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In this paper non-cylindrical flow variation in swan neck ducts with prescribed flow characteristics will be investigated. The flow will be characterized by the total head, H(ψ) a function of only the stream function, ψ (x, r) and a function of the circumferential velocity  u where the subscript  represents the circumferential component of the velocity vector u in cylindrical coordinates (x, r, ). The cylindrical flow variation is shown to be dependent on the zeros of the Bessel Cross product of order one. It is further shown for a class of swirling flows denoted in this paper as the Stokes-Poisson class that it is theoretically possible for cylindrical flow to be present for any inlet radius r1, with the different cylindrical flows given either by circular trigonometric functions or hyperbolic functions and being dependent only on the sign of the separation constant that arises naturally in this analysis

Investigation of Non-Cylindrical Flow in the Region Bounded by Two Coaxial Cylinders of Varying Radii