Abstract

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, <span id="cke_bm_84S" style="display: none"> </span><em>H</em><span id="cke_bm_84E" style="display: none"> </span>(<em>ψ</em>) a function of only the stream function, <span id="cke_bm_98S" style="display: none"> </span><span id="cke_bm_96S" style="display: none"> </span><em>ψ</em><span id="cke_bm_98E" style="display: none"> </span><span id="cke_bm_96E" style="display: none"> </span> (<span id="cke_bm_99S" style="display: none"> </span><em>x</em><span id="cke_bm_99E" style="display: none"> </span>, <em>r</em>) a<span id="cke_bm_100E" style="display: none"> </span>nd a function of the circumferential <span id="cke_bm_97E" style="display: none"> </span>velocity  u where the subscript  represents the circumferential component of the veloc<span id="cke_bm_85E" style="display: none"> </span>ity vector u in cylindrical coordinates (<span id="cke_bm_90S" style="display: none"> </span><em>x</em><span id="cke_bm_90E" style="display: none"> </span>, <em>r</em>, ). The cylindrical flow variation is sho<span id="cke_bm_91E" style="display: none"> </span>wn 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.