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Source and Sink
A line source and sink is the building block to represent profile thickness as will be seen later. If a source or a sink is placed in the plane, it is convenient to define a polar coordinate system with origin at the source or sink location. Let (r, в) represent the distance and polar angle of a point to the source/sink.
The velocity components are
Q 1
Vr = , ve = 0 (2.19)
2n r
Note that the perturbation velocity vanishes in the far field, which is consistent with the asymptotic condition. The potential and stream functions are given by
ф = ln r, f = в (2.20)
2n 2n
Q represents the source/sink intensity and has unit of volume flow rate per unit span (m2/s). Q > 0 is a source, Q < 0 a sink. The equipotential lines are circles and the streamlines are rays through the origin. See Fig.2.5.
