Lab2FREE AND FORCE VORTEX
Short Description
EXPRIMENTAL LAB...
Description
Abstract
The purpose of this experiment was to study the relationship between surface profile and spee speed d for for a free free vorte vortex x and and surf surface ace prof profil ilee with with angu angular lar velo veloci city ty for for a force forced d vorte vortex. x. In the the experiment of free vortex, water was pumped out through different orifice diameters of 24 mm, 16 mm, 12 mm and mm to create different surface profiles. The diameter from centre, height, pitot tube head difference and pressure head were recorded and calculated for each vortices formed. !rom there there,, a grap graph h of pres pressu sure re head head agai agains nstt 1"r 1"r 2 was was plot plotted ted,, where where the the grad gradien ientt was was used used in the the calculation of theoretical velocity. #oth actual $experimental% and theoretical velocities were then compared. &eanwhile, for the experiment of forced vortex, two trials were perfomed with each using different water flow rates. ' paddle was involved in the formation of the vortex. The angular velocities were calculated and a graph comparing the actual height theoretical height against the distance from centre was plotted.
1.0 Introdu Introductio ction n
(i)iuds undergo rotational motion, where they move in a circular motion. ' vortex is a region within fluid where the flow moves within a circular motion about an axis. 'ccording to *ueh $2+14%, water vortex is a phenomenon where water flow in swirl motion, always described by cylindrical coordi coordinat nates es with with tangen tangentia tial, l, radial radial and axial axial axis. axis. In macrosc macroscopi opicc level, level, such such phenom phenomeno enon n is common. ' vortex could be observed in nature through tropical cyclones, which also referred to by various names according to their location and strength, such as typhoon and hurricane $'lbert,2++-%. (i)uid vortex also occurs in many chemical engineering appliances, such as in centrifugal centri fugal pump, in a stirred vessel and in a cyclonetype separator $/oulson, 1---%. ' free vortex is formed as water throughout a central hole in the base of a container. The degree of vortex rotation is dependent to the speed of water flow. The form moves spirally as the water moves towards the centre with stream line in motion so that the energy per unit mass remains constant. 0hile the water mass is rotating, the central hole is plugged, the flow of water in the vertical plane ceases and the motion becomes one of a simple rotation in the horiontal plane and it is nown as free cylindrical vortex. 3nder steady condition, each particle will move with the same angular velocity and there will not be any relative motion between the particles. treamlines for such a flow will be concentric circles and the total energy is constant along a streamline but varies from one streamline to another. 0hen a cylinder cylinder containing containing water is rotated by an external external force, a forced vortex vortex is formed. formed. The motion of the fluid swirling rapidly is the vortex formed. ' forced vortex flow is that in which the fluid mass is made to rotate by means of some external force, which exerts a constant tor)ue on the fluid thus resulting for the whole mass of fluid to rotate at constant a angular velocity, 5. There is always constant external tor)ue re)uired to be applied to the fluid mass resulting in an expenditure of energy.
2.0 Obje Objectiv ctives es 2.1 !ree o ortex i. To stu study the surface face profile and speed. ii. ii. To fin find d the the rel relat atio ions nshi hip p bet betwe ween en sur surfa face ce pro profi file le and and spee speed. d. 2.2 !orced o ortex i. To stu study the the su surfac rfacee pro profi file le and and an angula gularr vel velo ocity city.. ii. ii. To find find the the rela relati tion onsh ship ip betw betwee een n sur surfa face ce prof profil ilee and and total total head head..
3.0 The Theory ory
7.1 !ree o ortex ' vortex is the motion of many fluid particles around a common center. !ree vortex contains radial velocity towards the center. 0ater 0ater passes through each segments of diameter, and the energy at any tube is constant, which then relates to8
+
9 : constant
7.2 !orced o ortex !orced vortex is formed when a body containing fluid is rotated by paddling. The total energy is constant along a streamline. ;owever it varies varies from streamline to streamline. The e)uation of the free vortex related to the angular velocity is given by
The radial pressure increases and shown by,
=
= ωr 2
dp = ρ ω
rdr
− = ω r −r
= r #ecause
=
h −h =
r
h =h +
r
, so
The e)uation of forced vortex is represented by8
z = 0hile the e)uation of distribution of total head can be represented by8
H = 0here8 : surface profile < : angular velocity r : radius g : gravity ; : total head The e)uation of acceleration of the radial,
and direction ,
is given by,
The e)uation of angular velocity is calculated by8
Ω=
4.0 Apparatus and Materials 4.1 =(T>? !ree and !orced ortex $&odel 8 !&42% 4.2 top watch 4.3 @ower supply 4.4 &easuring gauge 4.5 0ater 5.0 rocedure A.1 !ree ortex A.1.1 Beneral startup procedures were performed. A.1.2 'n orifice with diameter of 24 mm was selected and placed on the base of cylinder
A.1.7
tan. The output valve was closed and the inlet 7way valve was adCusted to let the water flows into the tan from two pipes with 12.A mm diameter. This results in the water
A.1.4
flow out through the orifice. The pump was switched on and the control valve on the hydraulic bench was slowly opened until the tan limit. 0ater level in the tan was maintained by adCusting the
A.1.A
control valve. The vortex profile was collected by measuring the vortex diameter for several planes
A.1.6
using the profile measuring gauge when the water level is stable. The profile measuring gauge was pushed down until the both of sharp point touches
A.1.D
the water surface. The height, h $from the top of the profile measuring gauge to the bridge% was recorded. The value of a $distance from the bridge to the surface of the water level%
A.1.
was obtained. The pitot tube was used to measure the velocity by sining it into the water at the depth of A, from the water surface. The depth of the pitot tube in the water, ; was
A.1.-
measured. teps 7 to were repeated using another three orifice with diameter of 12mm, 16mm
and mm respectively. A.1.1+ The coordinates of vortex profile for all diameter of orifice were plotted in graph and the gradient of the graph was calculated. A.1.11 The graph of velocity which is calculated from the pitot tube reading versus the radius of the profile was plotted A.2 !orced vortex A.2.1 The general startup procedures were performed. A.2.2 ' closed pump with two pedals was placed on the base of the cylinder tan.
A.2.7
The output valve was closed and the inlet 7way was adCusted to let the water flows into the tan from two pipes with -.+ mm diameter. The water will flow out through
A.2.4
another two pipes with 12.A mm diameter. The water flow out from the tan was ensured with the siphon effect by raising the
A.2.A
hose to above the water level in the tan. The outlet hose was ensured to fill with water before letting the water to flow into
A.2.6
the sump tan in the hydraulic bench. The angular speed of the pedals was measured by counting the number of circles in a
certain times. A.2.D The surface probe was pushed down until the sharp point touch the water surface. A.2. The height, ho $from top of the measuring gauge to bridge% was measured. A.2.- teps 4 to were repeated with different volumetric flow rate. A.2.1+ The coordinates of vortex profile for different angular velocity was plotted. A.2.11 The calculated vortex profile was plotted in the same graph.
!.0 "esults 6.1 !ree vortex
=rifice diameter : 24 mm EFistance from bridge to water surface, a : 11 mm Fiameter &easure at centre, d ;eight, F $mm% h $mm%
@itot Tube ;ead Fifference , ; $mm%
AA
D6
A7
r $mm%
r 2 $mm2%
6
@ressure elocity, ;ead " $mm"s% Fepth of the @itot Tube, G $mm% D7 747.1+7
2D.A
DA6.2A
D4
-
DA
42+.214
26.A
D+2.2A
4-
6-
12
+
4A.222
24.A
6++.2A
4
6
1A
1
A42.4-4
2A.+
62A.++
r $mm%
r 2 $mm2%
2
2
2
2
=rifice diameter : 16 mm Fistance from bridge to water surface : 1-2 mm Fiameter &easure @itot Tube @ressure elocity, at centre, d ;eight, ;ead ;ead " $mm"s% F $mm% h $mm% Fifference Fepth of , ; $mm% the @itot Tube, G $mm% A+ 1+4 A 74 717.2+-
2A.+
62A.++
4D
1+1
6
7D
747.1+7
27.A
AA2.2A
44
--
-
7-
42+.214
22.+
44.++
4+
-6
11
42
464.A64
2+.+
4++.++
=rifice diameter : 12 mm Fistance from bridge to water surface : 2+1 mm Fiameter &easure at centre, d ;eight, F $mm% h $mm%
@itot Tube ;ead Fifference , ; $mm%
4
11A
46
r $mm%
r 2 $mm2%
4
@ressure elocity, ;ead " $mm"s% Fepth of the @itot Tube, G $mm% 14 2+.147
24.+
AD6.++
111
D
1
7D+.A-4
27.+
A2-.++
47
1+D
1+
22
442.-4A
21.A
462.2A
7-
1+6
17
27
A+A.+7A
1-.A
7+.2A
r $mm%
r 2 $mm2%
2
2
2
2
=rifice diameter : mm Fistance from bridge to water surface : 2+ mm Fiameter &easure @itot Tube @ressure elocity, at centre, d ;eight, ;ead ;ead " $mm"s% F $mm% h $mm% Fifference Fepth of , ; $mm% the @itot Tube, G $mm% 4+ 11D 7 A 242.611
2+.+
4++.++
7D
117
A
-
717.2+-
1.A
742.2A
77
112
D
1+
7D+.A-4
16.A
2D2.2A
2-
11+
11
12
464.A64
14.A
21+.2A
6.2 !orced vortex Fistance from /entre $mm% + 7+ D+ 11+ Ho of evolutions in 6+ seconds 'ngular elocity $rad"s%
1st -2 -4 - 1+71
2nd D7 7 6 -2 72
7rd AA 64 6D4 74
7.2A
7.7A
7.A6
#.0 $a%ple &alculations D.1 !ree vortex !rom Braph 1
gradient,m=
Thus,
=18333.33
=18965.76 Theoretical velocity or calculated velocity,
v=
v=
689.664
v= v=
715.690
774.113
adius, r $mm%
'ctual elocity, v $mm"s%
2D.A 26.A 24.A 2A.+
747.1+7 42+.214 4A.222 A42,4-4
D.2 !orced vortex !or the first volumetric flowrate
an u ar ve o!it ,Ω =
v= 758.630
Theoretical elocity, v $mm"s% 6-.664 D1A.6-+ DD4.117 DA.67+
3.25
Theoretical height from top of the surface probe to bridge,
h =92 +
.
(30 )
h =92 +
.
h =h +
( 70 )
r
h =92 +
.
(110)
/alculated values Fistance from centre $mm% + 7+ D+ 11+ 'ngular velocity $rad"s%
h $mm% 1st
2nd
7rd
-2.++ -2.4 -4.64 -.A1
D7.++ D7.A1 DA.+ D-.-2
AA.++ AA.A A.1D 62.2
7.2A
7.7A
7.A2
!ull calculations are in the 'ppendices. Fata analyses were tabulated in 'ppendices.
'.0 (iscussion This experiment aims to investigate the relationship between surface profile and speed for
a free vortex and surface profile with angular velocity for a forced vortex. ' free vortex is formed when water flows out through a hole at the bottom of a tan while driven by the circular rotation of a pumping water vessel. ;ere, the water flows out through different orifice diameters of 24 mm, 16 mm, 12 mm and mm. =nce the flow had stabilied, the diameter at centre, height, pitot tube head difference and pressure head were recorded and calculated. !rom the results, 24 mm orifice diameter gave the biggest vortex diameter, followed by the 16 mm, 12 mm and mm. This is because as diameter of orifice decreases, the vortex diameter also decreases. 'lso, the theoretical velocities were calculated from the graph of pressure head against 1"r 2 that was plotted. !orced vortex on the other hand is formed when a li)uid is rotated by a paddle within a tan. The surface profile of forced vortex is a parabolic shape and is dependent to the angular velocity of the rotation. The rotational speed of the paddle was measured by counting the number of rotations in 6+ seconds. Two trials were conducted where both used different flow rates of water. The angular velocities were calculated where it was used to compare the actual and theoretical values centre between by plotting a graph of height against distance from centre. !or both experiments, there shows a deviation between the experimental and theoretical values. This is because there are a few errors that had occurred. =ne of the errors is that the end of the measuring gauge was not able to measure the diamter at the center of the vortex as the centre of the vortex was not in the middle of the tan. #esides that, the pitot tube did not sined into Amm from the surface. This affected the results when calculating the velocity by using the
formula
.
'lso, the flow of water had not achieved asteady state. (astly, the eyes were
not perpendicular to the reading scale and parallax error may have had occurred when the reading was taen. ).0 &onclusion -.1 !rom the experiment conducted free vortex and forced vortex have their own surface profile. -.2 !or free vortex, the diameter of the vortex is proportional with the diameter of orifice and the
velocity is inversely proportional to the radius. -.7 !or forced vortex, the angular velocity is proportional to the water flow rate and the height of vortex formed.
10.0
"eco%%endations
1.1 ' stable flow of water should be obtained to get more accurate readings of the surface profile by controlling the pump valve. 1.2 Fust free apparatus should be used. 1.7 /lear water without any particles should be used in the experiment. 1.4 =iling and greasing of the parts such as the paddle should be done at regular intervals.
"e*erences J.M Coulson & J. F Richardson , (1999), Chemical Engineering, Volume 1, Sixth Edition, Fluid Flow, Heat Transfer and Mass Transfer , Butterworth Heinnemann
Te /heng *ueh, $'pril 2+14%, Numerical Analysis of Water Vortex Formation for the Water Vortex Power Plant , retrieved from http8""pubs.rsc.org.eaccess.library.uitm.edu.my"en"content"chapterpdf"2++"-D14DAADA6+++71J isbn:-D+A4+41A6AKpdate:2++11+4Ksercode:bKpage:search, at 24th Fecember 2+14 'lbert BuiCarro, $2++-%, The Origin of Chirality in the Molecules of Life: A e!ision from Awareness to the Current Theories an" Pers#ecti!es of this $nsol!e" Pro%lem, retrieved from http8""search.pro)uest.com.eaccess.library.uitm.edu.my"docview"1A+D612A2-Jp)origsite:summon, at 24th Fecember 2+14
A+,(I&+$
i. Data nal!sis
Pressure Head VS 1/r2 82
80
78
76 Pressure Head, X (mm) 74
72
70
68 0
0
0
0
0
0
1/r2 (1/mm2 )
Graph 1
0
0
0
0
Pressure Head VS 1/r2 45 40 35 30 25 Pressure Head, X (mm)
20 15 10 5 0 0
0
0
0
1/r2 (1/mm2 ) Graph 2
0
0
0
Pressure Head VS 1/r2 25
20
15 Presssure Head, X (mm) 10
5
0 0
0
0
0
1/r2 (1/mm2 ) Graph 3
0
0
0
Pressure Head VS 1/r2 14 12 10 8 Pressure Head, X (mm)
6 4 2 0 0
0
0
0
1/r2 (1/mm2 ) Graph 4
ii.
/alculations for !ree ortex !rom graph 2
gradient,m=
Thus,
=5797.101
=10664.85
0
0
0.01
Theoretical velocity,
v=
.
v=
.
v=
426.594
453.823
v= 484.766
adius, r $mm%
'ctual elocity, v $mm"s%
2A.+ 27.A 22.+ 2+.+
717.2+747.1+7 42+.214 464.A64
!rom graph 7
gradient,m= .
.
Thus,
=9375.00
=13562.36 Theoretical velocity,
v=
.
v=
.
533.243
Theoretical elocity, v $mm"s% 426.A-4 4A7.27 44.D66 A77.247
v= 565.098
v=
v=
589.660
630.807
adius, r $mm%
'ctual elocity, v $mm"s%
24.+ 27.+ 21.A 1-.A
2+.147 7D+.A-4 442.-4A A+A.+7A
v= 695.506
Theoretical elocity, v $mm"s% A6A.+- A-.66+ 67+.+D 6-A.A+6
!rom graph 4
gradient,m= .
.
Thus,
=2000
=6264.18 Theoretical velocity,
v=
.
313.209
v= v=
.
338.604
v=
.
379.647
adius, r $mm%
'ctual elocity, v $mm"s%
2+.+ 1.A 16.A 14.A
242.611 717.2+7D+.A-4 464.A64
v=
.
432.012
Theoretical elocity, v $mm"s% 717.2+77.6+4 7D.64D 472.+12
Velocity VS Radius 900 800 700 600 Actual Velocity, v (mm/s)
500 Velocity, (mm/s)
Teo!etical Velocity, v (mm/s)
400 300 200 100 0 24
25
26
27
Radius, r (mm)
Graph !
28
Velocity VS Radius 600
500
400 Actual Velocity, v (mm/s) Velocity, (mm/s)
300
Teo!etical Velocity, v (mm/s)
200
100
0 19 20 21 22 23 24 25 26 Radius, r (mm)
Graph "
Velocity VS Radius 800 700 600 500 Actual Velocity, v (mm/s) Velocity, (mm/s)
400
Teo!etical Velocity, v (mm/s)
300 200 100 0 19 20 21 22 23 24 25 Radius, r (mm)
Graph #
Velocity VS Radius 500 450 400 350 300 Velocity, (mm/s)
Actual Velocity, v (mm/s)
250
Teo!etical Velocity, v (mm/s)
200 150 100 50 0 14 15 16 17 18 19 20 21 Radius, r (mm) Graph $
iii.
/alculations for !orced ortex
!or the 2nd volumetric flowrate
an u ar ve o!it ,Ω =
3.35
Theoretical height from top of the surface probe to bridge,
h =73 +
.
(30 )
h =73 +
.
( 70)
h =h +
r
h =73 +
.
(110)
!or the 7rd volumetric flowrate
an u ar ve o!it ,Ω =
3.56
Theoretical height from top of the surface probe to bridge,
h =55 +
.
(30 )
h =55 +
.
( 70)
h =h +
r
h =55 +
.
(110)
h VS %ista&ce 'rom e&tre
Actual (mm)
Heiht 'ro *op o' the Sur'ace Pro+e to ride, h (mm)
Graph -
teo!etical (mm)
h VS %ista&ce 'rom e&tre
Actual (mm)
Heiht 'ro *op o' the Sur'ace Pro+e to ride, h (m m)
Graph 1.
Teo!etical (mm)
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