AbstractThe purpose of this experiment was to study the relationship between surface profile and speed for a free vortex and surface profile with angular velocity for a forced vortex. In the experiment of free vortex, water was pumped out through different orifice diameters of 24 mm, 16 mm, 12 mm and 8 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. From there, a graph of pressure head against 1/r2 was plotted, where the gradient was used in the calculation of theoretical velocity. Both actual (experimental) and theoretical velocities were then compared. Meanwhile, for the experiment of forced vortex, two trials were perfomed with each using different water flow rates. A 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 IntroductionLiqiuds undergo rotational motion, where they move in a circular motion. A vortex is a region within fluid where the flow moves within a circular motion about an axis. According to Kueh (2014), water vortex is a phenomenon where water flow in swirl motion, always described by cylindrical coordinates with tangential, radial and axial axis. In macroscopic level, such phenomenon is common. A 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 (Albert,2009). Liquid vortex also occurs in many chemical engineering appliances, such as in centrifugal pump, in a stirred vessel and in a cyclone-type separator (Coulson, 1999).A 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. While 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 horizontal plane and it is known as free cylindrical vortex. Under steady condition, each particle will move with the same angular velocity and there will not be any relative motion between the particles. Streamlines for such a flow will be concentric circles and the total energy is constant along a streamline but varies from one streamline to another.When a cylinder containing water is rotated by an external force, a forced vortex is formed. The motion of the fluid swirling rapidly is the vortex formed. A forced vortex flow is that in which the fluid mass is made to rotate by means of some external force, which exerts a constant torque on the fluid thus resulting for the whole mass of fluid to rotate at constant a angular velocity, . There is always constant external torque required to be applied to the fluid mass resulting in an expenditure of energy.

2.0 Objectives2.1 Free Vortexi. To study the surface profile and speed.ii. To find the relationship between surface profile and speed.2.2 Forced Vortexi. To study the surface profile and angular velocity.ii. To find the relationship between surface profile and total head.

3.0 Theory

3.1 Free VortexA vortex is the motion of many fluid particles around a common center. Free vortex contains radial velocity towards the center. Water passes through each segments of diameter, and the energy at any tube is constant, which then relates to: + z = constant3.2 Forced VortexForced vortex is formed when a body containing fluid is rotated by paddling. The total energy isconstant along a streamline. However it varies variesfrom streamline to streamline.The equation of the free vortex related to the angular velocity is given by;

The radial pressure increases and shown by,

Because , so

The equation of forced vortex is represented by:

While the equation of distribution of total head can be represented by:

Where: z = surface profile = angular velocityr = radiusg = gravityH = total headThe equation of acceleration of the radial, and direction z, is given by,

The equation of angular velocity is calculated by:

4.0 Apparatus and Materials

4.1 SOLTEQ Free and Forced Vortex (Model : FM42)4.2 Stop watch4.3 Power supply4.4 Measuring gauge4.5 Water

5.0 Procedure5.1 Free Vortex 5.1.1 General start-up procedures were performed.5.1.2 An orifice with diameter of 24 mm was selected and placed on the base of cylinder tank.5.1.3 The output valve was closed and the inlet 3-way valve was adjusted to let the water flows into the tank from two pipes with 12.5 mm diameter. This results in the water flow out through the orifice.5.1.4 The pump was switched on and the control valve on the hydraulic bench was slowly opened until the tank limit. Water level in the tank was maintained by adjusting the control valve.5.1.5 The vortex profile was collected by measuring the vortex diameter for several planes using the profile measuring gauge when the water level is stable.5.1.6 The profile measuring gauge was pushed down until the both of sharp point touches the water surface.5.1.7 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) was obtained.5.1.8 The pitot tube was used to measure the velocity by sinking it into the water at the depth of 5, from the water surface. The depth of the pitot tube in the water, H was measured.5.1.9 Steps 3 to 8 were repeated using another three orifice with diameter of 12mm, 16mm and 8mm respectively.5.1.10 The coordinates of vortex profile for all diameter of orifice were plotted in graph and the gradient of the graph was calculated.5.1.11 The graph of velocity which is calculated from the pitot tube reading versus the radius of the profile was plotted

5.2 Forced vortex5.2.1 The general start-up procedures were performed.5.2.2 A closed pump with two pedals was placed on the base of the cylinder tank.5.2.3 The output valve was closed and the inlet 3-way was adjusted to let the water flows into the tank from two pipes with 9.0 mm diameter. The water will flow out through another two pipes with 12.5 mm diameter.5.2.4 The water flow out from the tank was ensured with the siphon effect by raising the hose to above the water level in the tank.5.2.5 The outlet hose was ensured to fill with water before letting the water to flow into the sump tank in the hydraulic bench.5.2.6 The angular speed of the pedals was measured by counting the number of circles in a certain times.5.2.7 The surface probe was pushed down until the sharp point touch the water surface.5.2.8 The height, ho (from top of the measuring gauge to bridge) was measured.5.2.9 Steps 4 to 8 were repeated with different volumetric flow rate.5.2.10 The coordinates of vortex profile for different angular velocity was plotted.5.2.11 The calculated vortex profile was plotted in the same graph.

6.0 Results 6.1 Free vortexOrifice diameter = 24 mm|Distance from bridge to water surface, a = 181 mmDiameter at centre, D (mm)Measured Height, h (mm)Pitot Tube Head Difference, H (mm)Pressure Head / Depth of the Pitot Tube, X (mm)Velocity, (mm/s)r (mm)r2 (mm2)

5576673343.10327.5756.25

5374975420.21426.5702.25

49691280485.22224.5600.25

48681581542.49425.0625.00

Orifice diameter = 16 mmDistance from bridge to water surface = 192 mmDiameter at centre, D (mm)Measured Height, h (mm)Pitot Tube Head Difference, H (mm)Pressure Head / Depth of the Pitot Tube, X (mm)Velocity, (mm/s)r (mm)r2 (mm2)

50104534313.20925.0625.00

47101637343.10323.5552.25

4499939420.21422.0484.00

40961142464.56420.0400.00

Orifice diameter = 12 mmDistance from bridge to water surface = 201 mmDiameter at centre, D (mm)Measured Height, h (mm)Pitot Tube Head Difference, H (mm)Pressure Head / Depth of the Pitot Tube, X (mm)Velocity, (mm/s)r (mm)r2 (mm2)

48115414280.14324.0576.00

46111718370.59423.0529.00

431071022442.94521.5462.25

391061323505.03519.5380.25

Orifice diameter = 8 mmDistance from bridge to water surface = 208 mmDiameter at centre, D (mm)Measured Height, h (mm)Pitot Tube Head Difference, H (mm)Pressure Head / Depth of the Pitot Tube, X (mm)Velocity, (mm/s)r (mm)r2 (mm2)

4011735242.61120.0400.00

3711359313.20918.5342.25

33112710370.59416.5272.25

291101112464.56414.5210.25

6.2 Forced vortexDistance from Centre (mm)

1st 2nd 3rd

0927355

30948364

70988669

1101099274

No of Revolutions in 60 seconds313234

Angular Velocity (rad/s)3.253.353.56

7.0 Sample Calculations7.1 Free vortexFrom Graph 1;

Thus,

Theoretical velocity or calculated velocity,

Radius, r (mm)Actual Velocity, v (mm/s)Theoretical Velocity, v (mm/s)

27.5343.103689.664

26.5420.214715.690

24.5485.222774.113

25.0542,494758.630

7.2 Forced vortexFor the first volumetric flowrate;

Theoretical height from top of the surface probe to bridge,

Calculated values;Distance from centre (mm)h (mm)

1st2nd3rd

092.0073.0055.00

3092.4873.5155.58

7094.6475.8058.17

11098.5179.9262.82

Angular velocity (rad/s)3.253.353.52

Full calculations are in the Appendices.Data analyses were tabulated in Appendices.

8.0 Discussion 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. A free vortex is formed when water flows out through a hole at the bottom of a tank while driven by the circular rotation of a pumping water vessel. Here, the water flows out through different orifice diameters of 24 mm, 16 mm, 12 mm and 8 mm. Once the flow had stabilized, the diameter at centre, height, pitot tube head difference and pressure head were recorded and calculated. From the results, 24 mm orifice diameter gave the biggest vortex diameter, followed by the 16 mm, 12 mm and 8 mm. This is because as diameter of orifice decreases, the vortex diameter also decreases. Also, the theoretical velocities were calculated from the graph of pressure head against 1/r2 that was plotted. Forced 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 60 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. For both experiments, there shows a deviation between the experimental and theoretical values. This is because there are a few errors that had occurred. One 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 tank. Besides that, the pitot tube did not sinked into 5mm from the surface. This affected the results when calculating the velocity by using the formula Also, the flow of water had not achieved asteady state. Lastly, the eyes were not perpendicular to the reading scale and parallax error may have had occurred when the reading was taken.

9.0 Conclusion9.1 From the experiment conducted free vortex and forced vortex have their own surface profile. 9.2 For free vortex, the diameter of the vortex is proportional with the diameter of orifice and the velocity is inversely proportional to the radius. 9.3 For forced vortex, the angular velocity is proportional to the water flow rate and the height of vortex formed.

10.0 Recommendations

10.1 A stable flow of water should be obtained to get more accurate readings of the surface profile by controlling the pump valve.10.2 Dust free apparatus should be used.10.3 Clear water without any particles should be used in the experiment.10.4 Oiling and greasing of the parts such as the paddle should be done at regular intervals.

ReferencesJ.M Coulson & J. F Richardson , (1999), Chemical Engineering, Volume 1, Sixth Edition, Fluid Flow, Heat Transfer and Mass Transfer, Butterworth HeinnemannTze Cheng Kueh, (April 2014), Numerical Analysis of Water Vortex Formation for the Water Vortex Power Plant, retrieved from http://pubs.rsc.org.ezaccess.library.uitm.edu.my/en/content/chapterpdf/2008/9781847558756-00031?isbn=978-0-85404-156-5&pdate=2008-11-04&sercode=bk&page=search, at 24th December 2014Albert Guijarro, (2009), The Origin of Chirality in the Molecules of Life: A Revision from Awareness to the Current Theories and Perspectives of this Unsolved Problem, retrieved from http://search.proquest.com.ezaccess.library.uitm.edu.my/docview/1507612529?pq-origsite=summon, at 24th December 2014

APPENDICESi. Data Analysis

Graph 1

Graph 2

Graph 3

Graph 4ii. Calculations for Free VortexFrom graph 2;

Thus,

Theoretical velocity,

Radius, r (mm)Actual Velocity, v (mm/s)Theoretical Velocity, v (mm/s)

25.0313.209426.594

23.5343.103453.823

22.0420.214484.766

20.0464.564533.243

From graph 3;

Thus,

Theoretical velocity,

Radius, r (mm)Actual Velocity, v (mm/s)Theoretical Velocity, v (mm/s)

24.0280.143565.098

23.0370.594589.660

21.5442.945630.807

19.5505.035695.506

From graph 4;

Thus,

Theoretical velocity,

Radius, r (mm)Actual Velocity, v (mm/s)Theoretical Velocity, v (mm/s)

20.0242.611313.209

18.5313.209338.604

16.5370.594378.647

14.5464.564432.012

Graph 5

Graph 6

Graph 7

Graph 8

iii. Calculations for Forced VortexFor the 2nd volumetric flowrate;

Theoretical height from top of the surface probe to bridge,

For the 3rd volumetric flowrate;

Theoretical height from top of the surface probe to bridge,

Graph 9

Graph 10

Graph 11