Contour Integral/Examples/Circulation of Fluid
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Example of Contour Integral
Let $\mathbf v$ be the velocity within a body $B$ of fluid as a point-function.
Let $\Gamma$ be a closed contour 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 contour integral:
- $\ds \int_\Gamma \mathbf v \cdot \d \mathbf l$
Sources
- 1951: B. Hague: An Introduction to Vector Analysis (5th ed.) ... (previous) ... (next): Chapter $\text {II}$: The Products of Vectors: $3$. Line and Surface Integrals