TABLE OF CONTENT
No
1
2
3
4
5
6
7
8
9
10
11
12
13
Title
Abstract……………………………….
Introduction…………………………..
Objectives……………………………..
Theory………………………………...
Material And Apparatus………………
Methodology………………………….
Data and Results………………………
Calculations…………………………...
Discussion…………………………….
Conclusion…………………………….
Recommendations…………………….
Reference……………………………...
Appendix……………………………...
SOLTEQ® FLOW OVER WIRES (FM 26)
Page
2
3
4
5–6
7
8
9 – 11
12 – 15
16 – 18
19
20
21
22
Page 1
1.0 ABSTRACT
The Flow over Weirs experiment was conducted to investigate the characteristics of flow over a
rectangular notch and triangular notch. The difference in flow rate of water that flows into both
of the channel was observed. Other than that, the experiment was capable to study the discharge
coefficient of fluid flow that determined by calculation of this experiment.
The experiment was started as follows the procedures, with the depth of water with
different height was tested by recording the time taken to collect 3L of water, which later will be
used to calculate the flow rate of the flow. The data obtained were further tabulated by
calculating the discharge coefficient, using the equation provided.
Then, graphs were constructed to analyze the characteristics of the flow. From the
constructed graphs, rectangular notch graph shows the discharge coefficient decrease slowly
before a constant value is reached. Meanwhile, the triangular notch graph shows the discharge
decrease smoothly, but the values are higher than the rectangular notch.
To conclude, triangular notch has a higher discharge coefficient than rectangular notch.
The experiment was successfully accomplished as all the objectives were gained.
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Page 2
2.0 INTRODUCTION
The flow rate in pipes and ducts is controlled by various kinds of valves. Liquid flow in open
channels, however, is not confined, and thus the flow rate is controlled by partially blocking the
channel. This is done by either allowing the liquid to flow over the obstruction or under it. An
obstruction that allows the liquid to flow over it is called a weir, and an obstruction with an
adjustable opening at the bottom that allows the liquid to flow underneath it is called an
underflow gate. Such devices can be used to control the flow rate through the channel as well as
to measure it. A weir is a flow control device in which the water flows over the obstruction.
In this experiment, the rectangular weirs and triangular weirs are been used. 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 broadcrested weirs will meet accuracy requirements only if they are calibrated.
SOLTEQ® FLOW OVER WIRES (FM 26)
Page 3
3.0
OBJECTIVE
The main objectives of this experiment is to observe the flow characteristics over a
rectangular notch and a V-notch. Besides, the other objectives is to determine the discharge
coefficients of the fluid flow. Then, to teach student how to plot a graph of
against Log H and
of
against H on rectangular notch. While on V-notch, learn how to plot graph
against H. Next, to estimate an average value of
least, to compare
against H, Log Q
for the range of the test. Last but not
values between rectangular notch and V-notch.
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4.0 THEORY
Flow over Weirs
Weirs are hydraulic structures consisting of an obstruction placed across a water channel with a
specially shaped opening or notch. The weir structure will increase the water level, which will be
measured. Water level-discharge relationships are available for standard-shaped openings or
notches.
Two types of weirs are widely used:
1. Rectangular shape opening
2. V-notch.
Stilling baffle is used to ensure minimum turbulence. The stilling baffle will act as a reservoir to
collect water volume and slowly disperse the water from the opening at the bottom of the stilling
baffle.
Types of Weirs
Rectangular Weir
The rectangular weir is able to measure higher flows than the v-notch weir and over a wider
operating range.
B, 33mm
89mm
Where
2
B 2g H
3
2
Q
= Cd
Cd
B
H
Q
= Coefficient of discharge
= Width of notch
= Head above bottom of notch
=Flow rate
SOLTEQ® FLOW OVER WIRES (FM 26)
3
eq. (1)
Page 5
V-Notch
The V-notch weir is a notch with a V shape opening. V-notch weir is typically used to
measure low flows within a narrow operating range. Typical Cd values for V-notch are in the
range of 0.58 to 0.62.
90 °
50mm
Where,
Cd = Coefficient of discharge
= Half the enclosed angle of the vee
H
= Head above bottom notch
Q
= Flow Rate
SOLTEQ® FLOW OVER WIRES (FM 26)
√
Page 6
5.0 MATERIAL AND APPARATUS
MATERIAL
1) Water
APPARATUS
1)
2)
3)
4)
5)
6)
F1-13 Stilling baffle
Rectangular notch
V- notch
Stopwatch
Spirit level
F1-10 Hydraulics Bench
1
2
5
7
3
4
6
8
Figure 1: F1-10 Hydraulics Bench
1. Stilling Baffle
5. Hydraulic Bench (FM 110)
2. Vernier
6. Flow Control Valve
3. Hook
7. Water Channel
4. Weir Plate (V or rectangular)
8. Sump Tank
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6.0 METHODOLOGY
Experimental Procedures
1) The hydraulic bench pump were confirmed is securely connected.
2) The collection tank drain valve is ensured left OPEN to allowed flow discharged back
into sump tank.
3) The flow over weirs apparatus were set up on the hydraulic bench.
4) Thumb nuts were confirmed securing the rectangular notch weir plate is fully secured.
General Shut Down Procedures
1) The hydraulic bench flow control valve were shut and water supply is closed.
2) The residue water from channel and sump tank was emptied by ensuring the drain tank
valve is left open.
Experiment 1: Flow Characteristics over Weirs
1) The weir apparatus on the hydraulic bench were levelled and the rectangular notch weir
is installed.
2) The hydraulic bench flow control valve were slowly opened to admit water to the channel
until the water discharged over the weir plate. The water level is ensured that it is even
with the crest of the weir.
3) The flow control valve is closed and allowed water level to stabilized.
4) The Vernier Gauge was set to gives a datum reading using the top of the hook.
5) The gauge is installed about half way between the notch plate and stilling baffle.
6) Water is admitted to the channel. The water flow were adjusted by using the hydraulic
bench flow control valve to obtain heads (H).
7) After water flow condition is stabilized, heads readings is recorded in every increasing of
about 1 cm.
8) Step 4 and 5 were repeated for different flow rate.
9) The readings of volume and time were taking using the volumetric tank to determined
flow rate.
10) The rectangular notch were replaced by the notch with v-notch.
11) The result was recorded in the tables.
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7.0 DATA AND RESULTS
Rectangular Notch
Volume
(L)
Rectangular
Notch
Height
(m)
3
3
3
3
0.0105
0.0197
0.0325
0.0434
T1
50
32
24
16
Q2/3
Log Q
Rectangular
Notch
-4.0988
-3.7700
-3.6140
-3.3010
Time
(s)
T2 T3
21
42
10
11
7
6
5
7
(
Average
37.6667
17.6667
12.3333
6.0000
Flow Rate,
Q
(m3/s)
7.9646 x 10-5
1.6981 x 10-4
2.4321 x 10-4
5.0000 x 10-4
Log H
-1.9788
-1.7055
-1.4881
-1.3625
Cd
)
1.8512 x 10-3
3.0665 x 10-3
3.8963 x 10-3
6.2996 x 10-3
0.7600
0.6305
0.4262
0.5678
0.3182
0.5970
0.9848
1.3152
Graph of Q2/3 Against Head Above Bottom of Notch, H
0.007
0.006
Q2/3 (m2/s2/3)
0.005
0.004
0.003
0.002
0.001
0
0
0.01
0.02
0.03
Head Above Bottom of Notch (m)
SOLTEQ® FLOW OVER WIRES (FM 26)
0.04
0.05
Page 9
Graph of Log Q Against Log H
0
-2.5
-2
-1.5
-1
-0.5
-0.5
0
-1
-1.5
Log Q
-2
-2.5
-3
-3.5
-4
-4.5
Log H
Graph of Coefficient of Discharge, Cd Against Head Above
Bottom of Notch, H
0.8
0.7
0.6
Cd
0.5
0.4
0.3
0.2
0.1
0
0
0.01
0.02
0.03
Head Above Bottom of Notch (m)
SOLTEQ® FLOW OVER WIRES (FM 26)
0.04
0.05
Page 10
V-Notch
Volume
(L)
V-Notch
3
3
3
3
Height
(m)
T1
79
35
28
17
0.0158
0.0244
0.0297
0.0413
Q2/5
(
Time
(s)
T2 T3
27
31
11
10
6
8
4
4
Average
45.6667
18.6667
14.0000
8.3333
Flow Rate,
Q
(m3/s)
6.5693 x 10-5
1.6071 x 10-4
2.1429 x 10-4
3.6000 x 10-4
Cd
)
2.1233 x 10-2
3.0368 x 10-2
3.4072 x 10-2
4.1930 x 10-2
V-Notch
0.8866
0.7319
0.5970
0.4398
Graph of Q2/5 Against Head Above Bottom of Notch, H
0.045
0.04
0.035
Q2/5
0.03
0.025
0.02
0.015
0.01
0.005
0
0
0.005
0.01
0.015 0.02 0.025 0.03 0.035
Head Above Bottom of Notch (m)
SOLTEQ® FLOW OVER WIRES (FM 26)
0.04
0.045
Page 11
8.0
CALCULATIONS
Sample Calculation of Flow Rates , Q
Rectangular Notch
V-Notch
Q1
Q1
Q2
Q2
Q3
Q3
Q4
Q4
Sample Calculation of Log Q
Rectangular Notch
Log Q1
Log Q2
Log Q3
Log Q4
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Sample Calculation of Log H
Rectangular Notch
Log H1
Log H2
Log H3
Log H4
Sample Calculation of
Rectangular Notch
(
)
(
)
(
)
(
)
SOLTEQ® FLOW OVER WIRES (FM 26)
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Sample Calculation of Coefficient of Discharge, Cd
Rectangular Notch
√
Where,
Cd = Coefficient of discharge
B
= Width of notch
H
= Head above bottom notch
Q
= Flow Rate
√
Cd1
√
Cd2
√
Cd3
√
Cd4
√
SOLTEQ® FLOW OVER WIRES (FM 26)
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V-Notch
√
Where,
Cd = Coefficient of discharge
= Half the enclosed angle of the vee
H = Head above bottom notch
Q = Flow Rate
√
Cd1
√
Cd2
√
Cd3
√
Cd4
√
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9.0
DISCUSSION
The Cd value is not constant for the rectangular notch. This is because the value for the flow
rates, Q and the head above bottom of notch, H obtained for both rectangular notch and V-notch
are different in each experiment. However, the Cd values of rectangular notch is smaller
compared to the Cd values of V-notch.
Calculation below shows the average value of Cd for rectangular notch for the range of the test:Cd
0.7600
0.6305
0.4262
0.5678
Based on the calculations for Cd values of V-notch, the Cd values gain decreases as the
flow rate decreases. Besides, as the head above bottom notch increases , the Cd values gain also
decreases. This shows that, the Cd values is dependent on the value of flow rate, Q and the value
of the head above the notch, H.
To prove whether Q and H relationship described by an empirical formula
graph of
against
is plotted, the derivation from the empirical is as follow:-
, the
Where, when the equation is ploted on a graph,
log Q = value on y-axis
log H = value on x-axis
log k = y-intercept
n
= the gradient of the graph
SOLTEQ® FLOW OVER WIRES (FM 26)
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Graph of Log Q Against Log H
0
-2.5
-2
-1.5
-1
-0.5
-0.5
0
-1
-1.5
Log Q
-2
-2.5
-3
-3.5
-4
Log H
-4.5
Based on the graph,
The gradient (n) of the graph is :-
The value k is :-
Thus, this shows that Q and H does relate and can be describe using the empirical formula
.
SOLTEQ® FLOW OVER WIRES (FM 26)
Page 17
Graph of Q2/5 Against Head Above Bottom of Notch, H
0.045
0.04
0.035
Q2/5
0.03
0.025
0.02
0.015
0.01
0.005
0
0
0.005
0.01
0.015 0.02 0.025 0.03 0.035
Head Above Bottom of Notch (m)
0.04
0.045
Based on the graph , the values of
increases as the head above the bottom of notch, H
increases. The Cd values can be obtained from the tangent of the graph on each point plotted.
Cd Calculated Using Formula
Cd Gain From Graph
Cd1 = 0.8866
Cd2 = 0.7319
Cd3 = 0.5970
Cd4 = 0.4398
From the data, there is difference between Cd calculated from formula and Cd calculated
using the plotted graph. The reason of this error could be because of the reading from the graph
is not as accurate as the calculation using formula which lead to about 0.2 – 0.4 result error.
SOLTEQ® FLOW OVER WIRES (FM 26)
Page 18
10.0 CONCLUSION
The smooth flow to and over the weir is essential to the determination of accurate rates of
flow since the distribution of velocities on the approach flow has a definite influence on the
discharge over the weir. As the flow rate increases, the discharge coefficient becomes more
accurate to the theoretical value. When the flow rate is to low it clings to the notch and flows
down it. This changes the coefficient of discharge because now the water is not only being
affected by gravity it is having to resist viscosity and the friction of the surface of the notch.
The limitations of the theory is it has to be level so the only force on the water is gravity,
there has to be a constant flow, and constant pressure.The theory behind this experiment makes
an assumption that there is a minimum height of water above the notch and any heights below
this start to deviate from theory at an increasing rate.The relationship between the head of the
weir and the discharge of the water over the weir is directly proportional. The lower flow rates
produce lower heights above the notch creating larger changes from the theoretical equations
SOLTEQ® FLOW OVER WIRES (FM 26)
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11.0 RECOMMENDATION
A weir is a barrier across a weirs designed to modify its flow characteristics. Weirs are
commonly used to alter the flow of rivers to prevent flooding, measure discharge, and help
render rivers navigable.
There are several of recommendations to estimate discharge when using a weirs because
it is very important to ensure that all flow enters by travelling over the weir and not around the
weir or under the weir. It must be noted that the weir should be extended into the ground to
minimize groundwater to pass under the weir. To ensure critical flow over the crest of the weir, it
is important to maintain a ‘free outfall’. As long as the flow conditions downstream of the weir
do not affect the flow over the weir, a free outfall is maintained.
First of all, before doing an experiment it is better to learn and understand first on how to
conduct the experiment. Moreover, the result of rectangular-notch and v-notch obtained must be
taken in 4 decimal points to get an accurate values.
Errors can never be ignored when it comes to laboratory work. The aim is to reduce the
error as much as possible to obtain accuracy in work. Ways to reduce the error are by repeating
the experiment for three times or more and then taking the average readings, by being extra
cautious during the experiment, by asking more than one person to record the readings and carry
out the experiment. It is important to keep the voice to a minimum while in a laboratory and
always listen to the instructor. If any guidelines are needed, then refer to the supervisor.
SOLTEQ® FLOW OVER WIRES (FM 26)
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12.0 REFERENCES
Books
1) Kundu, Pijush K.; Cohen, Ira M. (2008), Fluid Mechanics (4th revised ed.), Academic
Press
2) Hamilton Smith, 1886, Hydraulics, the Flow of Water Through Orifices, Over Weirs,
and Through Open Conduits and Pipes
Web
1) http://discoverarmfield.com/en/products/view/f1-13/flow-over-weirs , retrieve in
August 2015.
2) http://www.codecogs.com/library/engineering/fluid_mechanics/weirs/index.php ,
retrieve in August 2015.
3) https://en.wikipedia.org/wiki/Fluid_mechanics , retrieve in August 2015.
4) http://www.engineeringtoolbox.com/weirs-flow-rate-d_592.html , retrieve in August
2015.
5) http://www.lmnoeng.com/Weirs/RectangularWeir.php , retrieve in August 2015.
6) http://www.aquatext.com/calcs/weir%20flow.html , retrieve in August 2015.
7) http://accessengineeringlibrary.com/browse/applied-fluid-mechanics-for-engineers ,
retrieve in August 2015.
8) https://www.scribd.com/doc/34695544/Flow-of-Water-Over-Weirs , retrieve in
August 2015.
SOLTEQ® FLOW OVER WIRES (FM 26)
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13 APPENDIX
SOLTEQ® FLOW OVER WIRES (FM 26)
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