Calculating Flow Over a Weir

Understanding how to calculate flow over a weir is essential for anyone working in drainage, SuDS, river engineering, or flood risk management. Whether you’re designing a small site control structure or assessing conveyance in an open channel, weirs provide a simple, reliable way to measure and regulate flow. This guide breaks down the principles, equations, and practical considerations behind weir flow calculations—without drowning you in theory.

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What Is a Weir and Why Do We Use It?

A weir is a hydraulic control structure placed across an open channel to create a predictable relationship between upstream water level and discharge. Because the geometry is fixed and the flow behaviour is well understood, weirs are widely used for:
- Flow measurement
- Level control
- Flood attenuation
- Spillways and overflow structures
- SuDS features such as basins, ponds, and swales

The key advantage is simplicity: once you know the water head over the crest, you can calculate the flow with good accuracy.

Types of Weirs Used in Flow Calculation

Weir Type	Description	Typical Use
Rectangular weir	Straight horizontal crest	Channels, spillways, site control structures
V‑notch (triangular) weir	Crest shaped as a V, usually 90°	Low flows, SuDS, monitoring
Cipolletti weir	Trapezoidal shape	Improved accuracy over rectangular weirs
Broad‑crested weir	Wide flat crest	Rivers, flood structures, culvert inlets

The Core Principle: Head–Discharge Relationship

Q = C × L × H^(3/2)

Calculating Flow Over a V‑Notch Weir

Q = 1.38 × H^(5/2)

Example: H = 0.15 m → Q = 0.013 m³/s (13 L/s)

Calculating Flow Over a Rectangular Weir

Q = C × L × H^(3/2)

Example: L = 0.5 m, H = 0.2 m, C = 1.7 → Q = 0.076 m³/s (76 L/s)

Broad‑Crested Weirs

Q = C × L × H × √(2gH)

Practical Considerations

- Free vs submerged flow
- Crest condition
- Approach velocity
- Upstream measurement location
- Debris and maintenance

When to Use Each Weir Type

Situation	Best Weir Type	Why
Low flows	V‑notch	High sensitivity
Medium–high flows	Rectangular	Simple, robust
Large rivers	Broad‑crested	Stable at high flows
Limited space	Cipolletti	Self‑compensating geometry

Conclusion

Calculating flow over a weir is a fundamental skill in drainage and hydraulic design. By understanding the head–discharge relationship and selecting the right weir type, you can produce reliable flow estimates for SuDS features, channels, and flood structures.

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