A weir is a hydraulic structure constructed across an open channel or river to raise the upstream water level and to measure or regulate the discharge of water. Water flows over the crest of the weir under the action of gravity and falls freely on the downstream side.

Unlike an orifice or mouthpiece, where water flows through an opening under pressure, a weir allows water to flow over a barrier. The quantity of water flowing over the crest depends primarily on the head of water above the crest.

A broad-crested weir is one in which the width of the crest in the direction of flow is sufficiently large compared with the depth of water flowing over it. Such weirs provide stable flow conditions and are widely used for discharge measurement in open channels.

Everyday Intuition

The principle of a weir can be observed in many natural and engineering systems.

• Water flowing over a small dam.
• Irrigation canal regulators.
• Overflow structures in reservoirs.
• River barrages.

In each case, the height of water above the crest determines the amount of water flowing downstream.

The Weirs experiment demonstrates how the discharge over a hydraulic structure can be determined by measuring the upstream water level.

Experimental Relevance

The objective of the Weirs experiment is to determine the discharge over a broad-crested weir and evaluate its coefficient of discharge.

As water approaches the crest,

• The flow depth decreases,
• The flow velocity increases,
• Potential energy is converted into kinetic energy.

The discharge over the weir depends on the head of water above the crest.

The experiment involves:

• Measuring the upstream head,
• Determining the actual discharge,
• Calculating the theoretical discharge,
• Evaluating the coefficient of discharge.

The experiment also demonstrates the relationship between discharge and the head over the crest.

Mathematical Formulation

The flow over a broad-crested weir is governed by the principles of conservation of mass and conservation of energy.

Bernoulli's equation is

$$\frac{P}{\rho g} + \frac{V^2}{2g} + Z = \text{Constant}.$$

Hydraulic analysis shows that for maximum discharge over the crest,

$$h=\frac{2}{3}H,$$

where

• $H$ = Total head above the crest,
• $h$ = Depth of flow over the crest.

The theoretical discharge over a broad-crested weir is

$$Q_t=1.705LH^{3/2},$$

where

• $Q_t$ = Theoretical discharge,
• $L$ = Length of the crest,
• $H$ = Head over the crest.

The actual discharge is obtained experimentally as

$$Q_a=\frac{AV}{t},$$

where

• $A$ = Plan area of the measuring tank,
• $V$ = Rise of water level in the measuring tank,
• $t$ = Collection time.

The coefficient of discharge is

$$C_d=\frac{Q_a}{Q_t}.$$

The coefficient of discharge accounts for frictional and hydraulic losses and represents the efficiency of the weir as a flow-measuring device.

Application to the Broad-Crested Weir Apparatus

The experimental setup consists of

• An open channel,
• A broad-crested weir,
• A point gauge for measuring the upstream water level,
• A measuring tank for determining the actual discharge.

Water flows through the channel and passes over the crest of the weir.

As the head over the crest increases,

• The discharge increases,
• The velocity over the crest increases,
• The flow adjusts to critical conditions near the crest.

The upstream head is measured using the point gauge.

The actual discharge is determined by collecting water in a measuring tank over a known period of time.

The theoretical discharge is calculated from the broad-crested weir equation, and the coefficient of discharge is obtained by comparing the actual and theoretical values.

A graph of discharge versus

$$H^{3/2}$$

is commonly plotted to study the discharge characteristics of the weir.

Engineering Significance

Weirs are widely used for measuring and controlling the flow of water in open channels.

Important applications include:

• Irrigation canals,
• River gauging stations,
• Reservoir spillways,
• Water treatment plants,
• Flood-control structures,
• Hydroelectric projects,
• Hydraulic laboratories.

The Weirs experiment demonstrates the practical application of hydraulic principles to open-channel flow measurement and provides essential knowledge for the design and operation of water resources engineering systems.