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CHE 486: LAB 2 - FLOW OVER WEIRS
+ AMIRUL AZWAN BIN ARMEE (2019406066) + MUHAMMAD AMMIR ASHRAF BIN
MOKHTAR (2019207322) + MUHAMMAD SYAFIQ MUQRIS BIN RAFEE (2019415962) +
MUHAMMAD ZAKWAN BIN ABDULLAH ZAWAWI (20192573020) + MOHAMAD ZAMIR ARIF
BIN MOHAMAD ZAIMI (201422642) +
FACULTY OF CHEMICAL ENGINEERING
Abstract— The Flow over Weirs experiment is done to
resolve the varieties of flow over rectangular and V-
notch. Besides, the experiment was able to observe the
fluid flow and find discharge coefficient (Cd) for both
notches. Cd can be calculated from data that produced
from the experiment. The discharge coefficient is a
dimensionless number used to characterize the flow
and pressure loss reaction of nozzles in fluid system.
Orifices and nozzles are typically used to deliberately
reduce pressure, restrict flow or to measure flow rate.
In first objective, the experiment done by following the
procedures given. Collected data from the experiment
was tabulated. Cd then calculated by using equation
given. Graphs have been created to inspect the
behaviors of the flow. We can see that Cd decrease at
a slow pace before a constant value is reached in
rectangular notch while for the V-notch, Cd decrease
smoothly, and the values are larger than the
rectangular notch. In conclusion, the V-notch has
higher Cd than the rectangular notch.
Keywords— Rectangular and V-notch, fluid
flow and find discharge coefficient (Cd),
dimensionless number, flow rate.
I. INTRODUCTION
A weir is a monolithic and ashlar structure that is built
across the open channel to differentiate the water flow
peculiarity. (Anupoju, 2016). The ability to predict the
flow diverted over weirs is also useful in the design of
diversion structures and in flood alleviation works.
(Singh et al., 1994, p. 817) There are many variety of
weirs such as broad crested, short-crested and sharp-
crested. Sharp crested weirs can be termed as notches
that are created from sharp-edged thin plates. Sharp
crested weirs are the plain form of overflow spillway
that regularly used to resolve the flow rate in hydraulic
laboratories, industry and irrigation system, where
tremendously accurate discharge measurement are
necessary. (Bagheri & Heidarpour, 2009) By applying
Bernoulli’s equation, the correspondence between the
flow rate and water depth above the weir can be
derived and some assumption to be done due to head
loss, and pressure distribution of the flow passing over
the weir. Hence, due to this presumption, the
coefficient of discharge (Cd) must be experimentally
set on to resolve the errors in flow rate estimation. For
this experiment, we use rectangular notch and V-notch
to calculate the value of Cd. (Ahmari, 2019)
II. OBJECTIVES
The main purpose of this Flow Over Weirs
experiment is to resolve the flow peculiarity of water
over a rectangular notch and V-notch.Secondly , to
determine the coefficient of discharge (Cd) for the
both notch.Then ,to plot the graph Q^(2/3) against
H,log Q against log H and Cd against H for rectangular
notch..After that ,to plot the graph Q^(2/5) against H
and to determine the Cd value from the slope of the
graph for the V-notch.Lastly, to compare the value of
coefficient of discharge (Cd) from manual calculation
and the graph.
III. THEORY
Generally, weirs are defined as stable fences
across the width of a river or stream that can change
the flow characteristics of water(Ahmari and
Kabir,2020). Usually, the height of the water level
above the weir can be used to determine the flow rate
of water. The relationship of water level-discharge can
be used with standard-shaped weirs or notches. There
are two types of weirs that are commonly used which
is rectangular notch and V-notch.\
In this experiment, we will use hydraulics bench
to determine the discharge coefficients of the fluid
flow. There are some components which are important
to ensure the experiment is done well. The first
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component is stilling baffle. It is used to avoid any
disturbance in surrounding, so that the turbulence can
be minimized. The stilling baffle will collect the water
first and then disperse them slowly from the opening
at the bottom of stilling baffle. The second component
is vernier which is used to measure the height of water
which can make calculations to determine the
discharge coefficient.
The first type of weir is a rectangular weir. It is used
to measure water flow in large open
channels(Anupoju,2020).
Where C d
= Coefficient of discharge
B = Width of notch
H = Head above bottom of notch
Q = Flow rate
The second type of weir is V-Notch. It is a sharp-
crested with V- shaped opening notch. It is suitable for
small flow of water to measure discharge coefficient.
Where C d
= Coefficient of discharge
𝜃/ 2 = Half the enclosed angle
H = Head above bottom of notch
Q = Flow rate
IV. PROCEDURE
Firstly, the weir apparatus are levelled on the
hydraulic bench and the rectangular notch weir is
installed. Secondly, the hydraulic bench flow control
valve is opened slowly to admit water to the channel
until the water is discharged over the weir plate. It has
been ensured that the water level is even with the crest
of the water. Thirdly, The flow control valve is closed
and the water level is allowed to stabilize itself. The
Vernier Gauge is set to a datum reading using the top
of the hook. The gauge is put about halfway between
the notch plate and stilling baffle. Then, the water is
admitted to the channel. The water flow is adjusted by
using the hydraulic bench flow control valve to obtain
heads (H). The water flow condition is waited to
stabilize, the head readings are taken in every
increasing of about 1cm. Step 4 and 5 are repeated for
different flow rate. Next, the readings of volume and
time are taken using the volumetric tank to determine
flow rate. When the rectangular notch is finished, the
notch is replaced with v-notch. Finally, the results are
recorded in tables.
V. RESULT AND DISCUSSION
CALCULATION
Rectangular Notch
Rec
tangular
Notch
Volume Height
Time(s)
T1 T2 T
Average Flow Rate, Q Log H Log Q
44.12 1. 133 × 10
− 4
20.17 2. 479 × 10
− 4
4. 036 × 10
− 4
B=30mm
89mm
Q = C d
2/3B(√ 2 g) (H
3/
)
90
0
50mm
Q = C d
8/15( 2 𝑔) tan(𝜃/2) H
3/
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2. C
d
2. 479 × 10
− 4
3
2
3. C
d
( 4. 036 × 10
− 4
3
2
4. C
d
6. 002 × 10
− 4
3
2
5. C
d
( 8. 606 × 10
− 4
3
2
V-Notch
Calculation of flow rates, Q
Sample of calculation flow rates, Q:
𝟑
1
- 005 m
3
- 98 s
= 4. 951 × 10
− 5
3
2
- 005 m
3
- 05 s
= 1. 349 × 10
− 4
3
3
- 005 m
3
- 52 s
= 3. 698 × 10
− 4
3
4
- 005 m
3
- 74 s
= 6. 459 × 10
− 4
3
Calculation of Cd
Sample of calculation of coefficient of discharge,
Cd:
𝒅
𝟓
𝟐
𝒅
𝟓
𝟐
Where,
Cd= Coefficient of discharge
H= Head above bottom notch
Q= Flow rate
𝜽
𝟐
= Half the enclosed angle of the vee
𝑑 1
× 10
− 5
2 ( 9. 8 ) tan (
5
2
𝑑 1
× 10
− 4
tan
5
2
𝑑 3
× 10
− 4
2 ( 9. 8 ) tan (
5
2
𝑑 4
× 10
− 4
2 ( 9. 8 ) tan (
5
2
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DISCUSSION
This experiment was carried out to resolve
the flow peculiarity of water over a rectangular notch
and v-notch. Through this experiment, we obtained the
value of coefficient of discharge (Cd) for rectangular
notch by using manual calculation. For v-notch, we
determined the discharge coefficient by using two
methods which is manual calculation and the plotted
graph, then compared the value obtained from both
methods.
From the data that we get from the
experiment of flow over the weirs by using rectangular
notch, the value of flow rates, Q that we obtained is
1. 133 × 10
− 4
, 2. 479 × 10
− 4
, 4. 036 × 10
− 4
6. 002 × 10
− 4
and 8. 606 × 10
− 4
for respectively. So,
from the value of flow rates, Q, the value of Q
2 / 3
that
we calculated is 2. 341 × 10
− 3
, 3. 946 × 10
− 3
5. 461 × 10
− 3
, 7. 115 × 10
− 3
and 9. 048 × 10
− 3
respectively while for value of log Q is - 3.945, - 3.606,
- 3.394, - 3.222 and - 3.065 respectively.
Based on the value of head above the bottom
notch, H that we obtain through the experiment, the
value of log H that we get is - 2.000, - 1.698, - 1.523, -
1.398 and - 1.301 accordingly. By dividing the value of
H with width of notch, B which the value that we use
in this experiment is 0.030m, the value of H/B that we
have determine is 0.333, 0.667, 1.000, 1.333 and 1.
respectively.
By using the value of flow rates, Q and head
above the bottom notch, H from the table data, we can
get the value of Cd by using the formula of the
coefficient of discharge, Cd for rectangular notch
below:
𝑑
3
2
𝑑
3
2
Where the width of the notch is expressed by
B, H as the head above the bottom notch, and Q is the
flow rates. For a rectangular notch test, the value of Cd
is 1.2796, 0.9899, 0.8772, 0.8473 and 0.
respectively.
Figure 1
Based on the graph of Q
2 / 3
against head
above bottom of notch, H above, we can conclude that
as the head above bottom of notch increases, the value
of Q
2 / 3
also increases as well. This is due increases of
time as water need more time to flow from the weirs
when the height increases in each experiment.
Figure 2
Figure 2 shows the graph of log Q against log
H. Based on the result of the calculation that we get, it
shows that the value of log Q to become slightly
increase followed by the value of log H. Thus, we can
conclude that when the value of log Q increases so the
value of log H also increases as well.
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Q = 0. 0316 H
- 2272
Therefore, Q = 0. 0316 H
- 2272
proved that Q
and H can be described by using the empirical formula
which Q = kH
n
Next, for the V-notch test, the flow rates, Q is
4. 951 × 10
− 5
, 1. 349 × 10
− 4
, 3. 698 × 10
− 4
and
6. 459 × 10
− 4
respectively. The height for the notch,
H is 0.01m, 0.02m, 0.03m, 0.04m respectively. We
can conclude that when the flow rates increase so the
height also increases.
From the result, the value of Q
2 / 5
is
1. 896 × 10
− 2
, 2. 831 × 10
− 2
, 4. 238 × 10
− 2
and
5. 297 × 10
− 2
accordingly. To determine the Cd for
the V-notch we use the formula which is Cd:
Q = C
d
B 2gH
5
2
C
d
Q (
2g tan (
θ
) H
5
2
Where the angle of the vee is represent by 𝜽,
H as the head above the bottom notch, and Q is the
flow rates. The value of Cd obtained from the formula
are shown in table below with calculation of average
Cd for V-notch.
Cd for V-Notch
Average Cd =
Total of Cd value
n
In order to find the value of Cd through the
plotted graph we need to plotting the graph of Q
2 / 5
against head above the notch, H and create a tangent
line for each point plotted.
Figure 5
Based on the graph, as the values of Q
2 / 5
increase, the head above of the notch, H also increases.
The Cd values can be determined from the tangent of
each point plotted on the graph by calculating the
gradient of the tangent line.
Cd calculated
using formula
Cd gain from the graph
Cd
1
Cd
1
Cd
2
Cd
2
Cd
3
Cd
3
Cd
4
Cd
4
From the value of Cd obtain from both
method, there is a difference between the calculated
Cd from the formula and the calculated Cd using the
plotted graph. This is because the reading from the
plotted graph is not as accurate as the calculation using
a formula that could result in an error of about 0.1-1.1.
For the test with V-notch, we can conclude
that the value of Cd is also not constant in this
experiment. This can be shown based on the
calculation of Cd from the result in V-notch. The Cd
value decreases as the flow rate also decreases.
However, as the head above the notch increases, the
Cd value shown a decrease. Thus, we can conclude
that the Cd values are depends on the value of flow
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rate, Q, and the value of the head above bottom of the
notch, H.
VI. CONCLUSION
In conclusion, Cd average from the experiment that
calculated using formula shows that the V-notch,
1.2410 has larger value of Cd than the rectangular
notch, 0.97266. Cd calculated by using formula in
rectangular notch for Cd 1
, Cd
2
, Cd
3
, Cd
4
, Cd
5
is
1.2796, 0.9899, 0.8772, 0.8473, 0.8693 respectively.
For Cd calculated for V-notch by using formula for
Cd
1
, Cd
2
, Cd
3
, Cd
4
is 2.0958, 1.0095, 1.0042, 0.
each of them. While Cd for V-notch get from the graph
for Cd 1
, Cd
2
, Cd
3
, Cd
4
is 0.8049, 1.1667, 1.2500,
0.9535 respectively.
VII. RECOMMENDATIONS
A weir is an obstruction over a weirs intended to
alter its stream characteristic. Weirs are usually used
to adjust the progression of streams to forestall
flooding, measure release, and help render waterways
safe.
There are a few of suggestions to assess release
when utilizing a weirs since it is critical to make sure
that all stream enters by going over the weir and not
around the weir or under the weir. It must be noticed
that the weir need to be stretched out into the ground
to limit groundwater to pass under the weir. To
guarantee basic stream over the peak of the weir, it is
important to keep up a 'free outfall'. However if long
the stream conditions downstream of the weir don't
influence the stream over the weir, a free outfall will
maintained.
Above all else, prior to improving to learn and
see first on the best way to direct the experiment. In
addition, the result of rectangular-score and v-indent
acquired must be taken in 4 decimal focuses to get a
exact qualities.
Mistakes can never be disregarded with regards
to laboratory work. The point is to decrease the
mistake however much as could reasonably be
expected to acquire precision in work. Approaches to
reduce the mistake are by rehashing the test for
multiple times or more and afterward taking the
average readings, by being additional wary during the
analysis, by asking more than one individual to record
the readings and do the trial. It is critical to downplay
the voice while in a lab and consistently tune in to the
educator. On the off chance that any rules are required,
at that point allude to the administrator.
VIII. REFERENCES
ARTICLES
[1] Singh, R., Manivannan, D., & Satyanarayana, T.
(1994). Discharge Coefficient of Rectangular
Side Weirs. Journal of Irrigation and Drainage
Engineering, 120(4), 814 – 819.
https://doi.org/10.1061/(asce)0733-
[2] Bagheri, S., & Heidarpour, M. (2009, August 13).
Flow over rectangular sharp-crested weirs.
Irrigation Science.
https://link.springer.com/article/10.1007/s
1?error=cookies_not_supported&code=773d
685 - fad1-43c2-916c-8b599307c84f
WEBSITES
[1] Ahmari, H. (2019, August 14). Experiment #9:
Flow Over Weirs – Applied Fluid Mechanics
Lab Manual. Pressbooks. Retrieved
November 12, 2020, from
https://uta.pressbooks.pub/appliedfluidmech
anics/chapter/experiment-9/
[2] Sadanandam Anupoju, (n.d), WHAT IS A WEIR?
TYPES OF WEIRS AND FLOW OVER
WEIRS. (2016, June 11). Retrieved November
13, 2020, from
https://theconstructor.org/water-
resources/what-is-weir--types-flow-over-
weirs/11873/
[3] Schobeiri, M. T. (n.d.). Applied Fluid Mechanics
for Engineers. McGraw-Hill Education -
Access Engineering. Retrieved November
13, 2020, from
http://accessengineeringlibrary.com/content/
book/9780071800044?implicit-login=true
