On the viscous fluid flow around a semi-infinite needle situated on the axis of a conic diffuser

The viscous incompressible fluid steady flow around a semi-infinite needle in the conic diffuser is studied by methods of Power Geometry. It is considered the axially symmetric flow. The boundary conditions on the needle surface carry over to axis of the diffuser. Then tangential velocity component is obtained different from zero and the longitudinal velocity component profile has the deleted point. The obtained results concern to asymptotics of the solution at infinity for small Reynolds numbers.