TABLE OF CONTENT

CONTENT PAGE

ABSTRACT / SUMMARY 2

INTRODUCTION 2-3

AIMS / OBJECTIVE 4

THEORY 4-6

APPARATUS 7

PROCEDURE 8

RESULTS 9

CALCULATION 10-11

DISCUSSION 12

CONCLUSION 13

RECOMMENDATION 13

REFERENCES 14

APPENDICES 14

1

ABSTRACT / SUMMARY

From the experiment that have been done, we are going to determine the characteristics of a

rectangular notch and triangular ( vee ) notch. The flow pattern of water from both notches

are being observed. Other than that we are going to determined the best discharged coefficient

between both notches. The discharged coefficient are going to be determined from the

volumetric flowrate calculated from the time taken and the volume collected.

INTRODUCTION

Fluids mechanics has develop as an analytical discipline from the application of the classical

laws of statistics, dynamics and thermodynamics, to situations in which fluids can be treated

as continuous media. The particular laws involved are those of the conservation of mass,

energy and momentum and, in each application, these laws can be simplified in an attempt to

describe quantitatively the behaviour of the fluid.

A weir is an opening in the sidewall of a tank at top. The stream of liquid coming out the weir

is known as a nappe, sheet, or vein. There is no difference between a notch and weir except

that the former is a small structure and has sharp edges. A weir is generally an overflow

structure, with a broad crest, built across an open channel. The terms air and weirs are used

synonymously in general. The top of weir wall over which the liquid flows is known as the

sill or crest. The head under which the weir is discharging is measured from the crest to the

free surface. A weir or notch is generally used for measuring the flow of liquids. [1]

In this experiment, we are using the rectangular weirs and triangular weirs. Rectangular weirs

and triangular or v-notch weirs are often used in water supply, wastewater and sewage

systems. They consist of a sharp edged plate with a rectangular, triangular or v-notch profile

for the water flow.Broad-crested weirs can be observed in dam spillways where the broad

edge is beneath the water surface across the entire stream. Flow measurement installations

with broad-crested weirs will meet accuracy requirements only if they are calibrated. [3]

2

There are different types of weir. It may be a simple metal plate with a V-notch cut into it, or

it may be a concrete and steel structure across the bed of a river. A weir which causes a large

change of water level behind it, compared to the error inherent in the depth measurement

method, will give an accurate indication of the flow rate. Some of them are :

i) Broad-crested weir

A broad-crested weir is a flat-crested structure, with a long crest compared to the flow

thickness (Chanson 1999,2004, Henderson 1966, Sturm 2001). When the crest is “broad”, the

streamlines become parallel to the crest invert and the pressure distribution above the crest is

hydrostatic. The hydraulic characteristics of broad-crested weirs were studied during the 19th

and 20th centuries. Practical experience showed that the weir overflow is affected by the

upstream flow conditions and the weir geometry. [2]

ii) Sharp crested weir (fayoum weir)

A sharp-crested weir allows the water to fall cleanly away from the weir. Sharp crested weirs

are typically 1/4" or thinner metal plates. Sharp crested weirs come in many different shapes

such as rectangular, V-notch and Cipolletti weirs. [2]

iii) Combination weir

The sharp crested weirs can be considered into three groups according to the geometry of

weir: a) the rectangular weir, b) the V or triangular notch and c) special notches, such as

trapezoidal, circular or parabolic weirs. For accurate flow measurement over a wider range of

flow rates, a combination weir combines a V-notch weir with a rectangular weir. This is

typically used in pipes ranging from 4" to 15" in diameter. [2]

3

AIMS/ OBJECTIVE

i. To determine the characteristics of a rectangular notch and triangular ( vee ) notch.

ii. To determine the values of discharged coefficient for both notches.

THEORY

i) Rectangular Notch. [4]

A rectangular notch in a thin square edged weir plate installed in a weir channel as shown

in figure 2.

Figure 2 Rectangular Notch

Consider the flow in an element of height H at a depth h below the surface. Assuming that the

flow is everywhere normal to the plane of the weir and that the free surface remains

horizontal up to the plane of the weir.

In practice the flow through the notch will not be parallel and therefore will not be normal to

the plane of the weir. The free surface is not horizontal and viscosity and surface tension will

have an effect. There will be a considerable change in the shape of the nappe as it passes

through the notch with curvature of the stream lines in both vertical and horizontal planes as

indicated in Figure 3, in particular the width of the nappe is reduced by the contractions at

each end.

4

Figure 3 Shape of a Nappe

Qt = Cd 2/3 b √ (2g) H3/2

Where

Qt = volume flow rate ( m/s )

H = height above notch base (m)

b = width of rectangular notch ( 0.03 m)

Cd = the discharge coefficient, which has to be determined by experiment

The discharge from a rectangular notch will be considerably less, approximately 60%, of the

theoretical analysis due to these curvature effects. A coefficient of discharge Cd is therefore

introduced so that

Cd = 3Qt .

2b√(2g) H3//2

However, Cd is not a true constant tending towards a constant only for large heads and a low

velocity of approach in the weir channel.

5

ii) Triangular ( vee ) Notch [4]

Figure 4 Triangular or V Notch

Where

Qt = volume flow rate

H = height above notch base

B = width of rectangular notch

θ = angle of the Vee in the triangular notch

Cd = the discharge coefficient, which has to be determined by experiment

Thus,

Cd = 15Qt .

8 tan (θ/2) √ (2g) H5/2

For a rectangular notch the rate of discharged is proportional to the liquid depth raised to

power 1.5 and for the triangular notch to a power of 2.5. A triangular notch will therefore

handle a wider range of flowrates. It can be shown that the notch must have curved walls

giving a large width to the bottom of the notch and a comparatively small width towards the

6

Qt=Cd8

15tan( θ

2 )√2 gH52

top. The weir is frequently installed for controlling the flow within the unit itself, for instance

in a distillation column or reactor. [5]

APPARATUS

1. The F1-10 hydraulic bench which allows us to measure flow by timed volume

collection.

2. The F1-13 Stilling Baffle.

3. The F1-13 Rectangular and Vee notches.

4. Vernier Height gauge (supplied with F1-13).

5. Stop watch.

6. Spirit level

7

PROCEDURE

1. The hydraulic bench was positioned so that its surface is horizontal (necessary because

flow over notch is driven by gravity).

2. The rectangular notch plate was mounted into the flow channel and the stilling baffle

was positioned as shown in the diagram.

3. In order to measure the datum height (with the height gauge) of the base of the notch,

the instrument carrier was positioned in the opposite way round from that shown in the

diagram.

4. Then carefully the gauge was lowered until the point was just above the notch base

and the coarse adjustment screw was locked.

5. Then, using the fine adjustment, the gauge was adjusted until the point just touched

the notch bottom and a reading would be taken. Here we must be careful not to

damage the notch.

6. The instrument carrier was mounted as shown in the diagram and it would be

approximately located half way between the stilling baffle and the notch plate.

7. The bench control valve was opened and water was admitted to the channel.

8. The general features of the flow were observed and recorded.

9. To take an accurate height reading, the fine adjustment was used to lower the gauge

until the point just touched its reflection in the surface and the water flow are waited

till its flow are steady.

10. The flow rate was ensured large enough to prevent the outflow from the notch

“clinging” to the notch plate. It was projected clear of the plate.

11. The time are started when the ball valve close the tank outflow and stop until the

water level reach 3 litre.

12. After determined the volume collected, the valve was opened again at the end of the

measurement.

13. This procedure was repeated 6 times by having opened the bench valve further, to

produce an increase in depth of approximately 5 mm. The level was checked in stable

condition before taking readings.

14. The flowrates of the water flor are calculated.

8

15. The rectangular notch plate was replaced with the Vee notch plate and procedure

above was repeated.

RESULTS

RECTANGULAR NOTCH

Height, H

( m3 )

H3/2 Volume ( m3

)

Time ,t ( s ) Flowrate, Q (

m3/s )

Discharged

coefficient. Cd

0.005 3.536 x 10-4 3 x 10-3 32 9.375 x 10-5 2.993

0.010 1.000 x 10-3 3 x 10-3 24 1.250 x 10-4 1.411

0.015 1.837 x 10-3 3 x 10-3 15 2.000 x 10-4 1.229

0.020 2.828 x 10-3 3 x 10-3 9 3.330 x 10-4 1.329

0.025 3.953 x 10-3 3 x 10-3 8 3.750 x 10-4 1.071

0.030 5.196 x 10-3 3 x 10-3 6 5.000 x 10-4 1.086

TRIANGULAR ( VEE ) NOTCH

Height, H

( m )

H5/2 Volume ( m3

)

Time ,t ( s ) Flowrate, Q (

m3/s )

Discharged

coefficient.

Cd

0.005 1.768 x 10-6 3 x 10-3 208 1.442 x 10-3 3.453

0.010 1.000 x 10-5 3 x 10-3 130 2.308 x 10-5 0.977

0.015 2.750 x 10-5 3 x 10-3 65 4.615 x 10-5 0.709

0.020 5.675 x 10-5 3 x 10-3 36 8.333 x 10-5 0.602

0.025 9.882 x 10-5 3 x 10-3 19 1.579 x 10-4 0.676

0.030 1.559 x 10-4 3 x 10-3 13 2.308 x 10-4 0.627

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SAMPLE CALCULATION

RECTANGULAR NOTCH

b = 0.03 m

g = 9.81 m/s2

For H = 0.005 m

H 3/2 = ( 0.05 )3/2

= 3.536 x 10-6

Volumetric flowrate, Q = volume, m3

time, s

= 3× 10−3 m3

32 s

= 9.375 x 10-5 m3/s

Discharged coefficient, Cd = 3 Q

2 b √2 g H32

= 3× 9.375 ×10−5

2× 0.03√2× 9.81× 3.536 ×10−6

= 2.993

10

TRIANGULAR ( VEE ) NOTCH

θ = 90O

g = 9.81 m/s

For H = 0.005 m

H 5/2 = 1.768 x 10-6

Volumetric flowrate, Q = volume, m3

time, s

= 3 × 10−3 m3

208 s

= 1.442 x 10-5 m3/s

Discharged coefficient, Cd =

15 Q

8 tanθ2

√2g H52

= 15 × 1.442 × 10−5

8 tan902

√2g × 1.768× 10−6

= 3.453

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DISCUSSION

From the experiment, we are about to determine the discharged coefficient of the both

rectangular and the triangular notches. The discharged coefficient for the rectangular notch

are influenced by its H and also its volumetric flow rate while the triangular notch are

influenced by its θ, H and also its volumetric flow rate.

From the results, we can see that the volumetric flow rate of both notches are increased. These

showed that the water outflow increased as the H increased. These is supposed to happen as

the water level increased, the water outflow from the notch should be increased over time. But

from the discharged coefficient, we can see that the value of the both notches are not stable.

This may be from the friction at the head of the notches during the starter of the experiment.

The friction will effect the time taken to collected 3 litres of the water. Thus it will effect the

volumetric flow rate and also the discharged coefficient as the volumetric flow rate influenced

the value of the Cd.

These deviations of values are contributed by the errors during handling the experiment. If we

take it as overall errors, most of errors occurred when step of taking the height started. First,

we have to be careful about the height of datum. For convenience, it is recommended to take

your datum height as zero.Other than that, the time should be taken at least 3 times to take the

average so that the error during the time taken can be minimized. The purpose of doing it is to

minimize the errors. Besides that, we noticed that there is inconsistency in our readings

because of the error that occur.

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CONCLUSION

i) Rectangular weir has wide range variations of Cd. This is because this notch has

width,b with 0.03 m.

ii) V-notch has small range of variations for the value of Cd. This is because this

notch has an angle at its bottom where about 90o. This angle might effect the

values of flowrate and Cd.

iii) Therefore the best discharged coefficient, Cd is from the V-notch compared to

rectangular notch.

RECOMMENDATION

i) The data that was observed in the experiment that was time gain should be taken

twice. This can avoid the very wide deviation because of only take once of each

observation.

ii) Take care not to allow spillage to occur over the plate top adjacent to the notch. If

this happened, it would effect the collection of known volume.

iii) Once the data were taken, the procedure cannot be reverse to find the value of time

collection by adjusting the height. This would affect the value of height datum.

The height datum must be constant and the observation should be done once round

for the little increment of height especially for V-notch.

iv) The readings of height should be taken carefully by avoiding sight error. The time

collection should be taken much appropriately.

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REFERENCES

1. http://www.gitam.edu/eresource/environmental/murali/notches.htm

2. http://en.wikipedia.org/wiki/Weir

3. http://www.engineeringtoolbox.com/weirs-flow-rate-d_592.html

4. http://www.cussons.co.uk/SOFTWARE/Part5/PART5.HTM

5. Fluid Flow, Heat Transfer and Mass Transfer Volume 1, Sixth Edition, Coulson &

Richardson’s Chemical Engineering by J M Coulson & J F Richardson with J R

Backhurst and J H Harker.

APPENDICES

14

WeirsPosted in Hydraulics | Email This Post

Weir is defined as a barrier over which the water flows in an open channel. The edge or surface over which the water flows is called the crest. The overflowing sheet of water is the nappe.If the nappe discharges into the air, the weir has free discharge. If the discharge is partly under water, the weir is submerged or drowned.

Types of Weirs.

A weir with a sharp upstream corner or edge such that the water springs clear of the crest is a sharp-crested weir.All other weirs are classed as weirs not sharp crested. Sharp-crested weirs are classified according to the shape of the weir opening, such as rectangular weirs, triangular or V-notch weirs, trapezoidal weirs, and parabolic weirs. Weirs not sharp crested are classified according to the shape of their cross section, such as broad-crested weirs, triangular weirs, and trapezoidal weirs.

The channel leading up to a weir is the channel of approach. The mean velocity in this channel is the velocity of approach. The depth of water producing the discharge is the head.Sharp-crested weirs are useful only as a means of meas- uring flowing water. In contrast, weirs not sharp crested are commonly incorporated into hydraulic structures as control or regulation devices, with measurement of flow as their secondary function.

FLOW OVER WEIRS.

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1) Rectangular Weir

The Francis formula for the discharge of a sharp-crested rectangular weir having a length b greater than 3h is

Q=0.333*(b -nh)*[(h+h0)(3/2)-h0(3/2)]

whereQ= discharge over weir, ft3/s (m3/s)

b= length of weir, ft (m)

h= vertical distance from level of crest of weir to water surface at point unaffected by weir drawdown (head on weir), ft (m)

n= number of end contractions (0, 1, or 2)

h0= head of velocity of approach

If the sides of the weir are coincident with the sides of the approach channel, the weir is considered to be suppressed, and n=0. If both sides of the weir are far enough removed from the sides of the approach channel to permit free lateral approach of water, the weir is considered to be contracted, and n= 2. If one side is suppressed and one is contracted, n=1.

2) Triangular Weir

The discharge of triangular weirs with notch angles of 30°,60°, and 90° is given by the formulas as

Discharge of Triangular Weirs

Notch (vertex) angle Discharge formula

90° Q 0.685h2.45

60° Q 1.45h2.47

30° Q 2.49h2.48

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