This weir flow calculator is an essential tool in hydraulic engineering used to determine the volumetric flow rate of water passing over a weir. Weirs are barriers or dams built across rivers or channels to control water flow, measure discharge, or raise the water level upstream.
The calculator employs specific formulas based on the weir type (e.g., rectangular, triangular, or trapezoidal) and considers factors such as weir height, crest length, and head (water depth above the weir crest). It simplifies complex hydraulic calculations, providing quick and accurate results for various applications.
- A rectangular weir with a head of 0.3 meters might have a flow rate of 0.5 cubic meters per second.
- Converting to imperial units: 0.3 m ≈ 0.98 ft, and 0.5 m³/s ≈ 17.66 ft³/s.
Weir Flow Calculator
| Weir Type | Dimensions | Head (m) | Flow Rate (m³/s) |
|---|---|---|---|
| Rectangular | L = 4 m | 0.6 | 2.89 |
| Rectangular | L = 5 m | 0.7 | 4.05 |
| Rectangular | L = 3 m | 0.5 | 1.85 |
| V-Notch (60°) | θ = 60° | 0.4 | 0.076 |
| V-Notch (60°) | θ = 60° | 0.6 | 0.16 |
| V-Notch (90°) | θ = 90° | 0.2 | 0.025 |
| V-Notch (90°) | θ = 90° | 0.5 | 0.085 |
| Trapezoidal | b = 3 m, z = 2:1 | 0.5 | 2.18 |
| Trapezoidal | b = 4 m, z = 1:1 | 0.6 | 3.04 |
| Trapezoidal | b = 2 m, z = 1:2 | 0.4 | 1.12 |
| Trapezoidal | b = 5 m, z = 3:1 | 0.8 | 4.50 |
| Triangular | b = 3 m | H = 0.5 m | Q ≈ 0.44 |
| Triangular | b = 2 m | H = 0.6 m | Q ≈ 0.30 |
| Triangular | b = 4 m | H = 0.7 m | Q ≈ 1.00 |
Weir Flow Formula
The general weir flow formula is derived from the Bernoulli equation and is expressed as:
Q = C L H^(3/2)Where:
- Q = Volumetric flow rate
- C = Discharge coefficient
- L = Weir crest length
- H = Head above the weir crest
For rectangular weirs, the Francis formula is commonly used:
Q = 3.33 (L - 0.2H) H^(3/2)For a practical example, consider a rectangular weir with:
- Crest length (L) = 5 meters
- Head (H) = 0.4 meters
Applying the Francis formula: Q = 3.33 (5 – 0.2 0.4) * 0.4^(3/2)
Q ≈ 1.68 m³/s
This calculation illustrates how the formula accounts for end contractions by subtracting 0.2H from the crest length.
How To Calculate Flow Over a Weir?
Calculating flow over a weir involves several steps:
- Identify the weir type: Rectangular, triangular, or trapezoidal.
- Measure the weir dimensions: Crest length, notch angle (for V-notch weirs), or side slopes (for trapezoidal weirs).
- Determine the head: Measure the water depth above the weir crest.
- Select the appropriate formula: Based on weir type and conditions.
- Apply the formula: Insert measured values and calculate.
- Adjust for real-world factors: Consider discharge coefficients and end contractions.
Given:
- Bottom width (b) = 2 meters
- Side slope (z) = 1:1
- Head (H) = 0.5 meters
The formula for trapezoidal weirs is: Q = 1.86 (b + 0.4H) H^(3/2)
Plugging in the values: Q = 1.86 (2 + 0.4 0.5) * 0.5^(3/2)
Q ≈ 1.43 m³/sHow to Calculate Flow Through a V-Notch Weir?
Q = 2.49 tan(θ/2) H^(5/2)
Where:
- θ = Notch angle in degrees
- H = Head above the V-notch vertex
V-notch weirs, also known as triangular weirs, are particularly useful for measuring low flow rates with high accuracy.
Let’s calculate the flow through a 90° V-notch weir:
Given:
- Notch angle (θ) = 90°
- Head (H) = 0.3 meters
Applying the formula: Q = 2.49 tan(90/2) 0.3^(5/2)
Q ≈ 0.084 m³/sReferences
- U.S. Geological Survey. “Measurement of Peak Discharge at Dams by Indirect Methods.” https://pubs.usgs.gov/twri/twri3-a5/
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