UNIVERSITI TEKNOLOGI MARA FAKULTI FAKULTI KEJURUTERAAN KIMIA ENGINEERING CHEMICAL ENGINEERING LABORATORY (CHE465) NAME
: MUHAMMAD SOLAHUDIN BIN MUSA
STUD STUDE ENT NO NO..
: 2014 201434 3420 2085 85
GROUP
: EH 220
EXPERIMENT
: FREE AND FORCED VORTEX
DATE PERFORMED
: 12/10/2015
SEMESTER
:2
PROGRAMME / CODE
: EH 220
SUBMIT TO
: DR UL!IFLI ABDUL RASHID
N*+ / 2 4 5 6 9 : ; / // /2
T,-e A%ra#0S1mmar& I3r*$1#,*3 A,m T"e*r& Aara1 Me"*$*-*7&08r*#e$1re Re1- Ca-#1-a,*3 ,#1,*3 C* C*3#-1,*3 Re#*mme3$a,*3 Re
Remark! C"e#ke$ %&! ''''''''''''''''''''''''''' ae!
A--*#ae$ Mark (.) 5 / 5 / 5 / / / 2 5 5 5 /
Mark
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 safety against natural disaster. This experiment was carried out to study the relationship between the surface shape of free and forced vortex. It also to study on the angular velocity of a rotating liquid in a cylindrical tank. Theoretically, the 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.
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 safety against natural disaster. This experiment was carried out to study the relationship between the surface shape of free and forced vortex. It also to study on the angular velocity of a rotating liquid in a cylindrical tank. Theoretically, the 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"axis. curved"axis. #oreover, #oreover, the plurals of vortex are vortices and vortexes. vortexes. $xamples 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 characteri%ed 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. $xample( !lownet application. !orced vortex is also known as 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. !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. 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 of a 234mm diameter cylindrical, 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, 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 determined by a gauge, housed on a diametrically mounted bridge piece, 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, ;
student>s experiments to produce and measure free and forced vortices. It consists of a clear acrylic cylinder where the free vortex is generated by water discharging through an interchangeable orifice in the base of the cylinder. The resulting profile is then measured using a combined caliper and depth scale. The forced vortex is induced by a paddle rotated by jets of water at the cylinder base. The profile of the forced vortex is then determined using a series of depth gauges. Velocity at any point in the free or forced vortex may be measured using the appropriate pitot tube supplied. secondary flow at the base of the free vortex demonstrated by means of dye crystals -not supplied. ome of the important cases of forced vortexes are(
•
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 vertical plane ceases and the motion becomes one of simple rotation in 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 2 2 g
+ z = cons a3 t
!or hori%ontal plane, the relation becomes
p
+
pg
V 2 2 g
= cons a3 t
Integration of the above relation with r gives
/ dp V dV + + =4 + pg dr g dr -/ ?ext, consider a pair of stream line being divided with distance, @r and is in same hori%ontal plane and are linked by a fluid tube with wide @. The centrifugal force of the tube is balanced by the pressure difference between both ends, that is
pg +∂A+∂r+
pgV gr
V2
=
7r
2
=
dp dr
+∂r +∂ A
dp dr -2
*ombine -/ and -2 to produce
V
2
V dV =4 + gr g dr +
dV
+
V
dr
r
=4
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 p rofile as follow(
V 2 2 g
+ z = C (Cons a3 t ) -8
ubstitute -C into -8 2
K
2
2 gr
+ z = C 2
C − z =
K
2
2 gr
-3
yx
That is, equation for hyperbolic curve hori%ontal to % ) *
2
) 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. $quation for such situation can be generated by considering the water passes through round segments towards is diameter, where energy passing any tube and is kept constant until
p
+
pg
V
2
2 g
+ z = cons a3 t
If and V is surface area and velocity of a particular position while / and V/ are surface area and velocity at distance r from center circle, V ) /V/ ) *onstant 'y taking ) Br,
V =
r /V / r
If % is constant,
p pg p pg
2
+
r / V /
2
2
2 gr
= C 2
= C −
r / V /
2
2
2 gr
-9 lso,
p/
+
pg
V /
2
= C
2 g
p − p/
V /
=
pg
p − p/
=
pg
2
2
−
2
r / V /
2
2 g
2 gr
2
r /
/
V /
?/ − 2 > 2 g r / -D
!ree vortex can be said as combination of cylinder vortex and radial flow. Velocity is inversely proportional to radius in every case. ngle between flow axis and radius vector at any point is constant and these axis from the spiral pattern.
!orced Vortex s we know, angular velocity is constant, V) wr Increase in radial pressure is given by
dp dr
= p
V 2 r
p2
= pω r 2
r 2
∫ dp = pω ∫ rdr 2
p/
r /
/ 2 2 p2 − p/ = pω 2 (r 2 − r / ) 2 p/ = p4 'y taking
p2 = p
r / = 4 when
, and
p − p4 pg 'ecause, p:pg ) h, so
r 2 and
=
w2 2 g
2
r
=
r
2
ω
h − h4 =
2
2 g
r
2
ω
h = h4 +
2
2 g
r
This is a parabolic equation. urface profile for forced vortex can be represented by equation(
z =
Ω
2
r 2
2 g
Eistribution of total head can be represented by equation(
Ω r 2
H =
2
g
F ) surface profile
ῼ) angular velocity r ) radius g ) gravity G ) total head
ngular velocity can be calculated by(
Ω=
2η × revolution time(e#)
AI& ' OB($CTI)$S
$xperime*t 1: Free )ortex
/. To study on surface profile and speed. 2. To find a relation between surface profile and speed. $xperime*t +: Fore" )ortex /. To study on surface profile and angular velocity. 2+ To find a relation between surface profile and total head+
A,,ARATUS
Or,<,#e *< $,ameer :mm@ /2mm@ /6mm@ 24mm
8r*<,-e mea1r,37 7a17e
8a$$-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 hydraulic bench tank is filled with water. 2. The study bench is placed on the hydraulic bench. C. ll the accessories must be make sure are ready on the bench such as surface probe, profile measuring gauge, pitot tube, paddle and orifices. 8. The inlet and outlet hose is set up. 3. The stand of the equipment is adjusted to reach the hori%ontal position. .e*eral Shut Dow*:
/. The valves are closed and the pump is switched off. 2. The orifices, paddle and other accessories are removed from the cylindrical vessel. C. The water is drain off from the unit when it is not in used. Safet/ ,reautio*:
/. proper lab coat must be worn while doing the experiment. 2. The sharpened object is being aware during conducting the experiment. C. &hen water is splashed out from tank, that area must be mopped immediately to avoid slippery floor. $xperime*t 1: Free )ortex
/. The general start"up procedures are performed. 2. n orifice with diameter 28mm is selected and it is placed on the base of cylinder tank. C. The output valve is closed and the inlet C"way valve is adjusted to let the water flows into the tank from two pipes with /2.3 mm diameter. The water is flow out through the orifice.
8. The pump is switched on and the control valve on the hydraulic bench is opened slowly until the tank limit. The water level is maintained by adjusting the control valve. 3. fter the water level is stable, the vortex profile is collected by measuring the vortex diameter for several planes using the profile measuring gauge. 9. The profile measuring gauge is pushed down until the both of sharp point touch the water surface. D. The measured height, h -from the top of the profile measuring gauge to 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 tube is used to measure the velocity by sinking it 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 C to 5 are repeated for another orifice with diameter /9mm 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( 2
X =
K
+
/ 2
2 g r
//. The graph of velocity which is calculated from the pitot tube reading versus the radius of the profile is plotted.
V = ( 2 gH )
4+5
Theoretically, the velocity can be calculated by using the following equation(
V =
K r
$xperime*t +: Fore )ortex
/. The general start"up procedures are performed. 2. closed pump with two pedals is placed on the base of the cylinder tank. C. The output valve is closed and the inlet C"way valve is adjusted to let the water flows into 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 is being made sure flow out from the tank with the siphon effect by raising the hose to above the water level in the tank. 3. The outlet hose is being made sure filled with water before letting the water to flow into the sump tank in the hydraulic bench. 9. The angular speed of the pedals is measured by counting the number of circles in a certain times. D. The surface probe is pushed down until the sharp point touch the water surface. 5. The measured height, -from the top of the measuring gauge to bridge is recorded. 6. teps 8 to 5 are repeated with different volumetric flow 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 2
h = h4 +
ω
2 g
r 2
'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%ed:digital mechanism is needed to read the 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
/ 0iorgo E.V.-24/4. The +anque"Gilsch Vortex Tube /"2. 2 Gilsch, +. -/68D. The se of $xpansion of 0ases In *entrifugal !ield as *ooling Hrocess. The +eview of scientific Instruments, /5-2. C +ajpat, +.B.-24/4. Textbook of $ngineering Thermodynamics. ?ew Eelhi ( <J#I H'
24/3,
from
http(::www.sciencedirect.com:science:article:pii:/429C465/C444/D3 D *hapter D( !low of !luid -n.d. +etrieved /6 #ay, 24/3, from http(::www.nptel.ac.in:courses://2/48//5:lecture"2/:2/" 2NforcedNvortexNflow.htm 5 !ree and !orced Vortex -n.d. +etrieved
/6
#ay, 24/3, from
http(::www.jsme"fed.org:experiment"e:24//N2:44C.html 6 'ruce +. #unson, Eonald !. Koung, Mohn &iley L son, Inc, !?E#$?T< ;! !<IE #$*G?I*, 2nd edition.
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 in diameter of orifice has been used in this 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 vortex, the medium spirals 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 -the red area. &ithout a constant supply of energy to remove the medium from the centre, the !ree Vortex ceases to exist. If the fluid doesnOt exit the system, it no longer has any spiral nature, and becomes a forced vortex. The experiment was conducted to determine the relationship between 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 forceP 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, 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, 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. !or experiment of free vortex, an observation of vortex profiles was performed. In this experiment, three different si%es of orifices were used. !or the orifice si%e 5 mm, the vortex form was in the smaller radius. !or the second orifice which is /9 mm in si%e, the vortex formed was much larger than the vortex formed by the 5 mm orifice. The used of orifice in si%e of 28 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 centre 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 5 mm cause the flow rate of the water will decrease more than other orifice of /9 mm. Then the experiment was performed to discover the plotting profiles. The diameter of the vortex formed was increased 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, 28 mm orifice diameter gave the biggest vortex diameter, followed by the /9 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. Three 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 specified equation. The average 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 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 was used in order to achieve the objectives of this 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.
R$SU-TS CA-CU-ATIONS Free Vortex:
;rifice diameter ) 5mm Eistance from bridge to water surface a ) 284mm Eiamete r at centre, E -mm
#easure d Geight, h -mm
Hitot Tube Gead Eifferences , G -mm
/6 /D /3
/4.6 /4.D /4./
2 C 3
Hressur e Gead : Eepth of the Hitot Tube, J -mm D6./ D6.C D6.6
Velocity -mm:s
r -mm
rxr -mm2
/ :-r x r -/:mm2
/65.44/ 282.4// C/C.246
6.3 5.3 D.3
64.23 D2.23 39.23
4.4/// 4.4/C5 4.4/D5
Pressure Head (Pitot Tube depth) against 1/r2 79.35 79.3 79.25 79.2 79.15 79.1 79.05 79
Pressure Head ! (mm)
1/r2 (1/mm2) 1/r2 (1/mm2)
0radient of the graph ) /8D.54 mmC B2:2g ) /8D.54
Therefore, B ) /D42.5C mm2:s *alculated Velocity( V ) B : r ) /D42.5C : 6.3 ) /D6.283 mm:s
V ) B : r ) /D42.5C : 5.3 ) 244.CCC mm:s
V ) B : r ) /D42.5C : D.3 ) 22D.488 mm:s
s a result( r -mm 6.3 5.3 D.3
*alculated Velocity -mm:s /D6.283 244.CCC 22D.488
Velocity -mm:s /65.44/ 282.4// C/C.246
%e&o'it against adius 350 300 250 200
%e&o'it (mm/s)
150 100 50 0
"
#.5
7.5
$.5
9.5
adius (mm) Theoreti'a& %e&o'it
*+perimenta& %e&o'it
;rifice diameter ) /9mm Eistance from bridge to water surface, a ) 2C4mm Eiamete r at *entre, E -mm
#easure d Geight, h -mm
Hilot Tube Gead Eifferences , G -mm
34 C5 C9 C4 29
68 64 5C D6 D9
/4 // /3.3 /6 /6
Hressur e Gead : Eepth of the Hilot Tube, J -mm 9 /4 /D 2/ 28
Velocity -mm:s
r -mm
r2 -mm2
/:r2 -/:mm2
882.683 898.398 382.868 368.2DC 9/4.33D
23 /6 /D /3 /8
923.44 C9/.44 256.44 223.44 /69.44
4.44/9 4.4425 4.44C3 4.4488 4.443/
Pressure Head (Pitot Tube ,epth) against 1/r2 30 25 20 15 10 5 0
Pressure Head ! (mm)
1/r2 (1/mm2) 1/r2 (1/mm2)
0radient of the graph ) C53C.6 mmC B2:2g ) C53C.6 Therefore, B ) 5963.94C mm2:s
V ) B:r ) 5963.94C : 23 ) C8D.52 V ) B:r ) 5963.94C : /6 ) 83D.99 V ) B:r ) 5963.94C : /D ) 3//.3/
V ) B:r ) 5963.94C : /3 ) 3D6.D/ V ) B:r ) 5963.94C : /8 ) 92/.// s a result( r -mm 23 /6 /D /3 /8
*alculated Velocity -mm:s C8D.52 83D.99 3//.3/ 3D6.D/ 92/.//
Velocity -mm:s 882.683 898.398 382.868 368.2DC 9/4.33D
-hart Tit&e 700 #00 500 "00 300 200 100 0 10
1"
15 Theoreti'a& %e&o'it
17
19
*+periment a& %e&o'it
25
;rifice diameter ) 28mm Eistance from bridge to water surface, a ) 24Cmm Eiamete r at *entre, E -mm
#easure d Geight, h -mm
Hilot Tube Gead Eifferences , G -mm
3C 8D 84 CD C9
64 5C 62 D5 D2
5 /4 /3.3 /D 2/
Hressur e Gead : Eepth of the Hilot Tube, J -mm CD 88 C3 86 33
Velocity -mm:s
r -mm
r2 -mm2
/:r2 -/:mm2
C69./52 882.683 328.466 394.259 929.8/5
29.3 22.3 24.4 /6.4 /5.4
D42.23 349.23 844.44 C9/.44 C28.44
4.44/8 4.4424 4.4423 4.4425 4.44C/
Pressure h*, (Pitot Tube ,epth) against 1/r2 #0 50 "0 30
Pressure Head ! (mm)
20 10 0 5.0000000000000001*" 1/r2 (1/mm2)
0radient of the graph ) D693.5 mmC B2:2g ) D693.5 Therefore, B ) /234/.39 mm2:s
V ) B : r ) /234/.39:/5 ) 968.3Cmm:s
V ) B : r ) /234/.39:/6 ) 93D.D5mm:s
2*3
3.0999999999999999*3
V ) B : r ) /234/.39:24 ) 923.45mm:s
V ) B : r ) /234/.39:22.3 ) 333.92mm:s
V ) B : r ) /234/.39:29.3 ) 8D/.D9mm:s
r -mm /5 /6 24 22.3 29.3
*alculated Velocity -mm:s 968.3C 93D.D5 923.45 333.92 8D/.D9
Velocity -mm:s 929.8/5 394.259 328.466 882.683 C69./52
%e&o'it against adius $00 700 #00 500
%e&o'it mm/s
"00 300 200 100 0 1$
19
20
22.5
adius Theoriti'a& %e&o'it (mm/s)
*+perimenta & %e&o'it
2#.5
Forced Vortex:
Eistance from centre -mm 4 C4 D4 //4 ?o. of revolutions in 94s ngular Velocity -rad:s
!irst h-NN
econd h-NN
64 63 /44 /24 C5 C.65
ample *alculation( !or the /st volumetric flow rate( ?umber of revolutions in 94 seconds( C5
Q)
( 2 π ×revolution ) ÷ 60
) -2-C./82 x C5 : 94 ) C.65 rad:s
h-C4 ) h4 A - -w x w : 2g x -r x r ) 64 A --C.65 x C.65 : 2 -6.5/-/444 x -C4xC4 ) 64.DCmm
G-D4 ) h4 A - -w x w : 2g x -r x r ) 64 A --C.65 x C.65 : 2 -6.5/-/444 x -D4xD4 ) 6C.63mm
33 94 98 52 8/
Third h-NN
G-//4 ) h4 A - -w x w : 2g x -r x r ) 64 A --C.65 x C.65 : 2 -6.5/-/444 x -//4x//4 ) 66.D9mm
!or the 2nd volumetric flow rate( ?umber of revolutions in 94 seconds( 8/
Q)
( 2 π ×revolution ) ÷ 41
) -2-C./82 x C5 : 8/ ) 8.26 rad:s
h-C4 ) h4 A - -w x w : 2g x -r x r ) 33 A --8.26 x 8.26 : 2 -6.5/-/444 x -C4xC4 ) 33.58mm
G-D4 ) h4 A - -w x w : 2g x -r x r ) 33 A --8.26 x 8.26 : 2 -6.5/-/444 x -D4xD4 ) 36.94mm
G-//4 ) h4 A - -w x w : 2g x -r x r ) 33 A --8.26 x 8.26 : 2 -6.5/-/444 x -//4x//4 ) 99.C3mm
!or the Crd volumetric flow rate( ?umber of revolutions in 94 seconds( 84
Q)
( 2 π ×revolution ) ÷ 60
) -2-C./82 x 84 : 94 ) 8./6 rad:s
h-C4 ) h4 A - -w x w : 2g x -r x r ) 56 A --8./6 x 8./6 : 2 -6.5/-/444 x -C4xC4 ) 56.5/mm
G-D4 ) h4 A - -w x w : 2g x -r x r ) 56 A --8./6 x 8./6 : 2 -6.5/-/444 x -D4xD4 ) 6C.C5mm
G-//4 ) h4 A - -w x w : 2g x -r x r ) 56 A --8./6 x 8./6 : 2 -6.5/-/444 x -//4x//4 ) 66.5Cmm
*alculated Values( Eistance from *entre -mm 4 C4 D4
/st
2nd
Crd
64.44 64.DC 6C.63
33.44 33.58 36.94
56.44 56.5/ 6C.C5
//4 ngular Velocity -rad:s
66.D9 C.65
99.C3 8.26
66.5C 8./6
or'ed %orte+ (1st) 102 100 9$ 9# 9"
Height rom top o the sura'e probe to bridgr (mm)
92 90 $$ $# $"
0
30
70
,istan'e rom 'entre -a&' 1
*+p 1
110
or'ed %orte+ 2nd 90 $0 70 #0 50 2 to bridge (mm) Height rom top o the sura'e -a&' probe
*+p 2
"0 30 20 10 0
0
30
70
110
,istan'e rom 'entre (mm)
or'ed %orte+ (3rd) 120 100 $0
Height rom top o the sura'e probe to bridge (mm)
#0 "0 20 0
0
30
70
,istan'e rom 'entre (mm) -a&' 3
*+p 3
110
