UNIVERSITI TEKNOLOGI MARA FAKULTI FAKULTI KEJURUTERAAN KIMIA ENGINEERING CHEMICAL ENGINEERING LABORATORY (CHE465) NAME
: MUHAMMAD AMIRUL BIN HASHIM
STUD STUDE ENT NO NO..
: 2014 201420 2078 7844 44
GROUP
: EH 220 2A
EXPERIMENT
: FREE AND FORCED VORTEX
DATE PERFORMED
: 14/4/2015
SEMESTER
:2
PROGRAMME / CODE
: EH 220
SUBMIT TO
: MS NURUL DIANAH
N . 1 4 5 6 8 9 : .3 .. .1
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;a+e!ABSTRACT
Vortex is the rotation of fluid elements around a common center. Its concept was being used in various types of industry such as turbine design and creating standard safet safety y again against st natur natural al disas disaster ter.. This This exper experime iment nt
was was carr carried ied out to study study the
relationship relationship between the surface shape of free and forced vortex. It also to study on the angular angular velocity velocity of a rotating rotating liquid in a cylindri cylindrical cal tank. tank. Theoret Theoretica ically lly,, the angular angular velocity of the fluid was manipulated by adjusting the control valve to provide different flow rate of fluid flow. The height of vortex profile was measured when it maintained constantly at its maximum height. fter carried the experiment, it can be conclude that the height of vortex profile increased as the vortex radius decreased. This conclusion is obtained from the result of the experiment. !or forced vortex , when the angular velocity of the fluid in the cylinder increases, the depth of each pointer at the different vortex radius will also increase due to the formation of semi parabolic shape. Therefore, it was concluded that the height of water surface level is relative to the lowest point of the surface of a forced vortex flow was directly proportional to the angular velocity of a rotating liquid in a cylindrical tank and is inversely proportional to the squared radius at which it was measured.
INTRODUCTION
In fluid dynamics a vortex is a region, in a fluid medium, in which the flow is mostly rotating on an axis line, the vortical flow that occurs either on a straight"axis or a curved"a curved"axis. xis. #oreover, #oreover, the plurals plurals of vortex vortex are vortices vortices and vortexe vortexes. s. $xample $xamples s of vortices occur in nature, perhaps the most common being a tornado or a whirlpool. tornado is formed by high winds whirling around an area of extremely low pressure and characterised by a funnel shaped cloud. %hirlpools can occur where tides flowing in different directions meet or at the base of waterfalls where the effect is a spiraling or swirling of the water again producing a funnel shape. &asically there are two types of motion translation and rotation. The two may exist independently or simultaneously. If now an element is represented, it may be subjected to deformation. This can be linear or angular. If the motion of the particles is purely translational and the distortion is symmetrical, the flow is irrotational and the vorticity. vorticity. $xample' !lownet application. !orced vortex is also known as flywheel flywheel vortex. ( v ) r !ree vortex is also known as potential vortex. ( v r ). )ompound vortex combination of free and forced vortex also known as *ankine vortex. +piral vortex free vortex and a radial flow-. *otation of a fluid, moving as a solid, about an axis is called forced vortex motion. $very particle of fluid will have same angular velocity. velocity. !ree vortex motion is each particle moves in a circular path with speed varying inversely as the distance from the centre ( vr constant. This experiment is related to the free and forced vortex flow of fluid in rigid"body rotation within a cylindrical tank. s mentioned in paragraph , vortex is the rotation of fluid elements around a common center. #ostly the fluid flows in a spinning motion about an imaginary axis, straight or curved. That motion pattern is called a vortical flow. There are two types of vortices, which are forced and free. The fluid or gas- circles around a center in a forced vortex, while in a free vortex, the medium spirals towards the center.
In an industry and in a real world, the applications of the vortex flow can be seen in a various area such as turbine design, natural phenomenon and in creating safety against natural disaster. disaster. Thus, Thus, the findings of the experiment are very important to help the engineers to design a good turbine as the flow of water through the runner of turbine is a good example that used the principle of forced vortex flow. The findings also can help engineer in designing a good technology in minimi/ing the effect of natural disaster such as tornado and hurricane. !urthermore, the knowledge gain from this experiment will help students to apply the correct concept in a real situation related to vortex flow as they already experienced it. 0enerally, the apparatus for the study of the shape of 1free and forced vortices1 consists consists of a 234mm diameter cylindrical, transparent transparent vessel 54mm depth, having two pairs of diametrically opposed inlet tubes of 6.4mm and 2.3mm diameter. The 2.3 diameter inlet tubes which are angles at 37 to the diameter, so that a swirling motion is imparted to the liquid entering the vessel, are used as entry tubes for the free vortex experiment. smooth outlet is centrally positioned in the base of the vessel and a set of push"in orifices of 28, 9, 2 and 5mm diameter is supplied to reduce the outlet diameter to a suitable value. The profile of the vortex formed at the top of the vessel is deter determin mined ed by a gauge, gauge, hous housed ed on a diamet diametric rical ally ly mount mounted ed bridg bridge e piece piece,, which which measures the diameter of the vortex at various depths. This gives the co"ordinate points required to plot the vortex profile. The forced vortex is created in the vessel described above by using as the inlet the 64mm bore tubes which are angled at 947 to the diameter. The input water from these tubes impinges on a simple two blade paddle which acts as a stirrer : flow straightener. The water 1leaves1 the vessel via the 2.3mm diameter angled tubes which are used as 1entry tubes for the free vortex experiment. The two bladed paddle rotates on a vertical shaft supported by a bushed plug, in the hole used as the outlet for the free vortex experiment, and located at the top by a suitable hole in the bridge piece fitting across the diameter of the vessel. This bridge piece also houses the probes required to determine the co"ordinates of the vortex profile to be measured.
!or this experiment, +;
•
•
The movement of the liquids within the impeller of a centrifugal pump when there is no flow as, for example, when the outlet valves are closed. The rotation of the liquid within the confines of a stirrer in an agitated tank. The rotation of liquids in the basket of centrifuge
Figure 1 : shows the example of fore !ortex forme"
T#$OR%
!ree )ylindrical Vortex %hen a liquid is flowing out of a tank through a hole at the bottom of the tank, free vortex is formed with the number of oscillation depending on the distortion that created the flow. The liquid is moving spirally towards the center following current, energy per unit mass is assumed to be constant when energy loss by viscosity is neglected. If, while the mass of water is rotating, the central exit hole is plugged, the flow of water in the the verti vertica call plane plane cease ceases s and and the the motion motion becomes becomes one one of simpl simple e rotat rotation ion in the the hori/ontal plane. This is known as free cylindrical vortex. &ernoulli>s theorem can be used because the movement is along the flow axis,
p
+
pg
V 1 1 g
+ z = cons +a2 t
!or hori/ontal plane, the relation becomes
p pg
+
V 1 1 g
= cons +a2 t
Integration of the above relation with r gives
. dp V dV + =3 pg dr g dr ?ext, consider a pair of stream line being divided with distance, @r and is in same hori/ontal hori/ontal plane and are linked by a fluid tube with wide @. The centrifugal centrifugal force of the tube is balanced by the pressure difference between both ends, that is
pg ∂A∂r
V1 6r
=
dp dr
∂r ∂ A
pgV 1 gr
=
dp dr 2-
)ombine - and 2- to produce
V 1
V dV =3 gr g dr
+
dV dr
+
V r
=3
Integrate above relation to obtain ln r A ln V ( )onstant Vr ( B )onstant-
V =
K r
In free cylinder vortex, velocity is inversely proportional to distance from spiral axis, &ernoulli>s theorem is used to determine surface profile as follow'
V 1 1 g
+ z = C (Cons +a2 t ) 8-
+ubstitute C- into 8-
K 1 1
1 gr
+ z = C
C − z =
K 1 1 gr 1 3-
yx
1
That is, equation for hyperbolic curve hori/ontal to / ( )
( that is symmetry to axis of rotation and is
!ree Vortex #ovement in free vortex is different with free cylindrical vortex because free vortex contains radical velocity towards center. $quation for such situation can be generated by considering the water passes through round segments towards is diameter, where energy passing any tube and is kept constant until
p pg
+
V 1 1 g
+ z = cons +a2 t
If and V is surface area and velocity of a particular position while and V are surface area and velocity at distance r from center circle, V ( V V ( )onstant )onstant &y taking ( Br,
V =
r .V . r
If / is constant,
p pg p pg
1
+
r . V .
1
1
1 gr
= C 1
= C −
r . V .
1
1 gr 1 9-
lso,
p.
+
pg
V .
1
1 g
p − p.
V .
=
pg p − p.
=
pg
= C
V .
1
1
−
r . V .
1
1 g
1 gr 1
1
r .
.
?. − 1 > 1 g r . D-
!ree vortex can be said as combination of cylinder vortex and radial flow. Velocity is inversely proportional to radius in every case. ngle between flow axis and radius vector at any point is constant and these axis from the spiral pattern.
!orced Vortex s we know, know, angular velocity is is constant, constant, V( wr wr Increase in radial pressure is given by
dp dr
= p
V 1 r
p1
= pω r 1
r 1
∫ dp = pω ∫ rdr 1
p.
r .
. 1 1 p1 − p. = pω 1 (r 1 − r . ) 1 p. = p3 &y taking
r . = 3 when
p1 = p , and
p − p3 pg &ecause, p:pg ( h, so
r 1 = r and
=
w1 1 g
r 1
1
h − h3 =
ω
1 g
r 1
1
h = h3 +
ω
1 g
r 1
This is a parabolic equation. +urface profile for forced vortex can be represented by equation'
Ω r 1
z =
1
1 g
Eistribution of total head can be represented by equation'
Ω r 1
H =
1
g
F ( surface profile ῼ( angular velocity r ( radius g ( gravity G ( total head
ngular velocity can be calculated calculated by'
Ω=
1η × revolution time (e#)
AI& ' OB($CTI)$S
$xperime*t 1: Free )ortex )ortex
. To study study on on surface surface profi profile le and spee speed. d. 2. To find a relation between between surface surface profile profile and speed. $xperime*t +: Fore" )ortex )ortex . To study on on surface surface profile profile and angular angular velocity. velocity. 1 To find a relation between surface profile and total head
A,,ARATUS
Or*<*#e < $*ame+er 9mm@ .1mm@ .6mm@ 14mm
7r<*,e mea0r*2 a0e
7a$$,e
ssembly View
&ridge
2
Hrofile measuring gauge
C
6.4 mm diameter, ?o//le
8
Three way inlet valve
3
2.3 mm diameter, ?o//le
9
Inlet
D
+urface profile
5
;utlet valve
6
;utlet
4
Hitot tube
orifice
2
Haddle
&$T#ODO-O.%',ROC$DUR$
.e*eral Start Up:
. The hydrau hydraulic lic bench bench tank tank is filled filled with with water. water. 2. The study study bench bench is place placed d on the hydrau hydraulic lic bench. bench. C. ll the access accessorie ories s must be make make sure are ready ready on the the bench such such as surface surface probe, profile measuring gauge, pitot tube, paddle and orifices. 8. The inlet inlet and and outlet outlet hose is set set up. up. 3. The stand stand of the equipment equipment is adjusted adjusted to reach reach the hori/ontal hori/ontal position. position. .e*eral Shut Dow*:
. The valves valves are are closed closed and and the pump pump is switch switched ed off. off. 2. The The orific orifices es,, paddl paddle e and and othe otherr acces accessor sories ies are remov removed ed from from the cylindr cylindrica icall vessel. C. The water water is drain off off from from the unit unit when when it is not in used. Safet/ ,reautio*:
. proper lab coat coat must be worn worn while doing the experiment. experiment. 2. The sharpened sharpened object object is being being aware aware during during conducting conducting the experiment. experiment. C. %hen water water is splashed splashed out out from tank, tank, that area area must be mopped mopped immediately immediately to avoid slippery floor. $xperime*t 1: Free )ortex )ortex
. The genera generall start"up start"up proced procedures ures are are performed performed.. 2. n orifice with diameter diameter 28mm is selected selected and it is placed on on the base base of cylinder cylinder tank. C. The output output valve valve is closed and the inlet inlet C"way C"way valve is adjusted adjusted to let the water water flows into the tank from two pipes with 2.3 mm diameter. The water is flow out through the orifice.
8. The pump pump is switched switched on and the contro controll valve on the hydraul hydraulic ic bench bench is opened opened slowly until the tank limit. The water level is maintained by adjusting the control valve. 3. fter fter the water level level is stable, stable, the vortex vortex profile profile is collected collected by measuring measuring the vortex diameter for several planes using the profile measuring gauge. 9. The profile profile measuri measuring ng gauge gauge is pushed pushed down down until the both of sharp sharp point touch touch the water surface. D. The The measur measured ed height, height, h from from the top of the the profi profile le measuri measuring ng gauge gauge to the the bridge- is recorded. The value of a distance from the bridge to the surface of the water level bottom level of the cutout-- is obtained. 5. The pitot pitot tube is used used to measure measure the velocity velocity by sinking sinking it into into the water at the depth of 3 mm from the water surface. The depth of the pitot tube is measured in the water, G. 6. +teps +teps C to 5 are are repe repeate ated d for for anoth another er orifice orifice with with diame diameter ter 2mm, 2mm, 9mm 9mm and and 5mm respectively. 4.The coordinates of vortex profile is plotted for all diameter of orifice in graph and the gradient of the graph is calculated by'
K 1 . X = 1 1 g r . . The graph of velocity which is calculated from the pitot tube reading versus versus the radius of the profile is plotted.
V = (1 gH ) 35 Theoretically, the velocity can be calculated by using the following equation'
V =
K r
$xperime*t +: Fore )ortex )ortex
. The genera generall start"up start"up proced procedures ures are are performed performed.. 2. closed pump pump with two pedals pedals is placed placed on the base of the cylinder cylinder tank. tank. C. The output output valve valve is closed closed and the inlet C"way C"way valve is adjusted adjusted to let the water water flowsinto the tank from two pipes with 6.4 mm diameter. The water can flow out through another two pipes with 2.3 mm diameter. 8. The water water is being being made sure sure flow out from the the tank with the siphon effect effect by raising the hose to above the water level in the tank. 3. The outlet outlet hose is is being made sure sure filled with with water before letting letting the water to flow into the sump tank in the hydraulic bench. 9. The angular angular speed speed of the pedals is measured measured by counting counting the the number of circles circles in a certain times. D. The surface surface probe probe is pushed pushed down down until the the sharp point touch touch the water water surface. surface. 5. The measured measured height, from the top top of the measuring measuring gauge to bridgebridge- is is recorded. 6. +teps 8 to 5 are repeated repeated with different different volumetric flow rate. rate. 4.The coordinates of vortex profile is plotted for different angular velocity. . The calculated vortex profile in the same graph is plotted as they related as 1
h = h3 +
ω
1 g
r 1
&oth experimental and calculated profile is compared
R$CO&&$NDATIONS
There are few recommendations that can be considered while doing this experiment in order to get more accurate result' •
*epeat the experiment at least twice to get more accurate result, the more data we get, we can make comparison to determine the best result that can be pointed out.
•
$rror might happen while taking the time for the number of revolutions since the paddle that created the forced to the vortex is rotated at the fast rate and this is difficult for us to get the accurate time. It is best to get the time average.
•
The velocity of water need to be constant to get the best result so the water flow need to be adjust and be watched for the whole experiment.
•
%e must make sure that the needles touch the water surface accurately to get precise data to be used in the further calculations.
•
It is also important to make sure that the apparatus is in the good condition. It is because if the apparatus is it not in the good condition its will affect our result.
•
%hen we measure the length of the needles, use appropriate ruler such as long ruler and try to get the average reading which is more accurate.
•
better computeri computeri/ed:digit /ed:digitalal- mechanism mechanism is needed needed to read the revolution revolution of paddle associated with time which meant for more precise calculating number of revolution of paddle in forced vortex at the exact time.
R$F$R$NC$S'A,,$NDI0
- )engel, .. J )imbala )imbala K.#. 2449-. 2449-. !luid #echanics #echanics ' !undamenta !undamentals ls and pplications. pplications. !low !low in pipes. pipes. ?ew ork ' #c0raw Gill, C28-. C28-. 2-
DISCUSSION
%hen water flows out of a vessel through a central hole in the base, a free vortex is formed, the degree of rotation being dependent in initial disturbance. The water moves spirally towards the center with stream line in motion, so that, neglecting losses caused by viscosity, the energy per unit mass remains constant. If, while the mass is rotating, the central hole is plugged, the flow of water in the vertical plane ceases and the motion becomes one of simple rotation in the hori/ontal plane, and is known as free cylindrical vortex. The free vortex experiment needed us to make an observation upon the vortex formed while using different si/e of pitot which will give also different shape of vortex. Three different different in diameter of orifice has been used in this experiment experiment and it was found that the largest orifice>s diameter, give the larger and fast vortex produced and follows by orifice>s with medium diameter and the smallest vortex produces using smallest orifice diameter. This phenomena occurs because the vortex formed is depend on the si/e of the orifice used. !rom the experiment, clearly the larger the orifice used, the larger the vortex formed. This occurs because when the orifice si/e gets larger the more water can flow out from the tank and caused it not accumulated. This vortex was formed by the force of water flow in the tank and the flow pattern formed is in circumferential. There are two types of vortices, !orced vortex
!ree vortex
In a free free vort vortex ex,, the the medi medium um spir spiral als s
In a forced vortex, fluid or gas- circles
toward the centre
around a centre.
If the vortex is to have any longevity, once the material arrives at the centre, it must exit the system system the red area-. %ithout a constant constant supply of energy energy to remove the medium from the centre, centre, the !ree Vortex Vortex ceases to exist. exist. If the fluid doesnNt exit the system, it no longer has any spiral nature, and becomes a forced vortex. The The exper experime iment nt was was condu conducte cted d to dete determi rmine ne the the relat relation ionsh ship ip betw betwee een n the the velocity and angular velocity for free vortex and forced vortex respectively, with the vortex surface profile. The fluid mass for the free vortex rotates without external forceO only through internal action or some rotation previously imported to it .;n the other hand, forced vortex rotates by a constant torque exerted by some external source onto the fluid mass. Gere, the water flows out through different orifice diameters of 28mm, 9 mm, 2 mm and 5 mm. ;nce the flow had stabili/ed, the diameter at centre, height, pitot tube head difference and pressure head were recorded and calculated. Gere, the water flows out through different orifice diameters of 28mm, 9 mm, 2 mm and 5 mm. ;nce the flow had stabili/ stabili/ed, ed, the diamete diameterr at centre, centre, height, height, pitot pitot tube head differe difference nce and pressure head were recorded and calculated. !or !or exper experime iment nt of free free vorte vortex, x, an obser observa vatio tion n of vorte vortex x profi profiles les was was performed. performed. In this experiment, three different different si/es of orifices were used. !or the orifice si/e 6 mm, the vortex form was in the smaller radius. !or the second orifice orifice which is 3 mm in si/e, the vortex formed was much larger than the vortex formed by the 6 mm orifice. The used of orifice in si/e of 23 mm was the largest vortex formed. This phenomenon occurs because the vortex formed is dependent on the si/e of the orifice used. !rom the experiment, when the si/e of orifice gets larger, then the vortex formed will large too. This occurs because when the orifice si/e gets larger, the more water can flow out from the tank. Then it not accumulated. %hen more water gets out, the larger vortex formed. This vortex was formed by the force of water flow in the tank. The flow pattern formed is in circumferential.
!or the observation of destruction of the vortex, a core object has been placed at the center of the orifice. This action will destroy the vortex formed because the flow of water was block by the core object. %hen the blocking occurs, the flow rate of the water through the orifice will decrease. This give more effect on the smaller orifice of 6 mm cause the flow rate of the water will decrease more than other orifice of 3 mm. Then the experiment was performed to discover the plotting profiles. The diameter of the vortex formed was increased proportionally proportionally when the si/e of the orifices used is much larger. The used of the small orifices will formed the small diameter of vortex. The larger si/e of the orifice used the larger the diameter of the vortex formed. The diameter of the vortex formed is decreased when the depth of the vortex increased. The measurement of the diameter will result in decreased pattern if the measurement was taken proportionally to the depth of the vortex formed. !rom the results results,, 28 mm orifice orifice diameter diameter gave gave the biggest biggest vortex vortex diameter diameter,, followed by the 9 mm, 2 mm and 5 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 :r 2 that was plotted. !orced vortex on the other hand is formed when a liquid is rotated by a paddle within a tank. 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 94 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. In second experiment, the propeller was used to determine the revolution of the propeller per second rps-. s water flow into the container, it will force the propeller to move. fter increase the velocity, the propeller will spin with more speed. Then, the velocity of the water need to be maintains and we put the needle to touch the surface of the water.
s for the forced vortex experiment, we calculate the number of revolution based on the rotating blades that formed the forced vortex also the length of the needles when it touched the water surface and compare its value to the calculated length using specifie specified d equation. equation. The averag average e velocity velocity head, hc for the 4, 24, C4, 84, 34 and 94 revolutions in the forced vortex experiment was determined &ased on the graph, all angular speed gives the same result on the trend line which is when the radius increased, the depth decreased. !or all the graphs, some of the measured depth of the vortex is slightly different from the theoretical values. The different in height between the measured and the theoretical is due to the error that occurs during the experiment was conducted.
CONC-USION
These experiments were carried out in order to determine the surface profile of a forced vortex and to investigate the physical phenomena associated with a free vortex. n observation observation upon vortex that formed and found that small diameter of pitot tube created small vortex whereas large diameter of orifice created larger vortex. The speed of circulation of vortex is slow, moderate and fast depends on the si/e of pitot tube respectively. In the forced vortex experiment, the result as the average velocity head, hc for the complete revolution were obtained. In this experiment, Gydraulic &ench +ervice #odule and !ree and !orced Vortex pparatus pparatus was used in order to achieve achieve the objectives objectives of this experiment. experiment. ll of the criteria which are associated to both forced and free vortices have been determined. !rom the result of this experiment, the conclusion that can be made here is that the formation of the vortex is dependent on the si/e of the orifice used. The disturbance can destroy the orifice is when some core object blocks the flow of water through the orifice. The results that attained from this experiment is might deviate compared to the information found from the theory. The inaccuracy results occurred in this experiment may caused by some factor like human mistakes, equipment efficiency and other things. In conclusion, the objective is achieved. s the rotation in the cylinder increases, the radius of a vortex surface at the axis also will increase. !rom the results, graph for the three different speed, the theoretical value for the depth at different vortex radius is slightly lower than the actual value. ;verall, it can be seen that the depth of the vortex surface, F is inversely proportional to the radius of vortex, r.
A,,$NDI0
