Question

Describe the measurements of discharge at weirs and its potential errors associated with indirect methods weir in real-world application setting.

Answer 1

Weir-  A weir is a barrier across width of a river or stream that alters characteristics of flow and usually results in change in height of water level. Several types of weirs are designed for application in natural channels and laboratory flumes. Weirs can be broad-crested, short-crested, or sharp-crested.

Sharp-crested weirs, commonly referred to as notches, are manufactured from sharp-edged thin plates. The relationship between the flow rate and water depth above the weir can be derived by applying the Bernoulli’s equation and by making some assumptions with regard to head loss and pressure distribution of the flow passing over the weir.

A coefficient of discharge needs to be determined experimentally for each weir to account for errors in estimating the flow rate that is due to these assumptions.

The coefficients of discharge are determined by measuring the height of the water surface above the notch base and the corresponding flow rate. The general features of the flow can be determined by direct observation.

Measurement of discharge :  

The following equipment is required to perform the flow over weirs experiment:

• F1-10 hydraulics bench;
• F1-13 rectangular and triangular weirs;
• Vernier height gauge; and
• Stopwatch

The depth of water above the base of a weir is related to the flow rate through it; therefore, the weir can be used as a flow measuring device. The relationships of flow over weirs can be obtained by applying the energy equation from a point well upstream of the weir to a point just above the weir crest. This approach requires a number of assumptions, and it yields the following results:

• for a triangular weir :

• for a rectangular weir :

where:

Q : flow rate;

H : height above the weir base;

b : width of rectangular weir (R-notch);

: angle of triangular weir (V-notch);

C_d: discharge coefficient to account for the effects of simplifying assumptions in the theory, which has to be determined by experiment [9].

Figure 9.2: (a) Triangular weir, (b) Rectangular weir

• for a V-notch

• for a R-notch:

by calculating coeficient of discharge we can calculate discharge of a weir .

PRACTICAL APPLICATION

Weirs are commonly used to measure or regulate flow in rivers, streams, irrigation canals, etc. Installing a weir in an open channel system causes critical depth to form over the weir. Since there is a unique relationship between the critical depth and discharge, a weir can be designed as a flow-measuring device. Weirs are also built to raise the water level in a channel to divert the flow to irrigation systems that are located at higher elevations.