Streamlines of free vortex flow

Definition:
Free vortex flow is a type of fluid flow where the fluid particles rotate about a central axis in a circular path without any radial motion. The streamlines in free vortex flow are the paths followed by fluid particles in the flow field.

Nature of streamlines:
The nature of streamlines in free vortex flow is concentric. This means that the streamlines are circular and concentric around a central axis. The circular streamlines indicate that the fluid particles are rotating about the central axis, forming a vortex.

Explanation:
In free vortex flow, the fluid motion is induced by the rotation of a solid body or due to an external force. The streamlines in this type of flow are determined by the balance between the centrifugal force and the pressure gradient.

When a fluid particle is in free vortex flow, it experiences a centrifugal force due to its rotation about the central axis. This centrifugal force causes the fluid particle to move away from the central axis. However, the pressure gradient in the flow field is directed towards the center, acting as a restoring force. This pressure gradient balances the centrifugal force, resulting in a circular path followed by the fluid particle.

As a result, the streamlines in free vortex flow are concentric circles around the central axis. Each streamline represents a different circular path followed by the fluid particles in the flow. The radius of the streamlines increases as we move away from the central axis, indicating an increase in the velocity of the fluid particles.

Conclusion:
In summary, the nature of streamlines in free vortex flow is concentric. The streamlines are circular and concentric around a central axis, representing the paths followed by the fluid particles in the flow field.