In a free-vortex potential flow, the streamlines are concentric circles about a given point. This can be explained by considering the nature of the flow and the governing equations.

Explanation:
1. Free-vortex potential flow:
- A free-vortex potential flow is a type of ideal fluid flow where the motion is rotational and irrotational at the same time.
- In this flow, the velocity field is derived from a velocity potential function, and the flow is assumed to be inviscid and incompressible.

2. Streamlines:
- Streamlines are imaginary lines that represent the direction and magnitude of the fluid velocity at any given point in a flow field.
- They are defined as the path that a fluid particle would follow if it were to move with the flow.
- Streamlines are always tangent to the velocity vector at each point.

3. Concentric circles:
- In a free-vortex potential flow, the velocity field has a rotational component, which gives rise to a circular flow pattern around a central point.
- The streamlines in this type of flow are concentric circles that are centered at the point where the vortex is located.
- The circles represent the path that a fluid particle would follow as it rotates around the central point.
- The radius of the circles represents the distance from the central point, and the spacing between the circles represents the magnitude of the velocity.

4. Velocity distribution:
- The velocity distribution in a free-vortex potential flow is inversely proportional to the radius from the central point.
- This means that the velocity is highest at the center (where the radius is zero) and decreases as the radius increases.
- The velocity magnitude can be calculated using the equation v = k/r, where v is the velocity magnitude, k is a constant, and r is the radius.

In summary, in a free-vortex potential flow, the streamlines are concentric circles about a given point. This is because the flow has a rotational component, resulting in a circular flow pattern. The circles represent the path that fluid particles would follow as they rotate around the central point, and the spacing between the circles represents the magnitude of the velocity.