In this demo, we show the flux across a curve C(t). The window "The unit normals" shows the vecor field V(x,y) and the curve C(t); the red vectors are the unit tangent at certain points on the curve. The second window, "V(x,y) at C(t)" shows the vector field V(x,y) evaluated at (x,y)=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 normal at C(t). The flux across C(t) is then equal to the (signed) area under the curve, and you can read its value off the readout "Flux".