Sill Role Effect on the Flow Characteristics (Experimental and Regression Model Analytical)
Abstract
:1. Introduction
2. Materials and Methods
2.1. Experimental Equipment
2.2. Dimensional Analysis
2.3. Statistical Indicators
3. Results and Discussion
3.1. Energy Dissipation of Gate without Sill
3.2. Cd without Sill
3.3. Energy Dissipation of the Gate with Sill
3.4. Cd with Sill
4. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Gate Openings (m) | |||||
---|---|---|---|---|---|
0.01 | 0.02 | 0.04 | |||
q (m3/s·m) | R (kg/m) | q (m3/s·m) | R (kg/m) | q (m3/s·m) | R (kg/m) |
0.0111 | 7.77 | 0.0167 | 1.96 | 0.0278 | 0.21 |
0.0139 | 17.53 | 0.0194 | 4.02 | 0.0306 | 0.49 |
0.0167 | 35.52 | 0.0222 | 7.36 | 0.0319 | 0.69 |
0.0194 | 59.62 | 0.025 | 11.90 | 0.0333 | 0.93 |
0.0222 | 89.92 | 0.0278 | 17.58 | 0.0347 | 1.27 |
- | - | 0.0306 | 24.78 | 0.0361 | 1.61 |
- | - | 0.0333 | 35.61 | 0.0375 | 1.96 |
- | - | - | - | 0.0389 | 2.36 |
- | - | - | - | 0.0417 | 3.58 |
Q (L/min) | Sill widths (m) | |||||||
0.025 | 0.05 | 0.075 | 0.10 | |||||
αA | αB | αA | αB | αA | αB | αA | αB | |
450 | - | - | - | - | 1.024 | 1.002 | 1.045 | 1.003 |
500 | - | - | 1.021 | 1.001 | 1.018 | 1.005 | 1.040 | 1.006 |
550 | 1.022 | 1.001 | 1.013 | 1.002 | 1.015 | 1.008 | 1.030 | 1.009 |
575 | 1.019 | 1.002 | 1.009 | 1.009 | 1.007 | 1.025 | 1.015 | 1.018 |
600 | 1.010 | 1.008 | 1.003 | 1.030 | 1.005 | 1.038 | 1.005 | 1.038 |
625 | 1.008 | 1.020 | 1.002 | 1.065 | 1.002 | 1.065 | 1.001 | 1.062 |
650 | 1.006 | 1.050 | 1.001 | 1.075 | 1.001 | 1.080 | 1.001 | 1.095 |
675 | 1.001 | 1.075 | 1.000 | 1.095 | 1.001 | 1.098 | 1.001 | 1.100 |
700 | 1.001 | 1.090 | 1.000 | 1.100 | 1.000 | 1.105 | 1.001 | 1.108 |
750 | 1.001 | 1.100 | 1.000 | 1.105 | 1.000 | 1.130 | 1.000 | 1.119 |
Q (L/min) | Sill widths (m) | |||||||
0.15 | 0.20 | 0.25 | 0.30 | |||||
αA | αB | αA | αB | αA | αB | αA | αB | |
300 | - | - | - | - | 1.009 | 1.004 | - | - |
325 | - | - | - | - | - | - | 1.001 | 1.050 |
350 | - | - | - | - | 1.007 | 1.009 | 1.001 | 1.084 |
375 | - | - | - | 1.005 | 1.030 | 1.000 | 1.100 | |
400 | - | - | - | - | 1.001 | 1.075 | - | - |
450 | - | - | 1.020 | 1.002 | 1.000 | 1.098 | - | - |
500 | 1.030 | 1.002 | 1.015 | 1.005 | 1.000 | 1.107 | - | - |
550 | 1.028 | 1.004 | 1.012 | 1.009 | - | - | - | - |
575 | 1.028 | 1.006 | 1.007 | 1.020 | - | - | - | - |
600 | 1.015 | 1.008 | 1.003 | 1.055 | - | - | - | - |
625 | 1.010 | 1.010 | 1.001 | 1.085 | - | - | - | - |
650 | 1.008 | 1.020 | 1.000 | 1.140 | - | - | - | - |
675 | 1.001 | 1.055 | - | - | - | - | - | - |
700 | 1.001 | 1.085 | - | - | - | - | - | - |
750 | 1.000 | 1.130 | - | - | - | - | - | - |
Q (L/min) | Sill Widths (m) | |||||||||||
0.025 | 0.05 | |||||||||||
with α EA (m) | without α EA (m) | RE (%) | with α EB (m) | without α EB (m) | RE (%) | with α EA (m) | without α EA (m) | RE (%) | with α EB (m) | without α EB (m) | RE (%) | |
500 | - | - | - | - | - | - | 0.096 | 0.094 | 1.56 | 0.073 | 0.073 | 0.01 |
550 | 0.107 | 0.105 | 1.63 | 0.086 | 0.086 | 0.01 | 0.111 | 0.110 | 1.04 | 0.077 | 0.077 | 0.03 |
575 | 0.115 | 0.113 | 1.43 | 0.079 | 0.079 | 0.03 | 0.121 | 0.120 | 0.71 | 0.081 | 0.081 | 0.11 |
600 | 0.124 | 0.123 | 0.80 | 0.082 | 0.082 | 0.11 | 0.130 | 0.130 | 0.21 | 0.084 | 0.083 | 0.39 |
625 | 0.136 | 0.135 | 0.66 | 0.088 | 0.088 | 0.23 | 0.141 | 0.141 | 0.13 | 0.089 | 0.089 | 0.72 |
650 | 0.146 | 0.145 | 0.50 | 0.090 | 0.090 | 0.59 | 0.151 | 0.151 | 0.07 | 0.092 | 0.092 | 0.81 |
675 | 0.155 | 0.155 | 0.08 | 0.096 | 0.095 | 0.78 | 0.162 | 0.162 | 0.01 | 0.098 | 0.097 | 0.90 |
700 | 0.165 | 0.165 | 0.07 | 0.098 | 0.097 | 0.93 | 0.175 | 0.175 | 0.01 | 0.100 | 0.099 | 0.97 |
750 | 0.186 | 0.186 | 0.04 | 0.106 | 0.105 | 0.93 | 0.204 | 0.204 | 0.01 | 0.107 | 0.106 | 0.93 |
Q (L/min) | Sill widths (m) | |||||||||||
0.075 | 0.10 | |||||||||||
with α EA (m) | without α EA (m) | RE (%) | with α EB (m) | without α EB (m) | RE (%) | with α EA (m) | without α EA (m) | RE (%) | with α EB (m) | without α EB (m) | RE (%) | |
450 | 0.088 | 0.086 | 1.75 | 0.069 | 0.069 | 0.07 | 0.099 | 0.095 | 3.41 | 0.069 | 0.069 | 0.04 |
500 | 0.104 | 0.102 | 1.39 | 0.076 | 0.076 | 0.08 | 0.118 | 0.114 | 3.18 | 0.077 | 0.077 | 0.07 |
550 | 0.123 | 0.122 | 1.22 | 0.083 | 0.083 | 0.08 | 0.134 | 0.131 | 2.46 | 0.083 | 0.083 | 0.09 |
575 | 0.137 | 0.136 | 0.59 | 0.089 | 0.089 | 0.09 | 0.148 | 0.146 | 1.27 | 0.089 | 0.089 | 0.16 |
600 | 0.151 | 0.150 | 0.39 | 0.093 | 0.092 | 0.09 | 0.165 | 0.164 | 0.44 | 0.093 | 0.093 | 0.32 |
625 | 0.164 | 0.164 | 0.13 | 0.095 | 0.094 | 0.09 | 0.182 | 0.182 | 0.09 | 0.097 | 0.096 | 0.50 |
650 | 0.179 | 0.179 | 0.09 | 0.101 | 0.100 | 0.10 | 0.197 | 0.197 | 0.07 | 0.102 | 0.101 | 0.72 |
675 | 0.193 | 0.193 | 0.07 | 0.103 | 0.102 | 0.10 | 0.213 | 0.213 | 0.07 | 0.105 | 0.105 | 0.72 |
700 | 0.207 | 0.207 | 0.01 | 0.107 | 0.107 | 0.11 | 0.230 | 0.230 | 0.05 | 0.109 | 0.109 | 0.75 |
750 | 0.247 | 0.247 | 0.01 | 0.117 | 0.116 | 0.12 | 0.266 | 0.266 | 0.01 | 0.118 | 0.117 | 0.74 |
Q (L/min) | Sill widths (m) | |||||||||||
0.15 | 0.20 | |||||||||||
with α EA (m) | without α EA (m) | RE (%) | with α EB (m) | without α EB (m) | RE (%) | with α EA (m) | without α EA (m) | RE (%) | with α EB (m) | without α EB (m) | RE (%) | |
450 | - | - | - | - | - | - | 0.155 | 0.152 | 1.77 | 0.079 | 0.079 | 0.01 |
500 | 0.135 | 0.131 | 2.51 | 0.084 | 0.084 | 0.02 | 0.189 | 0.186 | 1.36 | 0.088 | 0.088 | 0.03 |
550 | 0.167 | 0.163 | 2.43 | 0.088 | 0.088 | 0.03 | 0.242 | 0.239 | 1.11 | 0.098 | 0.098 | 0.05 |
575 | 0.183 | 0.179 | 2.46 | 0.092 | 0.092 | 0.05 | 0.266 | 0.264 | 0.66 | 0.101 | 0.101 | 0.11 |
600 | 0.205 | 0.202 | 1.35 | 0.098 | 0.098 | 0.07 | 0.302 | 0.302 | 0.29 | 0.105 | 0.105 | 0.30 |
625 | 0.222 | 0.220 | 0.91 | 0.101 | 0.101 | 0.07 | 0.332 | 0.332 | 0.05 | 0.114 | 0.113 | 0.40 |
650 | 0.251 | 0.250 | 0.74 | 0.108 | 0.108 | 0.12 | 0.393 | 0.393 | 0.01 | 0.116 | 0.116 | 0.66 |
675 | 0.280 | 0.280 | 0.09 | 0.111 | 0.111 | 0.32 | - | - | - | - | - | - |
700 | 0.303 | 0.303 | 0.08 | 0.116 | 0.116 | 0.47 | - | - | - | - | - | - |
750 | 0.349 | 0.349 | 0.03 | 0.123 | 0.122 | 0.70 | - | - | - | - | - | - |
Q (L/min) | Sill widths (m) | |||||||||||
0.25 | 0.30 | |||||||||||
with α EA (m) | without α EA (m) | RE (%) | with α EB (m) | without α EB (m) | RE (%) | with α EA (m) | without α EA (m) | RE (%) | with α EB (m) | without α EB (m) | RE (%) | |
300 | 0154 | 0.153 | 0.83 | 0.062 | 0.062 | 0.03 | 0.375 | 0.375 | 0.08 | 0.068 | 0.068 | 0.25 |
325 | - | - | - | - | - | - | 0.425 | 0.425 | 0.06 | 0.073 | 0.072 | 0.40 |
350 | 0.214 | 0.213 | 0.62 | 0.073 | 0.073 | 0.05 | 0.492 | 0.492 | 0.04 | 0.078 | 0.078 | 0.45 |
375 | 0.256 | 0.255 | 0.48 | 0.076 | 0.076 | 0.17 | - | - | - | - | - | - |
400 | 0.315 | 0.315 | 0.08 | 0.085 | 0.084 | 0.34 | - | - | - | - | - | - |
450 | 0.398 | 0.398 | 0.01 | 0.094 | 0.094 | 0.42 | - | - | - | - | - | - |
500 | 0.495 | 0.495 | 0.01 | 0.103 | 0.103 | 0.42 | - | - | - | - | - | - |
Types of Channel | α Values | ||
---|---|---|---|
Min | Mean | Max | |
Regular channels, flumes, Spillways | 1.10 | 1.15 | 1.20 |
Natural channels | 1.15 | 1.30 | 1.50 |
Rivers with ice cover | 1.20 | 1.50 | 2.00 |
River valleys, over flooded | 1.50 | 1.75 | 2.00 |
B (m) | Without Sill G = 0.04 | 0.025 | 0.05 | 0.075 | 0.10 | 0.15 | 0.20 | 0.25 | 0.30 | ||
---|---|---|---|---|---|---|---|---|---|---|---|
Q (L/min) | 300 | ∆EAB/EA (%) | - | - | - | - | - | - | - | 59.3 | 71.5 |
350 | - | - | - | - | - | - | - | 65.7 | 77.3 | ||
400 | - | - | - | - | - | - | - | 73.2 | - | ||
450 | - | - | - | 19.9 | 27.4 | - | 47.8 | 76.5 | - | ||
500 | 21.5 | - | 22.6 | 25.9 | 32.8 | 36.3 | 52.5 | 79.2 | - | ||
550 | 25.8 | 27.7 | 29.9 | 32 | 36.5 | 46 | 59.2 | - | - | ||
600 | 29.7 | 33.5 | 35.8 | 38.3 | 43.2 | 51.6 | 65.1 | - | - | ||
650 | 34.3 | 38.1 | 39.4 | 44 | 48.9 | 56.9 | 70.6 | - | - | ||
300 | ∆EAB/EB (%) | - | - | - | - | - | - | - | 145.9 | 251.3 | |
350 | - | - | - | - | - | - | - | 191.8 | 340.2 | ||
400 | - | - | - | - | - | - | - | 273.1 | - | ||
450 | - | - | - | 24.8 | 38.8 | - | 91.6 | 326.4 | - | ||
500 | 27.3 | - | 29.2 | 34.9 | 48.8 | 57 | 110.4 | 380.7 | - | ||
550 | 34.7 | 38.3 | 42.7 | 47 | 57.5 | 85.3 | 144.9 | - | - | ||
600 | 42.3 | 50.4 | 55.8 | 62.2 | 76.2 | 106.8 | 186.8 | - | - | ||
650 | 52.2 | 61.5 | 65 | 78.5 | 95.5 | 131.8 | 239.7 | - | - |
B (m) | Without Sill | 0.025 | 0.025 | 0.075 | 0.10 | 0.15 | 0.20 | 0.25 | 0.30 | ||
---|---|---|---|---|---|---|---|---|---|---|---|
Q (L/min) | 350 | Cd (-) | - | - | 0.5554 | 0.5573 | 0.5683 | 0.5969 | 0.6515 | 0.6897 | 0.7797 |
375 | - | - | 0.5592 | 0.5617 | 0.5763 | 0.6083 | 0.6538 | 0.6860 | 0.7760 | ||
400 | 0.5377 | 0.5445 | 0.5604 | 0.5658 | 0.5769 | 0.6143 | 0.6520 | 0.6818 | - | ||
450 | 0.5667 | 0.5675 | 0.5820 | 0.5838 | 0.5938 | 0.6310 | 0.6625 | 0.6868 | - |
Mode | Mean AE (-) | Mean RE (%) | Max Relative Error (%) | Min Relative Error (%) | RMSE (-) | R2 |
---|---|---|---|---|---|---|
0.0134 | 3.12 | 14.49 | −15.31 | 0.0194 | 0.985 | |
0.0233 | 1.62 | 5.83 | −5.7 | 0.0410 | 0.998 |
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Abbaszadeh, H.; Norouzi, R.; Sume, V.; Kuriqi, A.; Daneshfaraz, R.; Abraham, J. Sill Role Effect on the Flow Characteristics (Experimental and Regression Model Analytical). Fluids 2023, 8, 235. https://doi.org/10.3390/fluids8080235
Abbaszadeh H, Norouzi R, Sume V, Kuriqi A, Daneshfaraz R, Abraham J. Sill Role Effect on the Flow Characteristics (Experimental and Regression Model Analytical). Fluids. 2023; 8(8):235. https://doi.org/10.3390/fluids8080235
Chicago/Turabian StyleAbbaszadeh, Hamidreza, Reza Norouzi, Veli Sume, Alban Kuriqi, Rasoul Daneshfaraz, and John Abraham. 2023. "Sill Role Effect on the Flow Characteristics (Experimental and Regression Model Analytical)" Fluids 8, no. 8: 235. https://doi.org/10.3390/fluids8080235