JET IMPACT

FACULTY OF CHEMICAL ENGINEERING

UNIVERSITI TEKNOLOGI MALAYSIA

FLUID MECHANICS LABORATORY

TITLE OF EXPERIMENT

FORCED VORTEX FLOW (E6)

Name

Matrix No.

Group / Section

Supervisor

Date of Experiment

Date of Submission

Marks obtained (%)

1.0Objective

The objective of this experiment is study the relationship between the surface shape of a forced vortex flow and the angular velocity of a rotating liquid in a cylindrical tank.2.0IntroductionA vortex is the rotation of fluid elements around a common center. There are two types of vortices, i.e. forced and free. In a forced vortex, fluid (or gas) circles around a centre, while in a free vortex the medium spirals toward the centre. The speed and rate of rotation of the fluid are greatest at the center, and decrease progressively with distance from the center.3.0Theory Figure 1 depicts a fluid contained in a cylindrical tank that rotates with a constant angular

velocity about the vertical z axis. The gravity vector acts in the negative z direction. For steady-state rotation, the fluid rotates with the tank as a rigid body.

Fig. 1: Fluid in rigid-body rotation within a cylindrical tank, which rotates around the vertical z axis with a constant angular velocity .The theoretical expression relating the change in fluid height in Fig. 1 to the angular velocity is given as

(1)where

h = initial (non-rotating) surface height of the fluid,

h0= height on the axis,

=angular velocity, radian/second

r = radius of the cylinder,

g = acceleration of gravity.

Taking ho as datum (i.e. ho = 0), the theoretical height (hth) of a vortex surface corresponding to a radius r from the axis at a constant angular velocity can be expressed as

(2)where N is the rotational speed of rotating fluid (revolution/sec , rps)

Thus, the theoretical height (zth) of a vortex surface relative to the actual measurement obtained from the experiment is zth = zo-hth

(3)where zo is the measured height of a vortex surface at the axis (i.e. r = 0)4.0ApparatusA Cussons P6238 Forced Vortex Apparatus for the study of the shape of forced vortices consists of a 250 mm diameter cylindrical, transparent vessel 180 mm depth, having two pairs of diametrically opposed inlet tubes of 9.0 mm and 12.5 mm diameter. The 12.5 mm diameter inlet tubes which are angled at 15 to the diameter, so that a swirling motion is imparted to the liquid entering the vessel, are used as entry tubes for the free vortex experiment. A smooth outlet is centrally positioned in the base of

the vessel and a set of push-in orifices of 24, 16, 12 and 8 mm diameter is supplied to reduce the outlet diameter to a suitable value.

The profile of the vortex formed at the top of the vessel is determined by a gauge, housed on a diametrically mounted bridge piece, which measures the diameter of the vortex at various depths. This gives the co-ordinate points required to plot the vortex profile. The forced vortex is created in the vessel described above by using as the inlet the 9 mm bore tubes which are angled at 60 to the diameter. The input water from these tubes impinges on a simple two blade paddle which acts as a stirrer/flow straightener. The two bladed paddle rotates on a vertical shaft supported by a bushed plug, in the hole used as the outlet for the free vortex experiment, and located at the top by a suitable hole in the bridge piece fitting across the diameter of the vessel. This bridge piece also houses the probes required to determine the co-ordinates of the vortex profile to be measured.

5.0Experimental Procedure1. Ensure that the control valve in closed condition (in clockwise direction) and the outlet valve for the flow from the cylinder is fully open (in anti-clockwise direction). Switch on the pump.

2. Gently, open the control valve (in anti-clockwise direction). The force of the flowing water which enter into the cylinder will push the peddle blade to rotate at required speed.

3. Ensure that the water level in the cylinder is at the maximum height and it is maintained constantly. Use the outlet valve to control the water level in the cylinder. To open the valve, turn the knob in anti-clockwise direction, to close it, turn the knob in clockwise direction.

4. After the level of water is constantly maintained at the maximum height of the cylinder, lower down each pointers of the vortex radius profile measurement gauge to the surface of the water profile. At the same time, clock the time taken (in second) for the peddle blade to rotate 50 cycle.

5. Measure the height of the vortex profile by measuring the height of each pointers of the vortex radius profile measurement gauge. Record the data in the given table.

6. Repeat procedures (2) to (5) for two other different flow rates.6.0Experimental data and analysisMeasurement of surface height of forced vortexNo.Time taken for 50 cycles of blade rotation (second)Rotational speed, N

(rps)Probe Measuring Depth, zmea (mm) at different vortex radius r (mm)

r = 110 r = 90 r = 70 r = 50 r = 30 r = 0

Comparison of measured and theoretical height of vortex surfaceN

(rps)Height of vortex surface (mm)Probe Measuring Depth, z (mm) at different vortex radius r (mm)

r = 110 r = 90 r = 70 r = 50 r = 30 r = 0

zmea

hth

zth= zo-hth

zmea

hth

zth= zo-hth

zmea

hth

zth= zo-hth

7.0Laboratory report1. See handout (Laboratory Report Format)

2. Additional report requirement

a. Plot a graph of measured and theoretical values of z versus r for different angular speeds. i. For each angular velocity, perform comparative analysis of measured and theoretical profile, comment on the difference and discuss possible sources of error.

ii. Comment on the forced vortex profile with respect to angular velocity.b. Plot a graph of measured and theoretical values of z versus r2 for different angular speeds. i. Calculate the slope (z/r2) of each graph. ii. Calculate the value of hth/r2 from equation 1

iii. Compare the values obtained in (i) and (ii) and comment the results with respect to angular velocityc. Briefly discuss factors contributing to errors or inaccuracy in experimental data and propose recommendation to improve the results

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