Axisymmetric flow of a viscous fluid near the vertex of a body

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Abstract
Axially symmetric motion of a viscous fluid in a cone is considered on the basis of the Stokes assumption. Near the apex of the cone the solution obtained reveals features quite similar to those of that near a sharp corner in two dimensions, which has been discussed already. An infinite sequence of eddies is induced near the apex for values less than about 80·9° of the semi-angle of the cone, which is measured from the symmetry axis lying in the fluid. The solution found by Pell & Payne for a spindle in a uniform stream offers a good illustration of the general discussion. Special attention is paid to the angle 120° for the spindle as well as the cone. The limiting case of zero angle of the cone corresponds to the flow occurring in a circular cylinder.

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