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INSTRUCTION MANUAL for

FREE VORTEX APPARATUS OBJECT: -

• To plot the surface profiles of various free vortices formed under different flow conditions.

THEROEM:- Generally vortex motion occurs when a constant torque is applied to the fluid mass. A Free Vortex Motion is that in which the fluid mass rotates without any external force being impressed on it. The motion of the fluid swirling rapidly around a center is called a vortex. The speed and rate of rotation of the fluid in a free (irrotational) vortex are greatest at the center, and decrease progressively with distance from the center, whereas the speed of a forced (rotational) vortex is zero at the center and increases proportional to the distance from the center. Both types of vortices exhibit a pressure minimum at the center, though the pressure minimum in a free vortex is much lower.

When fluid is drawn down a plug-hole, one can observe the phenomenon of a free vortex or line vortex. The tangential velocity v varies inversely as the distance r from the center of rotation, so the angular momentum rv is uniform everywhere throughout the flow; the vorticity is zero everywhere

The tangential velocity is given by:

where Γ is the circulation and r is the radial distance from the center of the vortex.

In non-technical terms, the fluid near the center of the vortex circulates faster than the fluid far from the center. The speed along the circular path of flow decreases as you move out from the center. At the same time the inner streamlines have a shorter distance to travel to complete a ring. If you were running a race on a circular track would you rather be on the inside or outside, assuming the goal was to complete a circle? Imagine a leaf floating in a free vortex. The leaf's tip points to the center and the blade straddles multiple streamlines. The outer flow is slow in terms of angle traversed and it exerts a backwards tug on the base of the leaf while the faster inner flow pulls the tip forwards. The drag force opposes rotation of the leaf as it moves around the circle.

A cylindrical free vortex motion is conceived in a cylindrical coordinate system with axis z directing vertically upwards where at each horizontal cross-section, there exists a planar free vortex motion with tangential velocity given by The total energy at any point remains constant and can be written as

• The pressure distribution along the radius can be found from by considering z as constant; again, for any constant pressure p, values of z, determining a surface of equal pressure, can also be found.

Again the distribution of fluid pressure in a free vortex can be found out by using following equation

)()(21

212

12

2212 ZZgrr

PP−+−=

−ω

ρ

The free vortex motion is essentially a rotational motion because every fluid particle, in such a motion rotates about its own axis as it moves along the curved path. Due to rotational motion, Bernoulli’s equation can be applied to the same streamline, since at any point on the free surface of liquid, the pressure is constant, being equal to the atmospheric pressure the free surface of liquid is a surface of constant pressure which is a parabolic equation.

i.e gxZ

2

22ω= z

DESCRIPTION:

Free vortex apparatus, for the study of the shape of free vortices consists of a 190mm diameter cylindrical transparent vessel of 300mm depth. The motion can be given to the rotating mass with the help of Nozzles provided in apparatus. A Rotameter has been provided to measure the flow rate

of water. At the down stream ends of the pipeline. Separate control valve is provided to regulate the flow of water to Vessel. The profile of vortex formed at the top of the vessel can be determined by the scale provided with the apparatus. This will give the co-ordinate points required to plot the vortex profile.

UTILITIES REQUIRED:

Water Supply Electricity 230 V Ac

PROCEDURE:

1. Clean the apparatus & make it free from dust.

2. Add water to Sump tank Up to ¾ th of the tank.

3. Adjust The Flow rate of water with he help of by pass valve provided with this equipment.

4. Wait till Steady state has been achieved.

5. Measure the horizontal & vertical distance at different points of vortices with the help of scale

provided at the top of the vessel.

6. Note down the Flow rate of Water.

7. Take different observations by Flow Rate of Water.

8. Switch off the power supply & drain the water.

OBSERVATION:- Diamer of tank = 190 mm Height of tank = 300mm OBSERVATION TABLE:

S.No Flow Rate(LPH)

X Y

PRECAUTIONS & MAINTENANCE INSTRUCTIONS:

1. Never run the apparatus if the power supply is less than 180 volts and above 230 volts. 2. Never switch ON mains power supply before ensuring that all the ON/OFF switches given on

the panel are at OFF position.

3. Keep all the assembly undisturbed. 4. Always note the readings very carefully.