What is the physical meaning of Stoke's theorem in relation to fluid rotation?

[mrajkumar]

Hi,
Could you tell me the physical meaning of the stoke's theorem which equates the area integral of vorticity and the line integral of the velocity? what is the meaning of taking a area integral of vorticity? Sorry i could not get the physical meaning of these integrations.

Thank you

 

[RandomGuy88]

The line integral of velocity around a closed contour is the definition of circulation in a fluid. The circulation can be thought of as a measure of the rotation in the fluid. When performing a line integral you project the vector onto the closed curve (you are interested in the component of velocity tangent to the curve). The application of Stoke's theorem gives you a relation between circulation (line integral of velocity on a close loop) and the flux of vorticity through the surface enclosed by the contour. So it gives you a relation between the rotation of a macroscopic fluid element (circulation) to the rotation at individual points within that area.