What is the Physical Meaning of Circulation in Vector Fields?

[Curl]

Meaning of "circulation"

Is there a physical meaning to circulation:

$$\Gamma=\oint_{C}\mathbf{V}\cdot\mathbf{dl}$$

For example, if the vector field represents a force field, the path integral denotes the work done on a particle moving along said path.

Here, its is velocity. What meaning does the path integral have? It is essentially velocity times distance, m²/s. Perhaps Area/sec? What meaning does that have, if any? I couldn't think of anything.

 

[hmg]

One take.
Velocity is a ratio of a change in space or distance to a change in time, but inverting the ratio can have the same meaning as the original form, just as a four minute (per) mile has the same physical meaning as fifteen miles per hour. Physically, with this in mind, the path integral product of a velocity gives the period of time for one circuit.

 

[Curl]

Not really, this is m/s times meters, not m/s divided by meters.

For example, in a conservative field the circulation is zero but the time for one circuit is non zero. (imagine a uniform field)