Line Integral/Examples/Circulation of Fluid

Example of Line Integral

Let $\mathbf v$ be the velocity within a body $B$ of fluid as a point-function.

Let $\Gamma$ be a closed curve in $B$.

Let $\d \mathbf l$ be a small element of length of $\Gamma$ at a point $P$.

Then the circulation of $B$ over $\Gamma$ is given by the line integral:

$\ds \int_\Gamma \mathbf v \cdot \d \mathbf l$