ME-313, IIT Gandhinagar, Dept. of Mechanical Engineering Page 1

Free Vortex

Aim

To observe the surface profile in a free vortex flow.

Apparatus

Cylindrical tank with orifice at the centre of the bottom

Pointer to measure the coordinates of the profile

Pump to circulate the water

Control valve to control the flow rate of fluid

Theory

Free vortex flow is an example of rotational flow where no external torque is required to rotate the fluid mass. Some examples of free vortex flow are Flow of liquid through a hole provided at the bottom of the container and a whirlpool in a river.

Streamlines for such a flow will be concentric circles and the total energy is constant along a streamline. However the energy varies from streamline to streamline.

The main characteristic of the forced vortex flow is that angular momentum (mωr2) remains constant throughout the flow as no external torque is being provided.

We know that, 𝑎𝑟 = 𝜔2𝑟 𝑎𝑧 = 𝑔

Where, 𝑎𝑟 and 𝑎𝑧 = acceleration in radial and z direction 𝑔 = acceleration due to gravity ω = angular velocity r = radius

However , Equation 1. 𝜔𝑟2 = 𝑘

As no external torque is present. Also,

Equation 2. 𝑠𝑙𝑜𝑝𝑒 =𝑑ℎ

𝑑𝑟=

𝑎𝑟

𝑎𝑧=

𝜔2𝑟

𝑔=

𝑘2

𝑔𝑟 3

Integrating above Equation 2. gives

ME-313, IIT Gandhinagar, Dept. of Mechanical Engineering Page 2

Equation 3. ℎ = −𝑘2

2𝑟2𝑔

Where, ℎ = height from the top surface of the Free vortex

Equation 2. explains why the slope is steeper a radius decrease. Whereas in Forced

vortex slope was zero at radius=0.

Equation 3. 𝜔 =2𝜋𝑁

60

Where, N = RPM of the motor

Equation 4. 𝐻 =𝜔2𝑟2

𝑔

Where, H = Total Head

Procedure

Close the drain valves provided.

Fill ¾ cylindrical tank with water

Open Flow Control Valve given on the discharge line.

Now switch on the Main Power Supply (220 V AC, 50 Hz) and switch on the

Pump.

Regulate the flow with control valve in order to maintain the constant height in the cylindrical

tank.

Now open the orifice at the center of the bottom of the cylindrical tank to allow discharge of

water at steady state.

When conditions become steady, take the surface profile readings with the help

of a pointer .

The surface elevation at r=0 is taken as the datum for all these readings.

Observation

Sr. No. 1 2 3 4 5 6 7 8

Radius(cm) 0.36 0.69 0.90 1.46 1.88 2.67 3.61 5.79

Height(cm) 16.51 18.84 19.37 21.41 22.12 22.53 22.80 23.39

ME-313, IIT Gandhinagar, Dept. of Mechanical Engineering Page 3

Profile

Precaution

Always keep apparatus free from dust.

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.

Error

Error may rise in a profile as the radius was not exact zero i.e. orifice at the bottom was not a

perfect sink.

Conclusion

The profile of Free vortex motion was observed.

-Vrushiket Patil(09003044)

Mechanical B’tech 2009

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surface profile