ABSTRACT
A flow is two-dimensional if the velocity lies on a plane, and does not depend on the coordinate normal to the plane. The volume flux across (circulation around) a loop is zero for an incompressible (irrotational) flow that has a stream function (Section 12.1) [potential (Section 12.2)]. A potential flow (Section 12.3) is both irrotational and incompressible, and thus has both potential (and stream function) that is the real (imaginary) part of the complex potential; the latter is a holomorphic function, whose derivative specifies the components of velocity, for example, for a flow source or sink (Section 12.4), a vortex (Section 12.5), or their superposition in a monopole (Section 12.6). The limit of opposing monopoles whose strength increases inversely with mutual distance leads in the coincidence limit to a dipole (Section 12.7); a similar limiting process may be repeated, to lead to a quadrupole (Section 12.8) and hydrodynamic multipoles (Section 12.9) of any order. The potential flow is one of the simplest, in that it is devoid of the effects of compressibility, vorticity, viscosity, turbulence, heat transfer, etc. As such it is the baseline flow against that all these effects can be compared at a subsequent stage.
