Note that since streamlines are tangent to the flow, the value of the stream function must be the same along a streamline. If there were a flux across a line, it would necessarily not be tangent to the flow, hence would not be a streamline.

The usefulness of the stream function lies in the fact that the velocity components in the *x*- and *y*- directions at a given point are given by the partial derivatives of the stream function at that point.