THE UNIVERSITY OF THE WEST INDIES,ST. AUGUSTINE.DEPARTMENT OF CIVIL & ENVIRONMENTAL ENGINEERING

Kirk Woo Chong809003758Group: J

Table of Contents

OBJECTIVES...................................................................................................................3

INTRODUCTION..............................................................................................................3

PROCEDURE..................................................................................................................3

Equipment....................................................................................................................3

Method..........................................................................................................................4

THEORY..........................................................................................................................4

RESULTS.........................................................................................................................6

SAMPLE CALCULATIONS..............................................................................................7

DISCUSSION AND ANALYSIS OF RESULTS..............................................................10

Froude Number at Broad Crested Weir Edge.............................................................10

Magnitude of Flow Rate and Effect on Discharge Coefficient Cd................................10

Relationship Between Cd and Flow Rate....................................................................10

Magnitude of Flow Rate and Effect on Velocity Coefficient Cv...................................10

Relationship Between Cv and Flow Rate.....................................................................10

Pattern of Water Over Weir........................................................................................11

Errors & Precautions..................................................................................................13

CONCLUSION...............................................................................................................13

REFERENCES...............................................................................................................13

OBJECTIVES

I. To determine characteristics of the flow over broad crested weir at various

discharge.

II. To calibrate the broad crested weir for a free flowing condition.

INTRODUCTION

A weir is commonly used in open channels for controlling upstream water levels

and measuring discharge. For both tasks it acts as an obstruction which promotes a

condition of minimum specific energy in sub critical flow. When used for the latter

purpose all weirs must be calibrated because theoretical predictions of discharge are

rendered inadequate by the effects of viscosity and the variations of flow geometry with

upstream depth. Broad crested weirs are generally constructed from reinforced

concrete and are widely used for flow measurement and regulation of water depth in

rivers, canals and other natural open channels.

PROCEDURE

Equipment

o A 305 mm rectangular flume with broad crested weir

o A gauge with graduated vernier scale

o Measuring tank with scale

o Stopwatch

Method

1. The flow rate was adjusted to give the required head of water over the weir to

allow steady conditions to develop.

2. The vernier scale was read when the tip of the gauge just pierced the water

surface upstream of the weir. The difference between this reading and the

reading obtained when the tip just touched the crest of the wave was the head of

water over the weir.

3. The vernier scale was read when the tip of the gauge just pierced the water

surface at the weir crest edge elevation. The difference between this reading and

the reading obtained when the tip just touches the crest of the weir was the

critical depth

4. The vernier scale was used to measure the water depth on the downstream side

of the crest of the weir.

5. The profile of the nappe on the crest of the weir was investigated for various

discharges.

6. The discharge was measured by noting the time taken to fill a known mass.

7. The process was repeated for six different head and discharge readings.

THEORY

A weir in general can take on many shapes, however broad crested weirs

operate more effectively than their sharp crested counterparts under higher downstream

water levels, and can be used to measure the discharge of rivers since the parallel flow

caused by the weir allows it to be accurately analyzed by the use of energy principles

and critical depth relationships.

It works on the principle that subcritical flow upstream of the weir moves over the

obstruction and this height of the weir causes critical flow, accelerating the liquid which

then transitions into supercritical nappe after the weir is crossed downstream. This

critical depth required to cause critical flow is not easily measured because its exact

location is not easy to determine and may vary with flow rate. However, the upstream

depth can be used to determine the flow rate through mass conservation which is a

more reliable measurement.

Experimentally, broad crested weirs can be used as a flow rate-measuring device

and has the advantage that it is simple to construct and has no edge that can wear and

thus alter the coefficient.

Using Bernoulli’s equation, it can be derived that Q=1.705 B[( v122 g )+H 1]1.5

.

Furthermore, the discharge is related to a coefficient of discharge for the weir, Cd,

defined by the equationQ=Cd Cv( 23 )B√ 2g3 H132

.

FIGURE 1

RESULTS

Run Number

Upstream Depth, Du / m

Critical Depth, Dc / m

Downstream Depth, Dd / m H1 / m

1 0.1300 0.0036 0.01070.126

5

2 0.1687 0.0201 0.01930.148

6

3 0.1811 0.0274 0.02390.153

7

4 0.1935 0.0343 0.03300.159

3

5 0.2057 0.0417 0.03610.164

1

6 0.2184 0.0513 0.04470.167

1

Table 1 showing the various depths associated witht the weir

Run Number

Average Time / s

Mass / kg

Volume / m3

Discharge / m3s-1

Upstream Velocity, vu /

ms-1

Critical Velocity, vc /

ms-1

1 31.31 50 0.05 0.0016 0.0403 0.1868

2 13.68 100 0.10 0.0073 0.1422 0.4437

3 9.60 100 0.10 0.0104 0.1887 0.5188

GRAPH 3

4 7.41 100 0.10 0.0135 0.2288 0.5800

5 6.40 100 0.10 0.0156 0.2492 0.6393

6 4.57 100 0.10 0.0219 0.3290 0.7095

Table 2 showing calcuated data for the weir

Run Number

Total Energy Head, ET / J

Ideal Discharge / m3s-1 Cd Cv

Critical Froude Number

1 0.1106 0.02340.068

21.00

1 7.889

2 0.0728 0.03010.243

01.01

0 2.694

3 0.0791 0.03190.326

91.01

8 2.402

4 0.0850 0.03390.398

51.02

5 2.226

5 0.0772 0.03550.439

61.02

9 1.925

6 0.1000 0.03730.587

61.05

0 1.974

Table 3 showing weir data specifics

SAMPLE CALCULATIONS

All readings for distance were taken in inches so a conversion factor of 0.0254 was

used to convert it to meters.

Height of entire channel, Dch = 0.0732 m

Height of channel from crest of weir = 0.1765 m

Width of weir = 0.3048m

(Note: the Vernier scale was in reverse, therefore the smaller the reading, the greater

the actual depth)

Upstream Depth = Upstream height – Total channel height

= 0.2032 – 0.0732 = 0.1300 m

Critical Depth = Crest height – Height of channel from crest of weir

= 0.1801 – 0.1765 = 0.0036 m

Volume of Water, V

Density = MassVolume

Volume =MassDensity

V = 501000

=¿0.05m3

H1 = Upstream depth – Critical depth

= 0.1300 – 0.0036 = 0.1265 m

Actual Discharge, Qa = VolumeTime

= 0.0531.31

= 0.0016 m3s-1

Upstream velocity, v1

Q=Av1 v1 = QA

v1 = 0.0016

(0.1300 x0.3048) = 0.0396 ms-1

Critical Velocity, Vc

Q=Av1 Vc = QAc

Vc = 0.0016

(0.0036 x 0.3048) = 1.473 ms-1

Ideal Discharge, Qt = 1.705B [ v122 g+H 1]32

= 1.705(0.3048) [ 0.0396219.62+0.1265]

32 = 0.0234 m3s-1

Co-efficient of Discharge, Cd = QaQ t

= 0.00160.0234

= 0.0682

Velocity Co-efficient, Cv Q = CdC v23B√ 2g3 H 1

32

Cv = Q /(Cd 23 B√ 2 g3 H 1

32) = 0.0016 ¿(0.0682x 0.67 x0.3048√ 19.623 x0.1265

32)

= 1.001

Froude Number, Fr = vc

√g Dc

= 1.473

√9.81x 0.0036 = 7.889

Total Energy Head, Ec –

Ec¿ [ vc22g ] = [ 1.473219.62 ] = 0.1106 J

DISCUSSION AND ANALYSIS OF RESULTS

Froude Number at Broad Crested Weir Edge

The Froude numbers calculated at the edge of the broad crested weir i.e. the

critical Froude numbers fell well out of the expected range. Since the flow upstream of

the weir was subcritical and the flow at the edge of the weir theoretically is supposed to

be critical, a value close to 1 was expected. However, the critical Froude numbers

obtained ranged from 1.974 to 7.889. This may have been due to erroneous

measurement or calculation. The only sense that could be made of these very high

Froude numbers is that the liquid achieved a very high velocity hence a high energy

(both total and specific).

Magnitude of Flow Rate and Effect on Discharge Coefficient Cd

It was found that as the magnitude of the flow rate increased, so did the

discharge coefficient. This may have been due to the shape of the weir which had a

rectangular control section. Since the height of the water increased with increased flow,

more friction lossed may have occurred.

Relationship Between Cd and Flow Rate

Experimental data showed that Cd increased with increasing flow rate.

Magnitude of Flow Rate and Effect on Velocity Coefficient Cv

It was found that as the magnitude of the flow rate increased, so did the velocity

coefficient.

Relationship Between Cv and Flow Rate

Experimental data showed that Cv increased with increasing flow rate.

Pattern of Water Over Weir

Test no.1

Test no.2

Test no.3

Test no.4

Test no.5

Test no.6

Errors & Precautions

Error due to parallax in reading the vernier scale and tank.

The flow may not have been fully stabilized when the readings were taken.

Reaction time error when using the stopwatch.

It was assumed that the density was for pure water however it should be noted

the water in the experiment was brown indicating it may have contained other

substances and impurities which may have caused erroneous momentum and

energy values.

CONCLUSION

Within the limits of experimental error, it was found that both the discharge and

velocity coefficient are directly influenced by the flow rate. Also, nappe patterns of flow

were observed.

REFERENCES

Borthwick, M., Chadwick, A., Morfett, J. 2004. Hydraulics in Civil and

Environmental Engineering. Taylor & Francis.

Massey, Bernard. 2006. Mechanics of Fluids. Taylor & Francis