In this demo, we show the circulation along a curve C(t). The window "The unit tangents" shows the vecor field V(x,y,z) and the curve C(t); the red vectors are the unit tangent at certain points on the curve. The second window, "V(x,y,z) at C(t)" shows the vector field V(x,y) evaluated at (x,y,z)=C(t).

In the third window we see a graph of the function that gives the value of the dot product of V(C(t)) with the unit tangent at C(t). The circulation along C(t) is then equal to the (signed) area under the graph, and you can read it off the readout "Circ".