Pressure-flow relationships are derived for the steady flow through an eccentric double circular tube whose cross section takes the form of an annulus bounded by two circles which are in general not concentric. The velocity distribution can be obtained by solving a two-dimensional Poisson equation with the use of conformal mapping. In a case when the two circles touch, a mapping function of different type is required to solve the equation. The relationships thus derived are reduced to the well-known formula for the limit of concentric circles. It is found that when the region between touching circles becomes sufficiently thin, the tube conductance behaves like the cube of the difference of radii of the two circles.
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Yaso'o Matunobu (1988) studied this question.