Application of Simple Crested Weirs to Control Outflows from Tiles Drainage
Abstract
:1. Introduction
1.1. Instrumental Methods to Measure Flow from Controlled Tile Drainages
1.2. Commonly Used V-Notch Weir Equations
- Qideal is the discharge (m3∙s−1);
- is the angle of the notch (°);
- is the gravitational acceleration (m∙s−2);
- is the height of water above the crest (m).
- QVnotch is the flow discharge (m3∙s−1);
- Cd is the discharge coefficient (-).
- QVnotch is the flow discharge (m3∙s−1);
- C is the discharge coefficient (-);
- h is the depth of water (head) behind the weir (m);
- k is the head correction factor (m).
- QVnotch is the flow discharge (m3∙s−1);
- h1e = h1 + kh (m);
- h1 is the high of water above the crest (m);
- kh is the head correction factor (0.001 m).
- QVnotch is the flow rate (m3∙s−1);
- is the height of water above the crest (m).
- QVnotch is the flow rate (m3∙s−1);
- is the height of water above the crest (m).
- H is the head over the weir measured [m];
- a and b are coefficients determined experimentally.
- (a)
- with a 90° notch (also known as Thomson weir) and flow formula:
- (b)
- with a half 90° notch (53°8’) and flow formula:
- (c)
- with a quarter 90° notch (9 = 28°4’) and flow formula:
2. Materials and Methods
2.1. Experimental Setup and Flow Measurement
- H is the water table level (m3∙s−1);
- ph is the hydrostatic pressure (kPa);
- patm is the atmospheric pressure (kPa);
- is the gravitational acceleration (m∙s−2);
- is the height of water above the crest (m);
- ρ is the liquid density (kg∙m−3);
- ×100 is the conversion factor resulting from the conversion of units;
- +2 is the correction for the logger, determining its position relative to the bottom of the well (cm).
2.2. Developing the Empirical Flow Equation
2.3. Comparison between Actual and Theoretical Discharges
- QVnotch is the flow rate (L∙s−1);
- is the height of water above the crest (cm).
- QVnotch is the flow rate (dm3∙min−1);
- is the high of water above the crest (cm).
- QVnotch is the flow rate (dm3∙min−1);
- is the height of water above the crest (cm).
3. Results and Discussion
3.1. Empirical Flow Equations with Regression Analysis
3.2. Comparison with Previously Reported V-Notch Weirs
4. Conclusions
Funding
Data Availability Statement
Conflicts of Interest
References
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Angle of slope | Calculated Equation (QCAL1) | R-Squared (R2) | Root Mean Square Error (RMSE) | Height of Water above the Crest H (cm) (Range) | Range of Flow Measurement Q (L∙min−1) |
---|---|---|---|---|---|
30° | Q = 0.298H2.266 | 0.9955 | 0.346 | 5.4–7.8 (2.45) | 13.60–31.38 |
45° | Q = 0.224H2.418 | 0.9981 | 0.255 | 4.2–7.3 (3.10) | 7.31–27.29 |
60° | Q = 0.256H2.325 | 0.9980 | 0.332 | 3.8–7.7 (3.90) | 6.00–29.45 |
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Napierała, M. Application of Simple Crested Weirs to Control Outflows from Tiles Drainage. Water 2023, 15, 3248. https://doi.org/10.3390/w15183248
Napierała M. Application of Simple Crested Weirs to Control Outflows from Tiles Drainage. Water. 2023; 15(18):3248. https://doi.org/10.3390/w15183248
Chicago/Turabian StyleNapierała, Michał. 2023. "Application of Simple Crested Weirs to Control Outflows from Tiles Drainage" Water 15, no. 18: 3248. https://doi.org/10.3390/w15183248