Expert: Paul Soderman - 7/6/2009

Question
what is an elemantary doublet? How does it differ from the infinitesimal dipole?

Answer
Doublets and dipoles are mathematical constructs used to represent certain flows and pressure fields in a fluid.  A doublet is a source-sink pair that are superimposed to create a stream function that has streamlines which look like circles of variable diameter all  tangent to a mirror at a point.  (A source is a point from which fluid issues in equal amounts along radial lines; a sink is the opposite - fluid flows into a point from all directions.)  That is - half the streamlines are above the line representing the mirror and half are below the line representing the mirror.  When added to a uniform flow mathematically, for example, a doublet will create a flow field of a circular cylinder in uniform flow.

A dipole is a mathematical pressure source that creates a pressure field resembling roughly the figure 8 rotated in the horizontal plane.  A laterally oscillating rigid sphere would create an acoustic pressure field having a dipole pattern.

Any elementary fluid mechanic book should give you the doublet equation.  The dipole equation can found in books dealing with wave motion or acoustics.  It is true that the streamlines of a doublet and the pressure field of a dipole resemble each other, but they are different functions with different applications.
Paul