UNIVERSITI TEKNOLOGI MARAFAKULTI KEJURUTERAAN KIMIA

CHEMICAL ENGINEERING LABORATORY II( CHE 523 )

NAME : MOHAMAD ARIF BIN MUSA

STUDENT NO : 2008297884GROUP : EH2203DEXPERIMENT : FREE AND FORCED VORTEX (LAB3) DATE PERFORMED : 19th AUGUST 2009SEMESTER : 3PROGRAMME / CODE : EH220SUBMIT TO : PN. SYAFIZA ABD HASHIB

No. Title Allocated Marks % Marks1 Abstract / Summary 52 Introduction 53 Aims / Objectives 54 Theory 55 Apparatus 56 Methodology/Procedures 107 Results 108 Calculations 109 Discussion 2010 Conclusion 1011 Recommendations 512 References 513 Appendices 514 Attendance ( Hands-on works )

100

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TABLE OF CONTENT

ABSTRACT…………………………………………………………..3

INTRODUCTION………………………………………………….4

OBJECTIVE………………………………………………………....5

THEORY……………………………………………………………...5

APPARATUS……………………………………………………….8

PROCEDURE……………………………………………………….8

RESULT……………………………………………………………...9

CALCULATION…………………………………………………...9

DISCUSSION……………………………………………………...15

CONCLUSION…………………………………………………….17

RECOMMENDATION…………………………………………18

REFERENCE……………………………………………………….19

APPENDICE………………………………………………………..20

ABSTRACT

The aim of this experiment is to determine the surface profile of a forced vortex and also to

investigate the physical phenomena associated with a free vortex. Vortex is a whirling mass of water or

air in which a force of suction operates, as a whirlpool or in the form of a visible column or spiral, as a

tornado. Vortex motion usually describes motions in a frictionless fluid. In such cases, the absence of

friction would make it impossible to create or to destroy vortex motion. In order to fulfil the objective of this

experiment, it has two kind of experiment was performed. Firstly for free vortex experiment, three different

size in diameter of arm pitot tube was used which are 15, 25 and 30 mm respectively. We made an

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 size of pitot tube respectively. In the other hand, for the forced vortex

experiment, the revolution of the blade was calculated and the height of datum was computed and our

result was slightly different with the theoretical value. In the second part of this experiment, the propeller

was used to calculate the rotation as planned in procedure in order to find out the velocity head. After

that, the height of the datum was observed. By the end of this experiment, it is clearly stated that, the free

and force vortex had difference type of characteristic based on the way their created and factors that

affect their condition. The average velocity head, hc for the 10, 20, 30, 40, 50 and 60 revolutions in the

forced vortex experiment was determined to be 0.0350m, 0.0512m, 0.0710m, 0.0552m, 0.0428m and

0.0231m respectively.

INTRODUCTION

Fluid mechanics has developed as an analytical discipline from the application of the classical

laws of static, dynamics and thermodynamics, to situations in which fluids can be treated as continuous

media. The particular laws involved are those of the conservation of mass, energy and momentum and, in

each application, these laws may be simplified in an attempt to describe quantitatively the behavior of the

fluid. The hydraulics bench service module, F1-10, provide the necessary facilities to support a

comprehensive range of hydraulic models each of which is designed to demonstrate a particular aspect of

hydraulic theory. The Free and Forces Vortex Apparatus, F1-23 is the specific hydraulic model that we

are concerned with for this experiment.

In common usage, a fluid motion dominated by rotation about an isolated curved line in space, as

in a tornado, a whirlpool, a hurricane, or a similar natural phenomenon. The importance of vortices is due

to two characteristics: general fluid flows can be represented by a superposition of vortices; and vortices,

once created, have a persistence that increases as the effects of viscosity are reduced. The aerodynamic

lift forces and most other contributors to the forces and moments on aircraft and other bodies moving

through fluids do not exist in the absence of vortices. See also Aerodynamic force; Hurricane; Tornado;

Waterspout.

The strength of rotation is measured by a vector called the vorticity, ω, defined as the curl of the

velocity vector. A region of flow devoid of vorticity is known as irrotational. The spatial distribution of the

vorticity vector provides a precise characterization of the rotation effects in fluids, and the nature of what

subjectively and popularly would be called a vortex. See also Calculus of vectors; Laplace's irrotational

motion.

. A vortex is a spinning, often turbulent, flow (or any spiral motion) with closed streamlines. The

shape of media or mass swirling rapidly around a center forms a vortex. It flows in a circular motion. A

vortex can be seen in the spiraling motion of air or liquid around a center of rotation. Circular current of

water of conflicting tides form vortex shapes. Turbulent flow makes many vortices. A good example of a

vortex is the atmospheric phenomenon of a whirlwind or a tornado or dust devil. This whirling air mass

mostly takes the form of a helix, column, or spiral.

The rotation of a fluid, moving as a solid, about an axis is called forced vortex motion. Every particle of

fluid has the same angular velocity. This motion is to be distinguish from free vortex motion, where each

particles moves in a circular path with a speed varying inversely as the distance from the centre. The

centrifugal effect in a vortex throws heavy liquid/air out to the perimeter whilst lighter air or liquid are

pushed to the center. Electrically, the air polarized with negative ions or as electrons will be pushed to the

center and down, the air with positive ion content will move upward and outward.

Some 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 force vortex formed

The discharge and the surrounding containment have to be regular in shape; otherwise more and

chaotic turbulences within the fluid accelerating through the discharge break the vortex symmetry and

hinder its progress. Regular does not mean a perfect cone, but a shape mimicking the structure of natural

turbulence. This shape is somewhat ropy walled parabolic cone as shown in the figure above.

OBJECTIVES

1. The main objective of this experiment is to determine the surface profile of a forced vortex.

2. Other goal of this experiment is to investigate the physical phenomena associated with a free

vortex.

THEORY

Based on the dictionary, vortex is a circular, spiral, or helical motion in a fluid (such as a gas) or

the fluid in such a motion. A vortex often forms around areas of low pressure and attracts the fluid (and

the objects moving within it) toward its center. Tornados are examples of vortexes; vortexes that form

around flying objects are a source of turbulence and drag. A vortex can be seen in the spiraling motion of

air or liquid around a center of rotation. Circular current of water of conflicting tides form vortex shapes.

Turbulent flow makes many vortices. A good example of a vortex is the atmospheric phenomenon of a

whirlwind or a tornado or dust devil. This whirling air mass mostly takes the form of a helix, column, or

spiral. Tornadoes develop from severe thunderstorms, usually spawned from squall lines and supercell

thunderstorms, though they sometimes happen as a result of a hurricane.

In the other hand, a vortex can be any circular or rotary flow that possesses vorticity. Vorticity is a

mathematical concept used in fluid dynamics. It can be related to the amount of "circulation" or "rotation"

in a fluid. In fluid dynamics, vorticity is the circulation per unit area at a point in the flow field. It is a vector

quantity, whose direction is (roughly speaking) along the axis of the swirl. Also in fluid dynamics, the

movement of a fluid can be said to be vortical if the fluid moves around in a circle, or in a helix, or if it

tends to spin around some axis. Such motion can also be called solenoidal. In the atmospheric sciences,

vorticity is a property that characterizes large-scale rotation of air masses. Since the atmospheric

circulation is nearly horizontal, the (3 dimensional) vorticity is nearly vertical, and it is common to use the

vertical component as a scalar vorticity. Mathematically, vorticity is defined as the curl of the fluid

velocity :

Free vortex

When water flows out of a vessel through a central hole in the base, a free vortex is formed. In a free

cylindrical vortex, the velocity varies inversely to the distance from the axis of rotation.

(1)

The equation governing the surface profile is derived from Bernoulli’s Theorem:

(2)

Thus, by substituting equation (1) into equation (2), it will give a new expression of equation

Which is the equation to a hyperbolic curve which is asymptotic to the axis of rotation and to the

horizontal through .

Forced vortex

For a constant speed of rotation,

Where = radius,

= velocity of flow at radius,

Then, head due to kinetic energy is equal to the velocity head,

Since this is a derivation from the Bernoulli’s theorem, the term of mass can be eliminated from above

equation.

If the horizontal plane passing through the nadir (lowest point) of vortex is taken as datum, theory shows

that , substituted term :

This is the equation of a parabola.

APPARATUS AND CHEMICALS

In order to complete the demonstration we need a number of pieces of following equipment:

• The F1-10 Hydraulic Bench.

• The F1-23 Free and Forced Vortex Apparatus.

• A stopwatch to allow us to determine the rotation speed of the paddle

• 15 mm, 25 mm, and 30 mm Pitot tubes.

• Blanking plug (stud) and paddle.

• Vernier callipers and ruler.

PROCEDURES

A. Forced vortex experiment:

1) The apparatus was positioned into the working channel of the bench and the supply was

connected.

2) The blanking plug was placed into the central hole in the base of the cylinder. The paddle was

pressed onto the stud. A flexible hole was connected to the outlet pipe and the outlet valve was

closed.

3) The bench pump was switched on, the bench control valve and the three-way inlet valve was

opened so that water enters the cylinder from the 9 mm tangential inlet ports, set at 60 degrees,

and was leaves through the larger ports, discharging into this volumetric tank.

4) The outlet pipe was raising and it was allowed to fill with water, and then it was lowered into the

volumetric tank.

5) For each value of flow rate the outlet valve was adjusted until water just flows through the

overflow cutouts.

6) When the water level was maintained at the red scale/spot (designated on the profile) the bridge

was placed with the measuring needles across the top of the cylinder. The profile of the surface

was determined by lowering the measured needles until the just touch the water surface.

7) The speed of rotation of the paddle was measured by timing the revolutions number of paddle

rotations using the maker spot as a reference. The numbers of revolution are 10, 20, 30, 40, 50,

and 60 and the time for the paddle to complete each revolution was recorded.

8) The bridge was removed and the length of each needle was recorded.

B. Free Vortex experiment:

1) The apparatus was positioned into the working channel of the bench and the supply was

connected. An orifice was placed into the center hole in the base of the cylinder.

2) The bench pump was switched on, the bench control valve and the three-way inlet valve was

opened so that water enters the cylinder from the 12 mm diameter tangential inlet ports set at 150

degrees and was discharges through the orifice into the volumetric tank.

3) The profile-mid hole was implanted with the 15 mm radius pitot tube.

4) Pitot tube orifice was attached and immersed until the nose is at the core profile surface. The

water was allowed to flow and the water flow was maintained.

5) The diameter of the vortex was measuring and then the flow pattern of vortex was observed and

drawn on the paper.

6) The experiment was repeated with the 25 mm 30 mm pitot tube.

RESULTS AND CALCULATIONS

A. FREE VORTEX

Arm pitot diameter (mm)

Diameter of

the vortex (mm)Observations Surface profile

15.00 18.00Slow speed of circulation and small size of vortex

25.00 41.00Medium speed circulation with medium size of vortex

30.00 55.00Fast speed of circulation with big size of vortex

B. FORCED VORTEX

a) 10 number of revolution

Number of Time, t Revolutions Radius of Measured Height Calculated

revolutions, N

(s) per second, ω (rps)

measuring needles, r (m)

needles length, l (m)

from datum, hm

(m)

height, hc (m)

105.72 10.98

0.1100 0.1410 0.0530 0.07440.0900 0.1570 0.0370 0.04980.0700 0.1720 0.0220 0.03010.0500 0.1850 0.0090 0.01540.0300 0.1860 0.0080 0.00550.0000 0.1940 0.0000 0.0000

Average calculated height, hc 0.0350

b) 20 number of revolution

Number of revolutions, N

Time, t (s)

Revolutions per second, ω (rps)

Radius of measuring needles, r (m)

Measured needles length, l (m)

Height from datum, hm

(m)

Calculated height, hc (m)

209.47 13.27

0.1100 0.1410 0.0530 0.10860.0900 0.1570 0.0370 0.07270.0700 0.1720 0.0220 0.04400.0500 0.1850 0.0090 0.02240.0300 0.1860 0.0080 0.00810.0000 0.1940 0.0000 0.0000

Average calculated height, hc 0.0512

c) 30 number of revolution

Number of revolutions, N

Time, t (s)

Revolutions per second, ω (rps)

Radius of measuring needles, r (m)

Measured needles length, l (m)

Height from datum, hm

(m)

Calculated height, hc (m)

3012.06 15.63

0.1100 0.1410 0.0530 0.15070.0900 0.1570 0.0370 0.10090.0700 0.1720 0.0220 0.06100.0500 0.1850 0.0090 0.03110.0300 0.1860 0.0080 0.01120.0000 0.1940 0.0000 0.0000

Average calculated height, hc 0.0710

d) 40 number of revolution

Number of Time, t Revolutions Radius of Measured Height Calculated

revolutions, N

(s) per second, ω (rps)

measuring needles, r (m)

needles length, l (m)

from datum, hm

(m)

height, hc (m)

4018.22 13.79

0.1100 0.1410 0.0530 0.11730.0900 0.1570 0.0370 0.07850.0700 0.1720 0.0220 0.04750.0500 0.1850 0.0090 0.02420.0300 0.1860 0.0080 0.00870.0000 0.1940 0.0000 0.0000

Average calculated height, hc 0.0552

e) 50 number of revolution

Number of revolutions, N

Time, t (s)

Revolutions per second, ω (rps)

Radius of measuring needles, r (m)

Measured needles length, l (m)

Height from datum, hm

(m)

Calculated height, hc (m)

5025.87 12.14

0.1100 0.1410 0.0530 0.09090.0900 0.1570 0.0370 0.06080.0700 0.1720 0.0220 0.03680.0500 0.1850 0.0090 0.01880.0300 0.1860 0.0080 0.00680.0000 0.1940 0.0000 0.0000

Average calculated height, hc 0.0428

f) 60 number of revolution

Number of revolutions, N

Time, t (s)

Revolutions per second, ω (rps)

Radius of measuring needles, r (m)

Measured needles length, l (m)

Height from datum, hm

(m)

Calculated height, hc (m)

6042.25 8.92

0.1100 0.1410 0.0530 0.04910.0900 0.1570 0.0370 0.03280.0700 0.1720 0.0220 0.01990.0500 0.1850 0.0090 0.01010.0300 0.1860 0.0080 0.00360.0000 0.1940 0.0000 0.0000

Average calculated height, hc 0.0231

SAMPLE OF CALCULATIONS

Experiment forced vortex- part (a);

Number of revolutions, N = 10

Time, t (s) = 5.72

Revolution per second, ω (rps) = t

N 2

= s

rev

72.5

210

= 10.98 rps

Radius of measuring needle, r (m) = 0.1100 m, 0.0900m, 0.0700m, 0.0500m, 0.0300m and 0.0m.

Measured needle length, l (m) = 0.1410 m

Height from datum, hm (m) = h0 – hn ; hn = l

hm = mm 1410.01940.0 = m0530.0

Calculation of height or velocity head, hc = g

r

2

22

hc at r = 0.1100m =

2

22

/81.92

1100.098.10

sm

m

= m0744.0

hc at r = 0.0900m =

=

hc at r = 0.0700m =

=

hc at r = 0.0500m =

=

hc at r = 0.0300m =

=

hc at r = 0.0000m =

=

Average velocity head, hc =

=

DISCUSSIONS

This experiment was performed in order to determine the surface profile of a forced vortex and to

investigate the physical phenomena associated with a free vortex. Vortex is a circular, spiral, or helical

motion in a fluid, such as a gas or the fluid in such a motion. A vortex often forms around areas of low

pressure and attracts the fluid (and the objects moving within it) toward its center. This experiment

consists of two type of experiment which is free vortex and force vortex experiment. For free vortex

experiment, it have three type of pitot tube which is 15 mm, 25 mm and 30 mm in diameter. During the

experiment, every tube of the pitot will make a circular motion when water flow at the constant velocity in

the cylindrical container. The diameter of the vortex that was produced by pitot tube of 15 mm, 25 mm

and 30 mm in diameter pass through the circulation of the water flow was established to be 18 mm, 41

mm and 55 mm respectively.

The free vortex experiment needed us to make an observation upon the vortex formed while using

different size 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 size

of the orifice used. From the experiment, clearly the larger the orifice used, the larger the vortex formed.

This occurs because when the orifice size 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.

For the second experiment, the propeller was used to determine the revolution of the propeller per second

(rps). As water flow into the container, it will force the propeller to move. After 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. As 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 10, 20, 30, 40, 50 and 60 revolutions in the forced vortex experiment

was determined to be 0.0350m, 0.0512m, 0.0710m, 0.0552m, 0.0428m and 0.0231m respectively.

As we going through the forced vortex experiment, the height for datum, hm that we get from the

experiment is almost near with the calculated height. There are still differences since there were some

errors occur while doing this experiment which will be discussed further as we go through in this

discussion section. Based on the theory, we can see ω or rotational per second is getting fast as we

increase the number of revolution. This is means that the rotational of the paddle is increasing with time.

This can affect the result even the increasing is at a small rate.

The results that we obtained in this experiment was might deviate from the information from the theory.

Based on our final result, we realized that we have made some errors and have faced a lot of problems

that lead to the inaccuracy of the collected data throughout the whole experiment. For example, While

taking the time for the number of propeller rotation, error might be occur since the water force the

propeller to spin with a high velocity. This is difficult to get the accurate time because the propeller that

spin at high rate is hard to get the time when it reach at its level. It is the best to have more data collection

by repeating the experiment at least twice. So that, the average time for the number of rotation can be

pointed out with less error.

On the other hand, the velocity of the water for forced vortex experiment is playing an important role since

it will determine the rotation of the propeller. The velocity of the water need to be constant all the time and

can be performed by adjusting the pipe. If the velocity is too much, the water will overflow. This is vital to

get the best result. By our own carelessness, we might not have the constant velocity of the water which

affects our last result. Alongside with that, the inaccuracy also might happen if the needles are far from

the surface accurately. This situation will make the result not accurate and can’t get the best result. This

part is needed to be done in a very high patient since it is hard to touch the surface accurately. Besides

that, to get more accurate result, use appropriate equipment such as long ruler and try to get the average

reading. So that, the percentage of inaccuracy can be reduce. Nevertheless, the result of this experiment

is acceptable.

CONCLUSIONS

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. For the free vortex experiment, we

attained the result for diameter of the vortex that was produced by pitot tube of 15 mm, 25 mm and 30

mm in diameter pass through the circulation of the water flow was established to be 18 mm, 41 mm and

55 mm respectively. We made an 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 size of pitot tube respectively. In the

forced vortex experiment, we obtained the result as the average velocity head, hc for the complete 10, 20,

30, 40, 50 and 60 revolutions was determined to be 0.0350m, 0.0512m, 0.0710m, 0.0552m, 0.0428m and

0.0231m respectively.

In this experiment, we have used the Hydraulic Bench Service Module and Free and Forced Vortex

Apparatus in order to achieve the objectives of this experiment. All of the criteria which are associated to

both forced and free vortices have been determined. From the result of this experiment, the conclusion

that can be made here is that the formation of the vortex is dependent on the size 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 we 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. However, we realized that we have faced a lot of

problem and made some errors while we performed this experiment. For example, we have not repeated

this experiment until to two or three trials in order to obtain the accuracy results by finding the average or

standard deviation for the data.

Beside the inaccuracy results, but I still consider this experiment has been a success since the objective

of experiment was achieved. After these experiments were carried out, I have gained some experiences

and new knowledge from it. I have understood the method to investigate the physical phenomena

associated with a free vortex and identify surface profile of forced vortex that is widely use especially in

industrial and engineering sector. Finally, I have gain some familiarity and become acquainted with the

basic laboratory procedures after experiment were done.

RECOMMENDATIONS

There are few recommendations that can be considered while doing this experiment in order to get more

accurate result:

Repeat 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.

Error 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.

We 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.

When 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.

A better (computerized/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.

REFERENCES

Bruce R. Munson, Donald F. Young, John Wiley & son, Inc, FUNDAMENTAL OF FLUID

MECHANICS, 2nd edition.

Laboratory Manual of CHE 465 Chemical Engineering Laboratory 1. Fakulti Kejuruteraan Kimia,

Universiti Teknologi Mara.

Nevers N.de. (2005). Fluid Mechanics for Chemical Engineers. Fluid friction in steady, one-

dimensional flow. 3rd ed. New York : McGraw Hill, (175 – 176).

Cengel, Y.A. & Cimbala J.M. (2006). Fluid Mechanics : Fundamentals and Applications. Flow in

pipes. New York : McGraw Hill, (324).

John A. Roberson and Clayton T. Crowe, (1997). Engineering Fluid Mechanics (6th ed.). John

Wiley & Sons, Inc.

Coulson & Richardson’s Fluid Dlow, Heat Transfer and Mass Transfer

Bruce R. Munson, Donald F. Young, Theodore H. Okiishi (2002). Fundamental Of Fluid

Mechanics (4th ed.). John Wiley & Sons, Inc.

http://www.engineeringtoolbox.com/reynolds-number-d_237.html

http://www.engr.uiuc.edu/communications/engineering_research/2005/html.php?

year=2004&phrase=selig&submit=Search

http:// www.armfield.co.uk/f1-21-datasheet.html

APPENDICES

Free and Forced Vortex Apparatus

There are two types of vortices,

Forced vortex Free vortex

In a free vortex, the medium spirals toward the centre

In a forced vortex, fluid (or gas) circles 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).  Without a constant supply of energy to remove the medium from the centre, the Free Vortex ceases to exist.  If the fluid doesn't exit the system, it no longer has any spiral nature, and becomes a forced vortex.