Recall that if [i]C[/i] is a piece-smooth, simple closed curve and [b]v[/b] is a vector field in two dimensions; then[br][br][center][b]Net outward flux[/b]=[math]\oint_C\mathbf{v\cdot\mathbf{n}}dS[/math] and [b]Circulation[/b]=[math]\oint_C\mathbf{v\cdot T}dS=\oint_C\mathbf{v}\cdot\mathbf{dr}[/math][/center]The following simulation shows some values of the net outward flux and circulation for [math]\mathbf{v}=y\mathbf{i}+\left(x+xy\right)\mathbf{j}[/math] and different curves.[br][br]Instructions:[br][list][*]Drag the center of the circle (left) to change its position.[/*][*]Change the curve: Line segment or semi-circle.[/*][/list][br][color=#ff0000]Note: [/color]The red arrows represent the unit vectors normal to the curve.