Viscous flow in pipes whose cross-sections are doubly connected regions

Abstract

Slow and steady viscous fluid flow in a pipe whose cross-section is bounded by an ellipse and a circle is considered. The method used is in deriving general solutions independently on the two boundaries using one or two conformal mapping functions and an attempt is made to make the complex potentials continuous in the doubly connected region. Numerical results are found and compared with those for the case of concentric circles and the case of concentric ellipses.