The second example is that of a source (or sink), the complex potential of which is

This is a pure radial flow, in which all the stream lines converge in the origin, where there is a discontinuity due to the fact that continuity cannot be satisfied: at the origin there is an input (source, m > 0) or output (sink, m < 0) of fluid. Throughout any closed line that do not include the origin the mass flux (and then the discharge) is always null. On the contrary, throughout any closed line that includes the origin the discharge is always nonzero and equal to m.

The thick magenta line on the left is related to the fact that the complex potential is, in this case, a multiple valued function of space. In any fixed point the potential is known up to a constant, the so called cyclic constant, that in this case has the value of . Since in general the potential is defined up to a constant, the fact that it is a multiple valued function of space does not create any problem in the determination of the flow field, which is univoquely determined deriving the complex potential W with respect to z.