In the last example we superimpose to the complex potential that gives the flow around a cylinder a vortex of intensity positioned in the center of the cylinder so that the total potential is now

The presence of the vortex does not alter the stream line describing the cylinder, while the two stagnation points move down.

The stream lines are closer on the upper part of the cylinder and more distant on the lower part. This indicates that the flow is accelerated on the upper face of the cylinder and decelerated on the lower part, with respect to the zero circulation case.

The resulting flow field corresponds to the case of a rotating cylinder, which accelerates (with respect to the case of no circulation) fluid particels on one face of the cylinder and decelerates them on the other face.

Note the presence of a discontinuity in the potential function that is related to the fact that the vortex potential (as mentioned in a previous section) has a nonzero cyclic constant.