ME-313, IIT Gandhinagar, Dept. of Mechanical Engineering Page 1 Forced Vortex Aim To obtain the surface profile and the total head distribution in a forced vortex flow and compare it with the theoretical values. Apparatus Cylindrical tank Power supply for motor: Single Phase, 220 volts, 50 Hz, 5 Amp with earth. Pointer to measure the coordinates of the profile. Theory Forced Vortex Forced vortex can be created by rotating the body containing the fluid or by paddling in fluid. 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 velocity (ω) remains constant even for two different streamlines. We know that, = 2 = Where, and = acceleration in radial and z direction = acceleration due to gravity ω = angular velocity r = radius
Transcript
ME-313, IIT Gandhinagar, Dept. of Mechanical Engineering Page 1
Forced Vortex
Aim
To obtain the surface profile and the total head distribution in a forced vortex flow and compare
it with the theoretical values.
Apparatus
Cylindrical tank
Power supply for motor: Single Phase, 220 volts, 50 Hz, 5 Amp with earth.
Pointer to measure the coordinates of the profile.
Theory
Forced Vortex
Forced vortex can be created by rotating the body containing the fluid or by paddling in fluid. 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 velocity (ω) remains
constant even for two different streamlines.
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
ME-313, IIT Gandhinagar, Dept. of Mechanical Engineering Page 2
Also,
Equation 1. 𝑠𝑙𝑜𝑝𝑒 =𝑑ℎ
𝑑𝑟=
𝑎𝑟
𝑎𝑧=
𝜔2𝑟
𝑔
Integrating above equation gives
Equation 2. ℎ =𝜔2𝑟2
2𝑔= 𝑍𝑡ℎ𝑒𝑜𝑟𝑒𝑡𝑖𝑐𝑎𝑙
Where, ℎ = height from the bottom surface of the Forced vortex
Equation 3. 𝜔 =2𝜋𝑁
60
Where, N = RPM of the motor
Equation 4. 𝐻 =𝜔2𝑟2
𝑔
Where, H = Total Head
Procedure
Fill half of the cylindrical tank with water.
Rotate the cylindrical tank with constant fast speed. Let the surface take steady parabolic shape.
Measure the speed of rotation.
In steady state, take the surface profile readings with the help of a pointer.
ℎ at 𝑟 = 0 is taken as the datum for all these readings.
Repeat the procedure for different RPM values.
ME-313, IIT Gandhinagar, Dept. of Mechanical Engineering Page 3
Observation
RPM=139 rev/min
Radius(cm) Zactual(cm) Ztheoretical(cm) Total Head, H(cm)
0 0 0 0
1.97 0.72 0.419105 0.83821
2.51 1.23 0.680358 1.360717
5.36 4.23 3.102558 6.205116
7.88 7.24 6.705679 13.41136
RPM=162 rev/min
Radius(cm) Zactual(cm) Ztheoretical(cm) Total Head, H(cm)
0 0 0 0
2.37 1.39 0.823925 1.647849
3.41 2.35 1.705688 3.411375
4.71 3.95 3.254112 6.508225
6.93 7.5 7.044614 14.08923
RPM=180 rev/min
Radius(cm) Zactual(cm) Ztheoretical(cm) Total Head, H(cm)
0 0 0 0
1.74 0.63 0.548282 1.096565
3.25 2.16 1.912813 3.825625
5.26 5.1 5.010456 10.02091
8.63 11.75 13.48737 26.97474
ME-313, IIT Gandhinagar, Dept. of Mechanical Engineering Page 4
Profiles
RPM=139 rev/min
RPM=162 rev/min
RPM=180 rev/min
0
2
4
6
8
10
12
14
16
-10 -5 0 5 10
Experimental Z
Theoretica Z
Total Head
0
2
4
6
8
10
12
14
16
-10 -5 0 5 10
experimental Z
theoretical Z
Total Head
0
5
10
15
20
25
30
-10 -5 0 5 10
Experimental Z
theoretical Z
Total Head
ME-313, IIT Gandhinagar, Dept. of Mechanical Engineering Page 5
Error
Human errors in measuring the profile readings.
Centre of Forced vortex was manually judged.
Conclusion
Surface profile and total head distribution profile for Forced vortex at various RPM have been
