovich | [36] | |
Machado B | [37] | |
SOFRELEC | [38] | |
Kotoulas | [39] | |
Chee and Padyar | [40] | |
Bisaz and Tschopp | [41] | |
Chee and Kung | [24] | |
Machado A | [37] | |
Jaeger | [42] | |
Rubinstein | [13] | |
Mason and Arumugam | [43] | |
Ghodsian et al. | [44] | |
Flip Bucket | A1 | A2 | A3 | A4 | B2 | B3 | B4 | C2 | C4 |
---|---|---|---|---|---|---|---|---|---|
R (m) | 0.20 | 0.20 | 0.20 | 0.20 | 0.30 | 0.30 | 0.30 | 0.40 | 0.40 |
α (°) | 0 | 15 | 30 | 45 | 15 | 30 | 45 | 15 | 45 |
h2 (m) | 0.00 0.06 | 0.00 0.06 | 0.00 0.06 | 0.00 0.06 | 0.00 0.06 | 0.00 0.06 | 0.00 0.06 | 0.00 0.06 | 0.00 0.06 |
Q (L/s) | 37.50 42.00 50.00 | 37.50 42.00 50.00 | 37.50 42.00 50.00 | 37.50 42.00 50.00 | 37.50 42.00 50.00 | 37.50 42.00 50.00 | 37.50 42.00 50.00 | 37.50 42.00 50.00 | 37.50 42.00 50.00 |
Author | MAE (m) | MRE | MAEs (m) | MREs | |
---|---|---|---|---|---|
Veronese B | [3] | 0.159 | 0.47 | 0.116 | 0.32 |
Damle A | [12] | 0.188 | 0.50 | 0.230 | 0.56 |
Damle B | [12] | 0.218 | 0.58 | 0.259 | 0.63 |
Damle C | [12] | 0.268 | 0.72 | 0.308 | 0.75 |
INCYTH | [30] | 0.072 | 0.22 | 0.054 | 0.14 |
Chian Min Wu | [23] | 0.050 | 0.13 | 0.069 | 0.16 |
Martins B | [35] | 0.053 | 0.15 | 0.055 | 0.13 |
Taraimovich | [36] | 0.238 | 0.64 | 0.277 | 0.68 |
Machado B | [37] | 0.528 | 1.50 | 0.479 | 1.23 |
SOFRELEC | [38] | 0.214 | 0.62 | 0.174 | 0.46 |
Schoklitsch | [2] | 0.734 | 2.07 | 0.686 | 1.75 |
Veronese A | [3] | 0.878 | 2.47 | 0.827 | 2.11 |
Eggenberger | [31] | 0.090 | 0.23 | 0.132 | 0.31 |
Hartung | [32] | 0.100 | 0.26 | 0.141 | 0.33 |
Franke | [33] | 0.184 | 0.49 | 0.225 | 0.55 |
Kotoulas | [39] | 0.237 | 0.64 | 0.275 | 0.67 |
Chee-Padiyar | [40] | 0.340 | 0.97 | 0.297 | 0.77 |
Bisaz-Tschopp | [41] | 0.443 | 1.26 | 0.396 | 1.02 |
Chee-Kung | [24] | 0.477 | 1.350 | 0.432 | 1.11 |
Machado A | [37] | 0.234 | 0.68 | 0.188 | 0.50 |
Jaeger | [42] | 0.461 | 1.299 | 0.430 | 1.099 |
Rubinstein | [13] | 0.283 | 0.765 | 0.313 | 0.756 |
Martins A | [34] | 0.293 | 0.791 | 0.282 | 0.680 |
Mason-Arumugam | [43] | 0.216 | 0.620 | 0.176 | 0.451 |
Ghodsian | [44] | 0.336 | 0.952 | 0.296 | 0.739 |
Mikhalev | [23] | 0.087 | 0.253 | 0.185 | 0.464 |
Mirtskulava | [15] | 1.687 | 4.628 | 1.493 | 3.758 |
Cheen-Kung | [24] | 0.418 | 1.151 | 0.369 | 0.937 |
Yildiz and Üzücek | [5] | 0.083 | 0.237 | 0.145 | 0.349 |
(a) (h2 = 0.0 m) | ||||||
Practice | Q (l/s) | α (°) | R (m) | t (m) | AR (m) | RE |
A2_h0_17 | 37.5 | 15 | 0.2 | 0.321 | 0.062 | 0.24 |
B2_h0_17 | 37.5 | 15 | 0.3 | 0.291 | 0.032 | 0.12 |
C2_h0_17 | 37.5 | 15 | 0.4 | 0.259 | - | - |
A2_h0_18 | 42.0 | 15 | 0.2 | 0.332 | 0.061 | 0.23 |
B2_h0_18 | 42.0 | 15 | 0.3 | 0.310 | 0.039 | 0.14 |
C2_h0_18 | 42.0 | 15 | 0.4 | 0.271 | - | - |
A2_h0_20 | 50.0 | 15 | 0.2 | 0.34 | 0.055 | 0.19 |
B2_h0_20 | 50.0 | 15 | 0.3 | 0.329 | 0.044 | 0.16 |
C2_h0_20 | 50.0 | 15 | 0.4 | 0.285 | - | - |
(b) (h2 = 0.0 m) | ||||||
Practice | Q (l/s) | α (°) | R (m) | t (m) | AR (m) | RE |
A3_h0_17 | 37.5 | 30 | 0.2 | 0.416 | 0.049 | 0.13 |
B3_h0_17 | 37.5 | 30 | 0.3 | 0.367 | - | - |
C3_h0_17 | 37.5 | 30 | 0.4 | - | - | - |
A3_h0_18 | 42.0 | 30 | 0.2 | 0.436 | 0.048 | 0.12 |
B3_h0_18 | 42.0 | 30 | 0.3 | 0.388 | - | |
C3_h0_18 | 42.0 | 30 | 0.4 | - | - | - |
A3_h0_20 | 50.0 | 30 | 0.2 | 0.441 | 0.034 | 0.08 |
B3_h0_20 | 50.0 | 30 | 0.3 | 0.407 | - | - |
C3_h0_20 | 50.0 | 30 | 0.4 | - | - | - |
(c) (h2 = 0.0 m) | ||||||
Practice | Q (l/s) | α (°) | R (m) | t (m) | AR (m) | RE |
A4_h0_17 | 37.5 | 45 | 0.2 | 0.457 | 0.108 | 0.31 |
B4_h0_17 | 37.5 | 45 | 0.3 | 0.405 | 0.056 | 0.16 |
C4_h0_17 | 37.5 | 45 | 0.4 | 0.349 | - | - |
A4_h0_18 | 42.0 | 45 | 0.2 | 0.475 | 0.114 | 0.32 |
B4_h0_18 | 42.0 | 45 | 0.3 | 0.421 | 0.060 | 0.17 |
C4_h0_18 | 42.0 | 45 | 0.4 | 0.361 | - | - |
A4_h0_20 | 50.0 | 45 | 0.2 | 0.490 | 0.087 | 0.22 |
B4_h0_20 | 50.0 | 45 | 0.3 | 0.443 | 0.040 | 0.10 |
C4_h0_20 | 50.0 | 45 | 0.4 | 0.403 | - | - |
(d) (h2 = 0.06 m) | ||||||
Practice | Q (l/s) | α (°) | R (m) | t (m) | AR (m) | RE |
A2_h6_17 | 37.5 | 15 | 0.2 | 0.264 | 0.029 | 0.12 |
B2_h6_17 | 37.5 | 15 | 0.3 | 0.253 | 0.018 | 0.08 |
C2_h6_17 | 37.5 | 15 | 0.4 | 0.235 | - | - |
A2_h6_18 | 42.0 | 15 | 0.2 | 0.285 | 0.035 | 0.14 |
B2_h6_18 | 42.0 | 15 | 0.3 | 0.275 | 0.025 | 0.10 |
C2_h6_18 | 42.0 | 15 | 0.4 | 0.250 | - | - |
A2_h6_20 | 50.0 | 15 | 0.2 | 0.303 | 0.034 | 0.13 |
B2_h6_20 | 50.0 | 15 | 0.3 | 0.291 | 0.022 | 0.08 |
C2_h6_20 | 50.0 | 15 | 0.4 | 0.269 | - | - |
(e) (h2 = 0.06 m) | ||||||
Practice | Q (l/s) | α (°) | R (m) | t (m) | AR (m) | RE |
A3_h6_17 | 37.5 | 30 | 0.2 | 0.317 | 0.042 | 0.15 |
B3_h6_17 | 37.5 | 30 | 0.3 | 0.275 | - | - |
C3_h6_17 | 37.5 | 30 | 0.4 | - | - | - |
A3_h6_18 | 42.0 | 30 | 0.2 | 0.320 | 0.021 | 0.07 |
B3_h6_18 | 42.0 | 30 | 0.3 | 0.299 | - | |
C3_h6_18 | 42.0 | 30 | 0.4 | - | - | - |
A3_h6_20 | 50.0 | 30 | 0.2 | 0.328 | 0.01 | 0.03 |
B3_h6_20 | 50.0 | 30 | 0.3 | 0.318 | - | - |
C3_h6_20 | 50.0 | 30 | 0.4 | - | - | - |
(f) (h2 = 0.06 m) | ||||||
Practice | Q (l/s) | α (°) | R (m) | t (m) | AR (m) | RE |
A4_h6_17 | 37.5 | 45 | 0.2 | 0.385 | 0.101 | 0.36 |
B4_h6_17 | 37.5 | 45 | 0.3 | 0.367 | 0.083 | 0.29 |
C4_h6_17 | 37.5 | 45 | 0.4 | 0.284 | - | |
A4_h6_18 | 42.0 | 45 | 0.2 | 0.410 | 0.113 | 0.38 |
B4_h6_18 | 42.0 | 45 | 0.3 | 0.380 | 0.083 | 0.28 |
C4_h6_18 | 42.0 | 45 | 0.4 | 0.297 | - | - |
A4_h6_20 | 50.0 | 45 | 0.2 | 0.440 | 0.122 | 0.38 |
B4_h6_20 | 50.0 | 45 | 0.3 | 0.423 | 0.105 | 0.33 |
C4_h6_20 | 50.0 | 45 | 0.4 | 0.318 | - | - |
(g) (h2 = 0.00 m) | ||||||
Practice | Q (l/s) | α (°) | R (m) | t (m) | AR (m) | RE |
A2_h0_17 | 37.5 | 15 | 0.2 | 0.321 | 0.136 | 0.30 |
B2_h0_17 | 37.5 | 30 | 0.2 | 0.416 | 0.041 | 0.09 |
C2_h0_17 | 37.5 | 45 | 0.2 | 0.457 | - | - |
A2_h0_18 | 42.0 | 15 | 0.2 | 0.332 | 0.143 | 0.30 |
B2_h0_18 | 42.0 | 30 | 0.2 | 0.436 | 0.039 | 0.08 |
C2_h0_18 | 42.0 | 45 | 0.2 | 0.475 | - | - |
A2_h0_20 | 50.0 | 15 | 0.2 | 0.340 | 0.150 | 0.31 |
B2_h0_20 | 50.0 | 30 | 0.2 | 0.441 | 0.049 | 0.10 |
C2_h0_20 | 50.0 | 45 | 0.2 | 0.490 | - | - |
(h) (h2 = 0.0 m) | ||||||
Practice | Q (l/s) | α (°) | R (m) | t (m) | AR (m) | RE |
A3_h0_17 | 37.5 | 15 | 0.3 | 0.291 | 0.114 | 0.28 |
B3_h0_17 | 37.5 | 30 | 0.3 | 0.367 | 0.038 | 0.09 |
C3_h0_17 | 37.5 | 45 | 0.3 | 0.405 | - | - |
A3_h0_18 | 42.0 | 15 | 0.3 | 0.310 | 0.111 | 0.26 |
B3_h0_18 | 42.0 | 30 | 0.3 | 0.388 | 0.033 | 0.08 |
C3_h0_18 | 42.0 | 45 | 0.3 | 0.421 | - | - |
A3_h0_20 | 50.0 | 15 | 0.3 | 0.330 | 0.113 | 0.26 |
B3_h0_20 | 50.0 | 30 | 0.3 | 0.407 | 0.036 | 0.08 |
C3_h0_20 | 50.0 | 45 | 0.3 | 0.443 | - | - |
(i) (h2 = 0.0 m) | ||||||
Practice | Q (l/s) | α (°) | R (m) | t (m) | AR (m) | RE |
A4_h0_17 | 37.5 | 15 | 0.4 | 0.259 | 0.09 | 0.26 |
B4_h0_17 | 37.5 | 30 | 0.4 | - | - | - |
C4_h0_17 | 37.5 | 45 | 0.4 | 0.349 | - | - |
A4_h0_18 | 42.0 | 15 | 0.4 | 0.271 | 0.09 | 0.25 |
B4_h0_18 | 42.0 | 30 | 0.4 | - | - | - |
C4_h0_18 | 42.0 | 45 | 0.4 | 0.361 | - | - |
A4_h0_20 | 50.0 | 15 | 0.4 | 0.285 | 0.118 | 0.29 |
B4_h0_20 | 50.0 | 30 | 0.4 | - | - | - |
C4_h0_20 | 50.0 | 45 | 0.4 | 0.403 | - | - |
(jl) (h2 = 0.06 m) | ||||||
Practice | Q (l/s) | α (°) | R (m) | t (m) | AR (m) | RE |
A2_h6_17 | 37.5 | 15 | 0.2 | 0.264 | 0.121 | 0.31 |
B2_h6_17 | 37.5 | 30 | 0.2 | 0.317 | 0.068 | 0.18 |
C2_h6_17 | 37.5 | 45 | 0.2 | 0.385 | - | - |
A2_h6_18 | 42.0 | 15 | 0.2 | 0.285 | 0.125 | 0.30 |
B2_h6_18 | 42.0 | 30 | 0.2 | 0.320 | 0.09 | 0.22 |
C2_h6_18 | 42.0 | 45 | 0.2 | 0.410 | - | - |
A2_h6_20 | 50.0 | 15 | 0.2 | 0.303 | 0.137 | 0.31 |
B2_h6_20 | 50.0 | 30 | 0.2 | 0.328 | 0.112 | 0.25 |
C2_h6_20 | 50.0 | 45 | 0.2 | 0.440 | - | - |
(k) (h2 = 0.06 m) | ||||||
Practice | Q (l/s) | α (°) | R (m) | t (m) | AR (m) | RE |
A3_h6_17 | 37.5 | 15 | 0.3 | 0.253 | 0.114 | 0.31 |
B3_h6_17 | 37.5 | 30 | 0.3 | 0.275 | 0.092 | 0.25 |
C3_h6_17 | 37.5 | 45 | 0.3 | 0.367 | - | - |
A3_h6_18 | 42.0 | 15 | 0.3 | 0.275 | 0.105 | 0.28 |
B3_h6_18 | 42.0 | 30 | 0.3 | 0.299 | 0.081 | 0.21 |
C3_h6_18 | 42.0 | 45 | 0.3 | 0.380 | ||
A3_h6_20 | 50.0 | 15 | 0.3 | 0.291 | 0.132 | 0.31 |
B3_h6_20 | 50.0 | 30 | 0.3 | 0.318 | 0.105 | 0.25 |
C3_h6_20 | 50.0 | 45 | 0.3 | 0.423 | - | - |
(l) (h2 = 0.06 m) | ||||||
Practice | Q (l/s) | α (°) | R (m) | t (m) | AR (m) | RE |
A4_h6_17 | 37.5 | 15 | 0.4 | 0.235 | 0.049 | 0.17 |
B4_h6_17 | 37.5 | 30 | 0.4 | - | - | - |
C4_h6_17 | 37.5 | 45 | 0.4 | 0.284 | - | - |
A4_h6_18 | 42.0 | 15 | 0.4 | 0.250 | 0.047 | 0.16 |
B4_h6_18 | 42.0 | 30 | 0.4 | - | - | - |
C4_h6_18 | 42.0 | 45 | 0.4 | 0.297 | - | - |
A4_h6_20 | 50.0 | 15 | 0.4 | 0.269 | 0.049 | 0.15 |
B4_h6_20 | 50.0 | 30 | 0.4 | - | - | - |
C4_h6_20 | 50.0 | 45 | 0.4 | 0.318 | - | - |
(a) | |||||
Practice | A1 extr | A1 exp | AE (m) | RE | |
A4_h0_17 | 0.891 | 0.895 | 0.004 | 0.005 | |
A4_h0_18 | 1.035 | 1.027 | 0.008 | 0.007 | |
A4_h0_18 | 0.983 | 0.974 | 0.008 | 0.009 | |
A4_h6_17 | 0.873 | 1.085 | 0.211 | 0.195 | |
A4_h6_18 | 0.991 | 0.916 | 0.075 | 0.082 | |
A4_h6_20 | 1.027 | 1.035 | 0.007 | 0.007 | |
B3_h0_20 | 1.158 | 1.210 | 0.051 | 0.042 | |
B3_h6_17 | 1.026 | 0.982 | 0.044 | 0.045 | |
B4_h6_18 | 0.989 | 1.052 | 0.063 | 0.060 | |
B4_h6_20 | 1.062 | 1.095 | 0.032 | 0.029 | |
C4_h0_17 | 1.032 | 1.001 | 0.031 | 0.031 | |
C4_h0_20 | 1.058 | 1.120 | 0.062 | 0.056 | |
C4_h6_17 | 0.920 | 0.878 | 0.042 | 0.048 | |
C4_h6_20 | 0.901 | 0.931 | 0.030 | 0.033 | |
MAEv | 0.048 | ||||
MREv | 0.046 | ||||
(b) | |||||
Practice | A2 extr | A2 exp | AE (m) | RE | |
A4_h0_17 | 1.163 | 1.244 | 0.081 | 0.065 | |
A4_h0_18 | 1.075 | 1.114 | 0.038 | 0.034 | |
A4_h0_18 | 1.285 | 1.516 | 0.231 | 0.152 | |
A4_h6_17 | 1.082 | 1.137 | 0.056 | 0.049 | |
A4_h6_18 | 1.042 | 1.280 | 0.238 | 0.186 | |
A4_h6_20 | 1.067 | 1.189 | 0.122 | 0.102 | |
B3_h0_20 | 1.468 | 1.519 | 0.051 | 0.034 | |
B3_h6_17 | 2.008 | 1.525 | 0.483 | 0.316 | |
B4_h6_18 | 1.027 | 0.997 | 0.030 | 0.030 | |
B4_h6_20 | 1.137 | 1.764 | 0.627 | 0.356 | |
C4_h0_17 | 1.426 | 1.245 | 0.181 | 0.145 | |
C4_h0_20 | 1.518 | 1.559 | 0.042 | 0.027 | |
C4_h6_17 | 1.650 | 1.517 | 0.133 | 0.088 | |
C4_h6_20 | 1.468 | 1.200 | 0.269 | 0.224 | |
MAEv | 0.184 | ||||
MREv | 0.129 | ||||
(c) | |||||
Practice | B1 extr | B1 exp | AE (m) | RE | |
A4_h0_17 | 0.787 | 0.795 | 0.009 | 0.011 | |
A4_h0_18 | 0.810 | 0.830 | 0.020 | 0.024 | |
A4_h0_18 | 0.915 | 0.813 | 0.102 | 0.125 | |
A4_h6_17 | 0.725 | 0.753 | 0.027 | 0.036 | |
A4_h6_18 | 0.914 | 0.844 | 0.070 | 0.083 | |
A4_h6_20 | 0.930 | 0.884 | 0.046 | 0.052 | |
B3_h0_20 | 0.930 | 1.256 | 0.326 | 0.259 | |
B3_h6_17 | 0.752 | 0.846 | 0.094 | 0.111 | |
B4_h6_18 | 0.736 | 0.734 | 0.003 | 0.004 | |
B4_h6_20 | 0.861 | 0.837 | 0.023 | 0.028 | |
C4_h0_17 | 1.033 | 1.087 | 0.054 | 0.050 | |
C4_h0_20 | 0.768 | 0.809 | 0.041 | 0.051 | |
C4_h6_17 | 0.579 | 0.694 | 0.115 | 0.166 | |
C4_h6_20 | 0.752 | 1.110 | 0.358 | 0.322 | |
MAEv | 0.092 | ||||
MREv | 0.094 | ||||
(d) | |||||
Practice | B2 extr | B2 exp | AE (m) | RE | |
A4_h0_17 | 0.900 | 0.979 | 0.079 | 0.080 | |
A4_h0_18 | 0.989 | 1.147 | 0.159 | 0.139 | |
A4_h0_18 | 0.999 | 1.113 | 0.114 | 0.103 | |
A4_h6_17 | 0.877 | 1.085 | 0.208 | 0.191 | |
A4_h6_18 | 0.892 | 1.136 | 0.244 | 0.215 | |
A4_h6_20 | 0.910 | 0.993 | 0.083 | 0.083 | |
B3_h0_20 | 0.794 | 0.921 | 0.127 | 0.138 | |
B3_h6_17 | 0.765 | 0.991 | 0.226 | 0.228 | |
B4_h6_18 | 0.772 | 1.043 | 0.271 | 0.260 | |
B4_h6_20 | 0.967 | 1.206 | 0.239 | 0.198 | |
C4_h0_17 | 0.708 | 0.813 | 0.105 | 0.129 | |
C4_h0_20 | 1.221 | 1.343 | 0.123 | 0.091 | |
C4_h6_17 | 0.744 | 0.920 | 0.175 | 0.191 | |
C4_h6_20 | 0.652 | 0.712 | 0.060 | 0.084 | |
MAEv | 0.158 | ||||
MREv | 0.152 |
Parameter | Lc(θ) (m) | Lc(R) (m) | A1 (m) | A2(m) (m) | A(m) (m) | A/B | B(m) (m) |
---|---|---|---|---|---|---|---|
MAEv (m) | 0.19 | 0.26 | 0.126 | 0.12 | 0.19 | 0.15 | 0.15 |
MREv (%) | 12.76 | 17.44 | 10.70 | 8.40 | 7.40 | 8.70 | 9.90 |
Validation Test | t (m) | cos2θ | A2_exp (m) | A2_cal (m) | Lc exp (m) | Lc (θ) (m) | Lc (R) (m) | Reached Trampoline | A2_cal > |
---|---|---|---|---|---|---|---|---|---|
A3_h0_20 | 0.441 | 0.62 | 1.568 | 1.785 | 1.594 | 2.061 | 2.228 | no | no |
A3_h6_18 | 0.320 | 0.68 | 1.694 | 1.800 | 1.607 | 1.612 | 1.637 | yes | yes |
A4_h0_17 | 0.457 | 0.39 | 1.163 | 1.271 | 1.596 | 1.819 | 2.287 | yes | no |
A4_h6_18 | 0.410 | 0.43 | 1.042 | 1.314 | 1.572 | 1.877 | 2.087 | no | no |
B2_h0_17 | 0.291 | 0.79 | 1.970 | 2.037 | 1.429 | 1.377 | 1.405 | yes | yes |
B2_h6_20 | 0.291 | 0.87 | 2.262 | 2.202 | 1.704 | 1.568 | 1.477 | yes | yes |
B3_h0_17 | 0.367 | 0.61 | 1.666 | 1.681 | 1.641 | 1.569 | 1.771 | yes | = |
B3_h6_20 | 0.318 | 0.66 | 1.627 | 1.769 | 1.756 | 1.548 | 1.584 | yes | yes |
B4_h0_18 | 0.421 | 0.37 | 1.098 | 1.202 | 1.514 | 1.443 | 1.999 | yes | no |
B4_h6_17 | 0.367 | 0.41 | 1.216 | 1.228 | 1.594 | 1.469 | 1.786 | no | no |
C2_h0_20 | 0.285 | 0.79 | 1.885 | 2.033 | 1.507 | 1.334 | 1.324 | yes | yes |
C2_h6_18 | 0.250 | 0.86 | 2.246 | 2.154 | 1.497 | 1.322 | 1.235 | yes | yes |
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Pellegrino, R.; Toledo, M.Á. Characterization of the Erosion Basin Shaped by the Jet Flow of Sky-Jump Spillways. Water 2023, 15, 2930. https://doi.org/10.3390/w15162930
Pellegrino R, Toledo MÁ. Characterization of the Erosion Basin Shaped by the Jet Flow of Sky-Jump Spillways. Water. 2023; 15(16):2930. https://doi.org/10.3390/w15162930
Chicago/Turabian StylePellegrino, Raffaella, and Miguel Á. Toledo. 2023. "Characterization of the Erosion Basin Shaped by the Jet Flow of Sky-Jump Spillways" Water 15, no. 16: 2930. https://doi.org/10.3390/w15162930