A free vortex flow is a type of fluid flow in which the velocity of the fluid particles at any point is dependent only on the distance from the center of the vortex. This type of flow is characterized by a swirling motion and is commonly seen in natural phenomena such as tornadoes and hurricanes.
Vorticity is a measure of the local rotation of a fluid element in a flow. In a free vortex flow, vorticity is constant and has a magnitude proportional to the angular velocity of the fluid particles. This means that the vorticity is highest at the center of the vortex and decreases as you move away from the center.
Streamlines are imaginary lines that represent the direction of fluid flow at a given point. In a free vortex flow, the streamlines are circular and centered around the vortex. This means that the fluid particles move along these circular paths as they swirl around the center of the vortex.
The eye of the vortex is the center of the swirling motion in a free vortex flow. It is a region of low pressure and low vorticity, where the fluid particles have the highest velocity. This is why the eye of a tornado or hurricane is often calm and clear, as the air is rising and moving away from this central point.
Free vortex flow is unique in that it is an idealized flow where there is no external force or pressure acting on the fluid particles. This means that the flow is purely rotational and there is no change in the velocity or shape of the vortex over time. In contrast, other types of fluid flow, such as laminar or turbulent flow, are affected by external forces and can change in velocity and direction over time.