understanding Weirs in Fluid Mechanics

Table of Contents

Weirs are one of the simplest and most practical tools in open channel flow. In many rural places such as rural irrigation systems, remote streams, small treatment plants; there’s no budget for sensors or flow meters. A weir gives accurate flow data using gravity and geometry.

What is a Weir?

A weir is a low dam or barrier built across a river or channel to control water flow. It forces water to pass over or through a specific opening, creating predictable flow patterns that engineers can measure and manage.

Think of a weir like a spillway on a bathtub. When you fill your tub with water, once it reaches a certain level, it spills over the edge at a controlled rate. A weir works the same way.

It’s a controlled spill point that keeps water from flowing freely and unpredictably downstream. The difference is their height and purpose.

Dams are massive structures to hold the flow and act as a storage for large reservoirs.

Weirs are smaller but it acts as a device to determine the flow rate and water level.

Basic Concepts of Weir

Head (H)
Vertical Distance from water surface to weir crest.

Discharge (Q)
Volume of fluid flowing per unit of time.

Types of Weir

Rectangular Weir

The simplest and most common type. Water flows over a rectangular opening. Easy to construct and easy to calculate flow through.

Straight notch with horizontal crest
Best for large, steady flows

$Q=\frac{2}{3}C \sqrt{2g}LH^{3/2}$

where:
Q – discharge or flow rate
C – coefficient of discharge
b – width of the weir opening
g – gravitational acceleration
H – head or the height of water above the weir crest

Triangular Weir (V-notch)

Water flows through a V-shaped notch cut into the weir. These are extremely accurate for measuring small flows because the V shape creates a wider opening for larger flows, and narrower opening for smaller flows.

$Q=\frac{8}{15}C\sqrt{2g}tan \frac{\theta}{2}H^{5/2}$

Triangular Weir, a type of weir based on shapes

V-shape opening (usually 90 degrees)
More accurate for low flows

Trapezoidal Weir (Cipolleti)

$Q=Q_{rectangle}+Q_{triangle}$

$Q=\frac{2}{3}C\sqrt{2g}LH^{3/2}+\frac{8}{15}C\sqrt{2g}tan \frac{\theta}{2}H^{5/2}$

Trapezoidal Weir, a type of weir based on shapes

Combines advantages of rectangular and v-notch

Design Consideration

1. Choose the right shape.

Rectangular	Best for moderate to high flows where a simple structure suffices
V-notch	Ideal for low flows or when the channel is shallow
Trapezoidal	Useful when the flow regime spans from low to high and a single weir can cover the entire range.

2. Determine the discharge coefficient Cd

Empirical studies (e.g., Chow, Maidment & Mays, 2007) suggest Cd values close to 0.62 for rectangular weirs with sharp crests. Field calibration, where feasible, can refine this value.

3. Account for upstream conditions

The weir assumes a rectangular channel cross‑section and that the water surface upstream is flat. In practice, channel roughness, sediment, and upstream flow variations introduce error; measuring the upstream water level with a simple staff gauge can help mitigate this.

4. Material Selection

Concrete is the most common choice, but in some remote areas timber or even packed earth can be used but the weir will not be for long-term.

5. Maintenance

Periodic inspection is needed to clear the sediments and trash that may accumulate at the crest.

Conclusion:

A weir is a simple yet useful solution born from 19th-century hydraulic research, that’s why it is still relevant today. For civil engineers working on rural irrigation, remote streams, and small treatment plants, a well-designed delivers reliable flow data without the overhead of modern sensors. Many projects before have shown that when budgets are tight but the need for accurate water management is high, a simple weir can be a game‑changer.