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 streamlines converge at
the origin, where there is a singularity due to the fact that
continuity can not be satisfied: at the origin there is an input (source,
*m* > 0) or output (sink, *m* < 0) of fluid. Traversing
any closed line that does not include the origin, the mass flux (and then
the discharge) is always zero. On the contrary, following 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 multi-valued function of
space. At 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 multi-valued function of
space does not create any problem in the determination of the flow
field, which is uniquely determined upon deriving the complex potential
*W* with respect to *z*.