6.
0 RESULT
1. Rectangular Notch
Volume = 3L = 0.003m3
B = 0.03m
Height,
H (m)
T1
Time (s)
T2
T3
Average
Time (s)
Flowrate,
Q (m3/s)
Log H
Log Q
Q2/3
Cd
H/B
0.01
2.93
4.6
2.2
3.24
9.26 x 10-4
-2.000
-3.033
0.0095
10.453
0.333
0.02
2.75
1.88
2.25
2.29
1.31 x 10-3
-1.699
-2.883
0.012
5.228
0.667
0.03
1.94
3.76
0.76
2.15
1.4 x 10-3
-1.523
-2.854
0.0125
3.041
1.000
0.04
1.64
2.85
1.51
2.0
1.5 x 10-3
-1.398
-2.824
0.0131
2.117
1.333
Log Q against Log H
Log Q
-2.85
-2.9
-1
.3
97
99
99
99
99
99
98
6
-2.8
-1
.5
22
99
99
99
99
99
98
6
-2.75
-1
.6
99
00
00
00
00
00
00
1
-2
-2.7
-2.95
-3
-3.05
Log H
Figure 6.1: A graph of Log Q against Log H for rectangular notch
Q2/3 against H
Q2/3
1.
00
00
00
00
00
00
00
05
E2
2.
00
00
00
00
00
00
00
11
E2
3.
00
00
00
00
00
00
00
02
E2
4.
00
00
00
00
00
00
00
22
E2
0.01
0.01
0.01
0.01
0.01
0
0
0
Figure 6.2: A graph of Q2/3 against H for rectangular notch
Q against H3/2
8.
00
00
00
00
00
00
01
23
E3
5.
19
60
00
00
00
00
00
53
E3
f(x) = 0x + 0
2.
82
80
00
00
00
00
00
02
E3
1.
00
00
00
00
00
00
00
13
E3
0
0
0
0
0
0
0
0
0
H3/2
Figure 6.3: A graph of Q against H3/2 for rectangular notch
Cd against H
4.
00
00
00
00
00
00
00
22
E2
3.
00
00
00
00
00
00
00
02
E2
2.
00
00
00
00
00
00
00
11
E2
Cd
1.
00
00
00
00
00
00
00
05
E2
12
10
8
6
4
2
0
Figure 6.4: A graph of Cd against H for rectangular notch
2. V-Notch
Volume = 3L = 0.003 m3
Height, H
(m)
Time (s)
Average
Time (s)
Flowrate, Q
(m3/s)
Q2/5
Cd
T1
T2
T3
0.01
21.11
20.51
25.83
22.48
1.33 x 10-4
0.0282
5.63
0.02
13.44
15.29
18.42
15.72
1.91 x 10-4
0.0325
1.429
0.03
4.85
8.18
6.68
4.49 x 10-4
0.0458
1.219
0.04
5.11
3.56
3.89
7.71 x 10-4
0.0569
1.02
Q2/5 against H
Q2/5
1.
00
00
00
00
00
00
00
04
E2
2.
00
00
00
00
00
00
00
07
E2
3.
00
00
00
00
00
00
00
02
E2
4.
00
00
00
00
00
00
00
15
E2
0.06
0.05
0.04
0.03
0.02
0.01
0
Figure 6.5: A graph of Q2/5 against H for V-notch
Q against H5/2
0
0
0
0
0
0
0
0
0
0
3.
20
00
00
00
00
00
00
24
E4
1.
56
00
00
00
00
00
00
08
E4
5.
66
00
00
00
00
00
00
14
E5
1.
00
00
00
00
00
00
00
04
E5
f(x) = 0x - 0
H5/2
Figure 6.6: A graph of Q against H5/2 for V-notch
7.0 SAMPLE CALCULATIONS
1. Average time, T
T=
T 1 +T 2 +T 3
3
2.93+ 4.60+2.20
3
3.24 s
2. Flow rate, Q
3
Volume( m )
Q=
Time(s)
0.003 m3
3.24 s
9.26 104 (
m3
)
s
3. H/B
H 0.01 m
=
B 0.03 m
0.33
4. Coefficient of discharge, Cd
a. Rectangular Notch
3
C d= Q
2
1
3
B 2 g( H 2 )
3
C d= 9.26 104
2
1
3
0.03 2 ( 9.81 ) (0.01 2 )
10.453
b. V-notch
C d=
15
Q
8
C d=
15
4
1.33 10
8
tan 2 g( H 2 )
2
1
5
90
tan 2(9.81)(0.01 2 )
2
5.63
Based on graph Q against H3/2 for rectangular notch, the equation obtained is:
y = 0.0002x + 0.0008
m = Cd x K
= 0.0002
Cd = 0.0002
K
= 0.0002
2
3
2g
= 2.258 x 10-3...............................
Based on graph of Q against H5/2 for V-notch, the equation obtained is:
y = 0.0002x 0.0002
m = Cd x K
= 0.0002
Cd = 0.0002
K
=
0.0002
8
15
2 g
H5/2 (tan
2 )
= 8.466 ...................................
8.0 DISCUSSIONS
All of the data are recorded in the results section. The coefficient of discharge, C d, for both notch were
calculated and determined. Graphs of Q versus H3/2 or H5/2, log Q against log H and C d against H were
all plotted.
The coefficient of discharge, C d, is an experimental correction factor which must be applied to
the theoretical discharge value to obtain the actual discharge. Because real flows do not meet all the
assumptions listed above, the actual flow will generally be less than the theoretically predicted flow.
Below is how we can obtain the value of Cd,
Based on the results obtained, the Cd for rectangular notch is 0.9155 and for V notch is 2.869. From
dimensional analysis and experiments, the average value of Cd for a rectangular weir is 0.622, and the
value of Cd for a V-notch weir 0.58 to 0.61.
For this experiment, the Cd value for both notch are not constant. Since Cd is not a constant, a
functional relationship needed to be created:
Qactual = a * Hn
Where a and n are constants
In order to find the value of a and n, a power fit or trend line in Excel needed to be used.
Q against H3/2
0
0
0
0
0
0
f(x) = 0 x^1.37
H3/2
Figure 8.1: A graph of Q against H3/2 for rectangular notch
Q against H5/2
0
0
0
0
0
0
f(x) = 0 x^1.62
H5/2
Figure 8.2: A graph of Q against H5/2 for V-notch
Based on both graphs above, the value of a and n for rectangular notch is 7 and 1.36999 respectively.
As for V notch, the value of a is 7 and the value of n is 1.6219.
The experiment did not produce the exact resuls as the theory maybe due to human careless mistakes.
However, the coefficient of discharge can still be determined eventhough there is a slight difference
between the theory.
