Fluid Mechanics Forced Vortex Free Vortex Experiment

Experiment-1

Ravi Agarwal 09003017

Aim (1.a):-To obtain the surface profile and the total head distribution in a forced vortex flow. Theory: - Forced vortex flow can be generated by rotating a cylinder containing water about its axis. Under steady conditions, each particle will move with the same angular velocity and there will not be any relative motion between fluid f luid 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.

As shown above Z and H at any radial distance r are measured with reference to the horizontal datum passing through the lowest point of surface profile. It can be proved that :-

-angular speed

ω

Z-distance with reference to horizontal datum line upto a point on surface profile at radial distance r from axis of rotation.

H-distance with reference to horizontal datum line upto a point on total energy line at radial distance r from axis of rotation.

Setup and utilities required:-

The setup consists of an open transparent cylinder which is free to rotate about its vertical axis. The cylinder is suitably mounted on a variable speed motor. The utilities required are:  

Power supply: Single Phase, 220 volts, 50 Hz, 5 Amp with earth. Water supply Drain

Procedure: 

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Cylinder is filled with water to a height lower than its half. Cylinder is rotated with a constant speed until a parabolic free surface is formed. Note the speed of rotation now. After steady state conditions are achieved, surface profile readings are taken by measuring different radiuses and the corresponding heights. The surface elevation at r=0 is taken as the datum for all these readings. Repeat the same procedure for two more speeds of rotation.

Observations and Calculations:Plot-1 (R.P.M-155) Radius (cm) Height (cm) 0 0 2.7 1 3.8 2

Plot-2 (R.P.M-172) Radius (cm) Height (cm) 0 0 1 3.3 2 4.3

Plot-3 (R.P.M-132) Radius (cm) Height (cm) 0 0 1.7 4.2 2.7 5.3

4.6 5.6 6.5

R.P.M-132 Radius 0 4.2 5.3 6.8 8.2

R.P.M- 155 Radius(cm) 0 2.7 3.8 4.6 5.6 6.5

3 4.5 6

5.6 6.4 7.3

Height 0 1.7 2.7 4.7 6.7

Height(cm) 0 1 2 3 4.5 6

6.8 8.2

4 6

4.7 6.7

8

2 2

Theoretical(.5*ω r /g) 0 1.7 2.7 4.5 6.6

2 2

Theoretical(.5*ω r /g) 0 0.98 1.94 2.64 4.2 5.7

Total head 0 3.4 5.4 9.2 13.3

Total Head

0 1.98 3.94 5.64 8.7 11.7

R.P.M-172 Radius 0 3.3 4.3 5.6 6.4 7.3

Height 0 2 3 5 7 9

2 2

Theoretical(.5*ω r /g) 0 1.8 3.1 5.1 6.7 8.8

Total head 0 3.8 6.1 10.1 13.7 17.8

Results: 

For all the values of speed plots obtained are prefect parabolas. The plots also show the theoretical values and the total head count which also shape of  parabolas.

Precautions:     

Do not run the pump at low voltage i.e. l ess than 180 Volts. Always keep apparatus free from dust. To prevent clogging of moving parts, rum pump at least once in a fortnight. Frequently Grease/Oil the rotating parts, once in three months. Always Use Clean Water. If the Apparatus is not in use for more than one month, drain the apparatus completely, and fill pump with cutting oil.

Aim (1.b):- To obtain the surface profile in a free vortex flow. Theory:-When 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 centre with stream line in motion, so that, neglecting losses caused by vi scosity, 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 horizontal plane, and is known as free cylindrical vortex. Some more examples of  free vortex flow are:    

Flow of liquid through a hole provided at the bottom of the container. Flow of liquid around a circular bend in a pipe. A whirlpool in a river. Flow of fluid in a centrifugal pump casing.

Under steady conditions, each particle will move with the same angular velocity and there will not be any relative motion between fluid 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.

Setup and Utilities required:The setup consists of an open transparent cylinder cylinder which is stationary at its base. At the bottom centre of the graduated carriage an orifice discharge has been given to create free vortex. Suitable arrangements for water supply, drainage and traveling of pointer are provided.

The utilities required are :  

Power supply: Single Phase, 220 volts, 50 Hz, 5 Amp with earth. Water supply Drain

Procedure:    

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Apparatus is cleaned and made dust free and then drain valves are closed. The tank is filled to ¾ of its height and then the open flow control valve is opened. All switches are checked to be on OFF position. Now main power supply and pump are switched ON. Flow control valve is now operated and the orifice at the bottom of the tank is opened so that the water can be discharged outside at a steady rate. Now surface profile readings are taken when steady state is reached re ached and surface elevation at r=0 is taken as the datum for all these readings.

Observations and calculations:-

Radius 0.9

Height 10.8

1.05 1.1

11.3 11.8

1.25

12.8

1.3 1.5

13.8 14.8

1.7

15.8

1.9 2.2

16.3 16.8

2.6 3.4

17.3 17.8

4.65

18.3

8.5

18.3

Results:

The surface profile is shown clearly by the plot.

Precautions:  

Dust free apparatus should be ensured. Clean water should be used. Oiling and greasing of the parts should be done at regular intervals.

Sources of Error:  

Apparatus/water Apparatus/water may be dirty. Parts might be rusted and not oiled properly. Error may be introduced if readings are taken before steady state.