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CALCULATION
FREE VORTEX
Orifice diameter = 24 mm
Distance from bridge to water surface, a = 205 mm
Diameter
at
center, D
(mm)
Measure
d height,
h (mm)
Pitot
tube
head,
differenc
es, H
(mm)
Pressure
head /
depth of
pitot
tube, X
(mm)
Velocity,
V (mm/s)
r (mm) r2 1
r2
69 115 10 10 442.94 34.5 1190.2
5
0.000840
2
62 110 10 15 442.94 31.0 961.00 0.001041
57 100 10 25 442.94 28.5 812.25 0.001231
Note: X(mm) = profile measuring gauge whole length (330mm) - h - a
0.0008 0.00085 0.0009 0.00095 0.001 0.00105 0.0011 0.00115 0.0012 0.00125 0.00130
5
10
15
20
25
30
f(x) = 38255.2064786148 x − 23.0192845342483
pressure head against 1/r2
1/r2
pres
sure
hea
d
Gradient of the graph = 38255 mm2
K2
2g=38255mm2
Therefore, K = 27396.41mm2/sec
V=(2gH )0.5 =442.94 mm/sec
V= Kr
=27396 .4134 .5
=794 .10
mm/sec
V=(2gH )0.5 =442.94 mm/sec
V= Kr
=27396 .4131 .0
=883 .76
mm/sec
V=(2gH )0.5 =442.94 mm/sec
V= Kr
=27396 .4128 .5
=961 .28
mm/sec
As a result;
r (mm) Calculated Velocity
(mm/sec)
Velocity
(mm/sec)
34.5 794.10 442.94
31.0 883.76 442.94
28.5 961.28 442.94
34.5 31 28.50
200
400
600
800
1000
1200
velocity against radius
calculated velocity velocity
radius
velo
city
Orifice diameter = 16 mm
Distance from bridge to water surface, a = 231 mm
Diameter
at
center, D
(mm)
Measure
d height,
h (mm)
Pitot
tube
head,
differenc
es, H
(mm)
Pressure
head /
depth of
pitot
tube, X
(mm)
Velocity,
V (mm/s)
r (mm) r2 1
r2
45 95 8 4 396.18 22.5 506.25 0.001975
40 91 10 8 442.94 20 400.00 0.002500
38 90 7 9 370.59 19 361.00 0.002770
Note: X(mm) = profile measuring gauge whole length (330mm) - h - a
0.0019 0.002 0.0021 0.0022 0.0023 0.0024 0.0025 0.0026 0.0027 0.0028 0.00290
2
4
6
8
10
12
f(x) = − 567.031381853257 x + 9.70278816431136
pressure head against 1/r2
1/r2
pres
sure
hea
d
Gradient of the graph = -567.03 mm2
K2
2g=−567 .03mm2
Therefore, K = 3335.44mm2/sec
V=(2gH )0.5 =396.18 mm/sec
V= Kr
=3335 .4422 .5
=148 .24
mm/sec
V=(2gH )0.5 =442.94 mm/sec
V= Kr
=3335 .4420
=166 .77
mm/sec
V=(2gH )0.5 =370.59 mm/sec
V= Kr
=3335 .4419
=175 .50
mm/sec
As a result;
r (mm) Calculated Velocity
(mm/sec)
Velocity
(mm/sec)
22.5 148.24 396.18
20 166.77 442.94
19 175.50 370.59
22.5 20 190
100
200
300
400
500
600
700
velocity against radius
calculated velocity velocity
radius
velo
city
Orifice diameter = 12 mm
Distance from bridge to water surface, a = 205 mm
Diameter
at
center, D
Measure
d height,
h (mm)
Pitot
tube
head,
differenc
Pressure
head /
depth of
pitot
Velocity,
V (mm/s)
r (mm) r2 1
r2
(mm) es, H
(mm)
tube, X
(mm)
39 120 5 5 313.21 19.5 380.25 0.002630
30 110 3 15 242.61 15.0 225.00 0.00444
25 105 6 20 343.10 12.5 156.25 0.00640
Note: X(mm) = profile measuring gauge whole length (330mm) - h – a
0.002 0.0025 0.003 0.0035 0.004 0.0045 0.005 0.0055 0.006 0.0065 0.0070
1
2
3
4
5
6
7
f(x) = 281.638363469587 x + 3.4017073687725
pressure head against 1/r2
1/r2
pres
sure
hea
d
Gradient of the graph = 281.64 mm2
K2
2g=281 .64mm2
Therefore, K = 2350.82mm2/sec
V=(2gH )0.5 =313.21 mm/sec
V= Kr
=2350 .8219 .5
=120 .55
mm/sec
V=(2gH )0.5 =242.61 mm/sec
V= Kr
=2350 .8215
=156 .72
mm/sec
V=(2gH )0.5 =343.10 mm/sec
V= Kr
=2350 .8212 .5
=188 .10
mm/sec
As a result;
r (mm) Calculated Velocity
(mm/sec)
Velocity
(mm/sec)
19.5 120.55 313.21
15.0 156.72 242.61
12.5 188.10 343.10
19.5 15 12.50
50
100
150
200
250
300
350
400
velocity against radius
velocity calculated velocity
radius
velo
city
Orifice diameter = 8 mm
Distance from bridge to water surface, a = 240 mm
Diameter
at
center, D
(mm)
Measure
d height,
h (mm)
Pitot
tube
head,
differenc
es, H
(mm)
Pressure
head /
depth of
pitot
tube, X
(mm)
Velocity,
V (mm/s)
r (mm) r2 1
r2
26 75 4 15 280.14 13 169 0.005917
22 70 6 20 343.10 11 121 0.008246
20 60 3 30 242.6 10 100 0.010000
Note: X(mm) = profile measuring gauge whole length (330mm) - h - a
0.0055 0.006 0.0065 0.007 0.0075 0.008 0.0085 0.009 0.0095 0.01 0.01050
1
2
3
4
5
6
7
f(x) = − 182.39663147189 x + 5.80354883362731
pressure head against 1/r2
1/r2
pres
sure
hea
d
Gradient of the graph = -182.4 mm2
K2
2g=−182 .4mm2
Therefore, K = 1891.74mm2/sec
V=(2gH )0.5 =280.14 mm/sec
V= Kr
=1891 .7413
=145 .52
mm/sec
V=(2gH )0.5 =343.10 mm/sec
V= Kr
=1891 .7411
=171 .98
mm/sec
V=(2gH )0.5 =242.6 mm/sec
V= Kr
=1891 .7410
=189 .17
mm/sec
As a result;
r (mm) Calculated Velocity
(mm/sec)
Velocity
(mm/sec)
13 145.52 280.14
11 171.98 343.10
10 189.17 242.6
13 11 100
50
100
150
200
250
300
350
400
velocity against radius
velocity calculated velocity
radius
velo
city
Forced Vortex
Distance From Center (mm)
h0 (mm)
First Reading Second Reading
Third Reading
0 83 85 83
30 85 110 87
70 94 117 90
110 96 125 100
No. of revolution in 60 sec
30 32 34
Angular velocity (rad/sec)
3.142 3.35 3.561
For the first volumetric flow rate :
Number of revolutions in 60 seconds: 30
Ω=2Π×revolution60
=
2(3 .142 )x30 ¿60 ¿
¿¿=3.142 rad/sec
h=
h0+w2
2gr2
=
83+(3 .142)2
2( 9810)(30 )2
= 83.45 (calculated)
h=
h0+w2
2gr2
=
83+(3 .142)2
2( 9810)(70 )2
= 85.47
h=
h0+w2
2gr2
=
83+(3 .142)2
2( 9810)(110 )2
= 89.10
0 20 40 60 80 100 12075
80
85
90
95
100
height from top of measuring gauge to bridge against distance from centre
H H calculated
Graph for first trial
For the second volumetric flow rate :
Number of revolutions in 60 seconds: 32
Ω=2Π×revolution60
=
2(3 .142 )x32 ¿60 ¿
¿¿=3.35 rad/sec
h=
h0+w2
2gr2
=
85+(3 .35 )2
2(9810 )(30 )2
= 85.51
h=
h0+w2
2gr2
=
85+(3 .35 )2
2(9810 )(70 )2
= 87.80
h=
h0+w2
2gr2
=
85+(3 .35 )2
2(9810 )(110)2
= 91.92
30 70 1100
20
40
60
80
100
120
140
height from top of measuring gauge to bridge against distance from centre
H calculated H
Graph of second trial
For the third volumetric flow rate :
Number of revolutions in 60 seconds: 34
Ω=2Π×revolution60
=
2(3 .142 )x34¿60 ¿
¿¿=3.56 rad/sec
h=
h0+w2
2gr2
=
83+(3 .56 )2
2(9810 )(30 )2
= 83.58(calculated)
h=
h0+w2
2gr2
=
83+(3 .56 )2
2(9810 )(70 )2
= 86.17
h=
h0+w2
2gr2
=
83+(3 .56 )2
2(9810 )(110)2
= 90.81
0 20 40 60 80 100 1200
20
40
60
80
100
120
height from top of measuring gauge to bridge against distance from centre
H H calculated
Graph for third trial
