TABLE OF CONTENT
NO TITLE PAGE
1.0 INTRODUCTION 2
2.0 OBJECTIVES 2
3.0 THEORY 3
4.0 EQUIPMENTS 4
5.0 PROCEDURES 5-6
6.0 RESULTS AND ANALYSIS 7-8
7.0 DATA CALCULATIONS 9-13
8.0 DISCUSSION 14
9.0 CONCLUSION 15
10.0 REFERENCES 15
1.0 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 V-notch weir are been used.
Rectangular weirs and 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.
2.0 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 and study the relation between flowrate
and total head above the cress level of the rectangular notch and V notch.
2
3.0 THEORY
The notch is similar to that observed at a sharp edged orifice, and has the same
effect of reducing the discharge rate. Therefore rewrite the equation from sharp-edged
weirs as:
a) Rectangular notch weir
2
= ( 2) 3/2
3
Where,
Cd Flowrate Coefficient
B Breadth of notch
H Head or depth of the point below the undisturbed surface level.
b) V-notch weir
8
= ( ) 2 tan (H5/2 )
15 2
Where,
Cd = Flowrate Cofficient
= Half angle of the V notch
2
H = Head or depth of the point below the undisturbed surface level
3
4.0 EQUIPMENT
i) Hydraulic Bench
ii) Rectangular and V-Notch
iii) Stop watch
Figure 1 : Rectangular notch in hydraulic bench
Figure 2 : V notch in hydraulic bench
4
5.0 PROCEDURE
A) PROCEDURE OF RECTANGULAR NOTCH
1. The apparatus was first connected to the supply and levelled. Then the water were
admitted from the bench supply until the level is approximately correct.
2. The point gauge was read and set to zero when it was exactly at the level of the crest
of the notch.
3. The point gauge was brought exactly to the water surface when the correct level
obtained.
4. Then, we read the level at the gauge.
5. The bench hole was closed and the time was taken referred to the volume.
6. The bench hole was opened at the hydraulic bench.
7. Step 4 to 6 were repeated for different water level.
5
B) PROCEDURE OF V NOTCH
1. The apparatus was first connected to the supply and then levelled. Then,the water were
admitted from the bench supply until the level is approximately correct..
2. The point gauge was then read or set to zero when it was exactly at the level of the crest
of the notch.
3. When the correct level has been obtained, the point gauge was also brought exactly
to the water surface, and the calibrated dial either read or, if adjustment was possible, set
to zero.
4. Level at the gauge were taken.
5. Then, the bench hole was closed and the time were taken refer to the volume. 6. The
bench hole was opened at the hydraulic bench.
6. Step 4 to 5 were repeated for different water level
6
6.0 RESULTS AND ANALYSIS
Table 1: Rectangular Notch
3
Theory
H V T Q 2
H Cd Q
m m s m s m m s
3 3
3
H1 0.05 0.005 70 7.14x105 0.010 0.00885 7.84 106
H 2 0.04 0.005 65 7.69x105 0.008 0.00885 6.27 106
H 3 0.03 0.005 60 8.33x105 0.005 0.00885 3.92 106
H 4 0.02 0.005 52 9.62x105 0.003 0.00885 2.35 106
H 5 0.01 0.005 30 1.67x104 0.001 0.00885 7.84 107
Table 2: V-Notch
5
Theory
H V T Q 2
H Cd Q
m m s m s m m s
3 3
3
H1 0.05 0.005 86 5.81x105 5.59x104 0.16257 2.15 104
H 2 0.04 0.005 75 6.67x105 3.20x104 0.16257 1.23 104
H 3 0.03 0.005 72 6.94x105 1.56x104 0.16257 5.99 105
H 4 0.02 0.005 49 1.02x104 5.66x104 0.16257 2.17 105
H 5 0.01 0.005 28 1.79x104 1.00x104 0.16257 3.84 106
7
3
Graph Q vs H 2
0.00018
0.00016
0.00014
0.00012
0.0001
Q
0.00008
0.00006
0.00004
0.00002
0
0 0.002 0.004 0.006 0.008 0.01 0.012
Slope from the graph, = 0.00885
5
Graph Q vs H 2
0.0002
0.00018
0.00016
0.00014
0.00012
0.0001
Q
0.00008
0.00006
0.00004
0.00002
0
0 0.0001 0.0002 0.0003 0.0004 0.0005 0.0006
Slope from the graph, = 0.16257
8
7.0 DATA CALCULATIONS
For flow rate, Q
TABLE 1: RECTANGULAR NOTCH TABLE 2: V -NOTCH
1 0.005 3 5 1 0.005 3 5
Q= = 7.14 10 3 / Q= = 5.81 10 3 /
70 s 86 s
2 0.005 3 5 2 0.005 3 5
Q= = 7.69 10 3 / Q= = 6.67 10 3 /
65 s 75 s
3 0.005 3 5 3 0.005 3 5
Q= = 8.33 10 3 / Q= = 6.94 10 3 /
60 s 72 s
4 0.005 3 5 4 0.005 3 4
Q= = 9.62 10 3 / Q= = 1.02 10 3 /
52 s 49 s
5 0.005 3 4 5 0.005 3 4
Q= = 1.67 10 3 / Q= = 1.79 10 3 /
30 s 28 s
For Head of the notch, H
TABLE 1: RECTANGULAR NOTCH TABLE 2: V -NOTCH
H 5/2 = (0.05)5/2 = 5.59 x 104
1 H 3/2 = (0.05)3/2 = 0.010 1
2 H 3/2 = (0.04)3/2 = 0.008 2 H 5/2 = (0.05)5/2 = 3.20 x 104
H 3/2 = (0.03)3/2 = 0.005 H 5/2 = (0.05)5/2 = 1.56 x 104
3 3
H 3/2 = (0.02)3/2 = 0.003 H 5/2 = (0.05)5/2 = 5.66 x 104
4 4
H 3/2 = (0.01)3/2 = 0.001 H 5/2 = (0.05)5/2 = 1.00 x 105
5 5
9
Calculations for Theory Q using Coefficient of Discharge, from the graph:
RECTANGULAR NOTCH
2
= ( 2) 3/2
3
Where,
Cd Flowrate Coefficient
B Breadth of notch
H Head or depth of the point below the undisturbed surface level.
1 2
= 0.00885 ( (0.03)2(9.81)) (0.010)
3
1 = 7.84 106 3 /
2 2
= 0.00885 ( (0.03)2(9.81)) (0.008)
3
2 = 6.27 106 3 /
3 2
= 0.00885 ( (0.03)2(9.81)) (0.005)
3
3 = 3.92 106 3 /
4 2
= 0.00885 ( (0.03)2(9.81)) (0.003)
3
4 = 2.35 106 3 /
5 2
= 0.00885 ( (0.03)2(9.81)) (0.001)
3
5 = 7.84 107 3 /
10
V-NOTCH
8
= ( ) 2 tan (H5/2 )
15 2
Where,
Cd = Flowrate Cofficient
= Half angle of the V notch
2
H = Head or depth of the point below the undisturbed surface level
8 90
1 = 0.16257 ( ) 2(9.81) tan (5.59 104 )
15 2
1 = 2.15 104 3 /
8 90
2 = 0.16257 ( ) 2(9.81) tan (3.20 104 )
15 2
2 = 1.23 104 3 /
8 90
3 = 0.16257 ( ) 2(9.81) tan (1.56 104 )
15 2
3 = 5.99 105 3 /
8 90
4 = 0.16257 ( ) 2(9.81) tan (5.66 105 )
15 2
4 = 2.17 105 3 /
8 90
5 = 0.16257 ( ) 2(9.81) tan (1.00 105 )
15 2
5 = 3.84 106 3 /
11
Calculations for Coefficient of Discharge, using formula:
RECTANGULAR NOTCH
3 1
= ( )
2 2 3/2
Where,
Cd Flowrate Coefficient
B Breadth of notch
H Head or depth of the point below the undisturbed surface level.
1 3 1
= (7.14 105 ) ( )
2 (0.03) 2(9.81)(0.010)
= 0.081
2 3 1
= (7.69 105 ) ( )
2 (0.03) 2(9.81)(0.008)
= 0.109
3 3 1
= (8.33 105 ) ( )
2 (0.03) 2(9.81)(0.005)
= 0.188
4 3 1
= (9.62 105 ) ( )
2 (0.03) 2(9.81)(0.003)
= 0.362
5 3 1
= (1.67 104 ) ( )
2 (0.03) 2(9.81)(0.001)
= 1.885
12
V-NOTCH
15 1
= ( )
8 5/2
2 tan (2 )
Where,
Cd = Flowrate Cofficient
= Half angle of the V notch
2
H = Head or depth of the point below the undisturbed surface level
15 1
= (5.81 105 ) ( )
8 90 4
1 2(9.81) tan ( 2 ) (5.59 10 )
= 0.044
15 1
= (6.67 105 ) ( )
8 90 4
2 2(9.81) tan ( 2 ) (3.20 10 )
= 0.088
15 1
3 = (6.94 105 ) ( )
8 90 4
2(9.81) tan ( 2 ) (1.56 10 )
= 0.188
15 1
= (1.02 104 ) ( )
8 90 5
4 2(9.81) tan ( 2 ) (5.66 10 )
= 0.771
15 1
= (1.79 104 ) ( )
8 90 5
5 2(9.81) tan ( 2 ) (1.00 10 )
= 7.578
13
8.0 DISCUSSION
The differential value between QExperiment with Qtheory for rectangular is shown in table below.
Q QExperiment Qtheory Differential value
1 7.14 105 3 / 7.84 106 3 / 6.356 105
2 7.69 105 3 / 6.27 106 3 / 7.063 105
3 8.33 105 3 / 3.92 106 3 / 7.938 105
4 9.62 105 3 / 2.35 106 3 / 9.385 105
5 1.67 104 3 / 7.84 107 3 / 1.662 104
By using the Coefficient of Discharge, Cd from the graph, one of the calculated Qtheory is
2
= ( 2) 3/2
3
Rectangular Notch V-Notch
2 8 90
= 0.00885 ( (0.03)2(9.81)) (0.010) = 0.16257 ( ) 2(9.81) tan (5.59 104 )
3 15 2
1 = 7.84 106 3 / 1 = 2.15 104 3 /
On the experiment, the flow of the fluid was smooth before measuring the head
on weir. It was because to the distribution of velocities in approach affect the discharge
over the weir. When the water level decreased, the head become decrease. This is
resulted in the change of the fluid flow. The decrease in head, H will affect the time
taken for the water to discharge. As shown in the result, the time taken for water
discharge for both the rectangular notch and V-notch are decrease. Hence, it will result
a not constant value in flow rate.
The gravity is one of the major forces that influence the flow rate in this
experiment. The experiment was conducted in a constant flow, and constant pressure.
An assumption can be made which is 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 of water level
above the notch and creating larger changes from the theoretical value.
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9.0 CONCLUSION
The smooth flow to and over the weir is essential to the determination of
accurate rates of flow. Rather than gravity, kinetic energy correction factor can account
for the variation in the approach velocity. The value of the coefficient of discharge
depends on the degree of non-uniformity of the approach velocity distribution. It was
also noted that the head affects the flow of water. Aside from the velocity and the head,
temperature variations influence the fluid properties like viscosity and surface tension.
The variations in these fluid properties in turn will influence the discharge over the
weir. However, the effect of small temperature variations on the water flow over weirs
is negligible.
In conclusion, the flow rate in the experiment for both rectangular notch and V-
notch are affected by the time taken for water discharge, t. The difference between
experimental flow rate value and theoretical value are in the range of acceptable. Many
improvement can be made to get more accuracy.
10.0 REFERENCES
1. http://site.iugaza.edu.ps/mymousa/files/Experiment-6-hydraulics-lab-.pdf
2. https://web.njit.edu/~washd/cet413_eve/download/lab/Fluid_lab_weir.doc
3. http://users.rowan.edu/~jagadish/resources/wre/lab3.pdf
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