Short Answer:

A weir measures flow in open channels by forcing the water to flow over a specially shaped notch or barrier, where the height of the water above the bottom of the weir (called head) is directly related to the flow rate. By measuring this head, the discharge can be calculated using standard formulas.

The weir works on the principle that higher water levels above the weir crest mean more flow. Common types include rectangular weirs, V-notch weirs, and cipolletti weirs, and they are widely used in irrigation, canals, drainage, and wastewater systems.

Detailed Explanation:

How a weir measures flow in open channels

A weir is a hydraulic structure built across an open channel to measure or control the flow of water. It creates an obstruction in the path of water, forcing it to pass over the crest of the weir. The basic idea is that the height of water flowing over the weir (called the head) is related to the flow rate. By measuring this head, engineers can calculate how much water is passing through the channel.

Weirs are simple, cost-effective, and commonly used in civil engineering for managing water in canals, irrigation systems, streams, rivers, and treatment plants.

Principle of Operation

Weirs operate based on flow-over-obstacle theory and are derived from Bernoulli’s equation and continuity equation. When water flows towards a weir:

It accumulates and builds up a head above the crest (top edge) of the weir.
As water flows over, it accelerates, converting potential energy (due to head) into kinetic energy.
The rate of flow depends on the height of water above the crest, the shape of the weir, and gravitational acceleration.

For a rectangular weir, the general discharge formula is:

Q=Cd⋅L⋅H3/2Q = C_d \cdot L \cdot H^{3/2}Q=Cd⋅L⋅H3/2

Where:

QQQ = discharge (m³/s)
CdC_dCd = coefficient of discharge
LLL = length of the weir crest
HHH = head (height of water above crest)

For a V-notch weir, the formula becomes:

Q=815⋅Cd⋅tan⁡(θ2)⋅H5/2Q = \frac{8}{15} \cdot C_d \cdot \tan\left(\frac{\theta}{2}\right) \cdot H^{5/2}Q=158⋅Cd⋅tan(2θ)⋅H5/2

Where θ\thetaθ is the notch angle.

Types of Weirs

Rectangular Weir: Simple straight weir, suitable for large flows.
V-Notch Weir: Triangular shape, more accurate for small flows.
Cipolletti Weir: Trapezoidal shape, self-corrects for end contraction errors.
Broad-Crested Weir: Used for wider channels with slow-moving water.

Measuring Procedure

A staff gauge or point gauge is installed upstream of the weir to measure the head accurately.
The measurement is taken at a specific distance upstream (usually 3–4 times the head) to avoid turbulence.
The flow rate is calculated using the standard formula corresponding to the weir type.

Applications in Civil Engineering

Irrigation canals to regulate water usage
Stormwater drains to monitor runoff
Sewage systems for flow monitoring
Hydrological studies in rivers and streams
Wastewater treatment for flow measurement and load assessment

Advantages

Simple to construct and use
No moving parts
Suitable for a wide range of flows
Provides visual observation of flow
Can be used for continuous monitoring

Limitations

Accuracy depends on proper installation and maintenance
Sediment buildup can affect measurements
Not ideal for very low-head conditions unless using V-notch
Flow must be free and not submerged for accurate readings

Conclusion:

A weir measures flow in open channels by creating an obstruction and allowing water to flow over its crest. The height of water above the crest is directly related to the discharge, which can be calculated using standard formulas. Civil engineers use weirs widely in water management systems for reliable and simple flow measurement.