# FREE & FORCED VORTICES APPARATUS Modelk FM 14

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# FREE & FORCED VORTICES APPARATUS Modelk FM 14

The *Sci-tech***Free and Forced Vortices Apparatus Model FM 14 **has been designed to generate free and forced vortices. It is possible to measure surface profiles and total head distributions in the vortex flow field. The apparatus consists of a transparent cylindrical tank having a hole in the center of the base to fix interchangeable push-in orifices while conducting free vortex experiments. The cylinder is mounted on a base plate having leveling screws. The free vortex is generated by discharging water from the tank through the orifice in the base. Two 12mm diameter flow entry tubes placed diametrically opposite near the wall at the base and angled at about 20^{0} to the diameter supply water imparting swirling motion to the liquid entering the vessel. Forced vortex experiments are conducted by closing the orifice at the base by a bushed plug. The forced vortex is generated in the tank by rotating the two bladed paddle positioned at the base.

Size: | 60cm x 50cm x 50cm (LxWxH) |

Weight: | 15 kg |

### Item Description

The concept of vortex flows is important in many engineering applications of fluid mechanics. The flow circulates about a fixed center and the stream lines are concentric circles. The classification of vortex flows depends upon the functional relationship between the flow velocity and radius. In the free vortex, the flow velocity is inversely proportional to the radius and the total head in the flow field remains constant. In the forced vortex, the whole body of the fluid rotates as if it is a solid and the flow velocity is directly proportional to the radius. It is essential to demonstrate free and forced vortex flows to understand the basic concepts of fluid mechanics*. *The *Sci-tech***Free and Forced Vortices Apparatus Model FM 14**is an important experimental set-up necessary for any fluid mechanics and physics laboratories of an educational institution.

The *Sci-tech***Free and Forced Vortices Apparatus Model FM 14 **has been designed to generate free and forced vortices. It is possible to measure surface profiles and total head distributions in the vortex flow field. The apparatus consists of a transparent cylindrical tank having a hole in the center of the base to fix interchangeable push-in orifices while conducting free vortex experiments. The cylinder is mounted on a base plate having leveling screws. The free vortex is generated by discharging water from the tank through the orifice in the base. Two 12mm diameter flow entry tubes placed diametrically opposite near the wall at the base and angled at about 20^{0} to the diameter supply water imparting swirling motion to the liquid entering the vessel. Forced vortex experiments are conducted by closing the orifice at the base by a bushed plug. The forced vortex is generated in the tank by rotating the two bladed paddle positioned at the base.

The paddle rotates on a vertical shaft which is supported by the bushed plug at the base and a suitable hole in the bridge piece fitted across the diameter of the tank at the top. Water jets from the two 8mm diameter flow entry tubes placed diametrically opposite and angled at about 70^{0} to the diameter impinge on the blades and rotate the paddle. Water is drained using the 12mm diameter tubes. The bridge piece accommodates depth gauges required to map the vortex profiles. The total head in the free and forced vortex flow field is measured using a pitot probe. Colored dye can be injected into the flow using hypodermic tubes to visualize streamlines. The FM00 Hydraulic bench or any other standard hydraulic bench models can be used to supply water. A constant head overhead tank can also be used to supply water at controlled flow rate. The complete unit is manufactured from corrosion resistant material.

**FREE VORTEX**

A free vortex is formed when water flows out of a vessel through a central hole in the base. The degree of the rotation depends on the initial disturbance. In a free cylindrical vortex, the velocity varies inversely with the distance from the axis of rotation.

### Technical Specifications

**FREE VORTEX**

A free vortex is formed when water flows out of a vessel through a central hole in the base. The degree of the rotation depends on the initial disturbance. In a free cylindrical vortex, the velocity varies inversely with the distance from the axis of rotation.

v = \frac{k}{r}\qquad (1)

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

\frac{v^2}{2g}+z = C \qquad (2)

Substituting Equation (1) into (2) will give a new expression:

\frac{k^2}{2gr^2}+z = C \qquad (3)

or:

C-z = \frac{k^2}{2gr^2} \qquad (4)

which is the equation of a hyperbolic curve of nature y= \frac{A}{x^2}

This curve is asymptotic to the axis of rotation and to the horizontal plane through z=c.

**FORCED VORTEX**

When water is forced to rotate at a constant speed (\omega ) the velocity will be also constant and equal to:

v = \omega r\qquad (5)

The velocity head (or kinetic energy) can be calculated as:

hc = \frac {v^2}{2g} \qquad (6)

Substituting Equation (5) into (6) results in:

hc = \frac {r^2\omega^2}{2g} \qquad (7)

If the horizontal plane passing through the lowest point of the vortex is selected as datum, the total energy is equal to:

H =ho+h_c\qquad (8)

where ho is the pressure head at the datum. Substituting hc from Equation (7) into (8) gives:

H =h_o+\frac{r^2\omega^2} {2g}\qquad (9)

At r=0: H=0, therefore, ho=0 , and :

H =\frac{r^2\omega^2} {2g}\qquad (10)

This is the equation of the water surface profile, which is a parabola

**Specifications **

- Cylindrical tank, clear acrylic, diameter: 275mm, height; 275mm mounted on base plate with leveling screws, complete with pipe work, valve fittings and connections.
- Height of overflow point: 200mm.
- Orifice diameters: 8, 16 and 24mm.
- Depth gauges at 0, 20, 40, 60, 80, 100 and 110mm from center.
- Pitot probes, 0.9mm OD, nose at 15, 25, 35 and 45mm from center.
- Flow inlet tubes, 8 and 12 mm diameter.
- Paddle, two bladed, 240mm overall diameter.
- Bridge piece with scale.
- Hypodermic tube for dye injection with dye tank and flow control valve.
- Water manometer.
- Bushed plug.
- Hydraulic Bench (Not offered as part of the trainer)

**Services required **

- Single phase electrical supply, 220-240 V, 50 Hz for Hydraulic Bench.
- Water supply and drainage.

**Overall dimensions **

550 X 450 X 450 mm.

**Experiments **

- Demonstration of free and forced vortices.
- Determination of surface profile of a free vortex.
- Determination of total head variation in free vortex.
- Dye flow visualization of stream lines in free vortex.
- Determination of surface profile of a forced vortex.
- Determination of total head variation in forced vortex.
- Dye flow visualization of stream lines in forced vortex.
- Comparison of results with theoretical predictions.

### Model Number

FM 14

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