AXISYMMETRIC FLOW OF AN IDEAL INCOMPRESSIBLE FLUID ABOUT A SOLID TORUS
- 1 August 1952
- report
- Published by Defense Technical Information Center (DTIC)
Abstract
An exact solution in series form is presented for irrotational, axisymmetric flow of an ideal, incompressible fluid past a solid torus of circular cross section. At infinity the fluid is assumed to be in a state of uniform motion parallel to the axis of the torus. The solution, based on the use of toroidal coordinates, is given in terms of Legendre functions of fractional order as well as complete and incomplete elliptic integrals of the first and second kind. The individual component solutions are interpreted physically through their relation to the basic ring singularities represented by source and vortex rings. The problem is first approached via Stokes' stream function and is subsequently re-solved independently in terms of the velocity potential. The convergence of the pertinent series developments was unusually favorable, and a complete stream line pattern, corresponding to an illustrative numerical example, is included.Keywords
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