Kelvin S Circulation Theorem

Statement

Kelvin’s Circulation Theorem states that in an inviscid, barotropic fluid with conservative body forces, the circulation around a closed material contour moving with the fluid is constant in time.

Mathematical Form

$\frac{D\Gamma}{Dt} = 0$ where $\Gamma = \oint_C \mathbf{v}\cdot d\mathbf{s}$.

Relationships

• Related: Vorticity, Potential Flow