8/2/2019 Vortex Motion

1/11

8/2/2019 Vortex Motion

2/11

A vortex is a spinning , often turbulent ,flow of fluid . Any spiral motion withclosed streamlines is vortex flow. Themotion of the fluid swirling rapidly around acenter is vortex.

http://en.wikipedia.org/wiki/Rotationhttp://en.wikipedia.org/wiki/Turbulencehttp://en.wikipedia.org/wiki/Fluidhttp://en.wikipedia.org/wiki/Spiralhttp://en.wikipedia.org/wiki/Streamlines,_streaklines_and_pathlineshttp://en.wikipedia.org/wiki/Center_(geometry)http://en.wikipedia.org/wiki/Center_(geometry)http://en.wikipedia.org/wiki/Streamlines,_streaklines_and_pathlineshttp://en.wikipedia.org/wiki/Spiralhttp://en.wikipedia.org/wiki/Fluidhttp://en.wikipedia.org/wiki/Turbulencehttp://en.wikipedia.org/wiki/Rotation

8/2/2019 Vortex Motion

3/11

The speed and rate of rotation of the fluid in afree (irrotational) vortex are greatest at the

center, and decrease progressively with distancefrom the center, whereas the speed of a forced(rotational) vortex is zero at the center andincreases proportional to the distance from the

center. Both types of vortices exhibit a pressureminimum at the center, though the pressureminimum in a free vortex is much lower.

http://en.wikipedia.org/wiki/Rotationhttp://en.wikipedia.org/wiki/Rotation

8/2/2019 Vortex Motion

4/11

The tangential velocity is given by:

where is the angular velocity and r isthe radial

distance from the center of the vortex.

http://en.wikipedia.org/wiki/Angular_velocityhttp://en.wikipedia.org/wiki/Angular_velocity

8/2/2019 Vortex Motion

5/11

1.All fluid particles rotate with the same angular velocity like asolid body. Hence a forced vortex flow is termed as a solid body

rotation .2.The vorticity for the flow field can be calculated as

8/2/2019 Vortex Motion

6/11

Therefore, a forced vortex motion is not irrotational; rather it is arotational flow with a constant vorticity 2. This equation is used todetermine the distribution of mechanical energy across the radiusas

8/2/2019 Vortex Motion

7/11

Integrating the equation between the two radii onthe same horizontal plane, we have,

Thus, we see from this eq. that the total head(total energy per unit weight) increases with anincrease in radius. The total mechanical energy atany point is the sum of kinetic energy, flow workor pressure energy, and the potential energy

8/2/2019 Vortex Motion

8/11

Therefore the difference in total head between any two points in thesame horizontal plane can be written as,

8/2/2019 Vortex Motion

9/11

Substituting this expression of H 2-H1 in above Eq., we get

The same equation can also be obtained by integrating theequation of motion in a radial direction as

8/2/2019 Vortex Motion

10/11

To maintain a forced vortex flow, mechanical

energy has to be spent from outside and thus anexternal torque is always necessary to be appliedcontinuously.

Forced vortex can be generated by rotating avessel containing a fluid so that the angularvelocity is the same at all points.

8/2/2019 Vortex Motion

11/11