AXISYMMETRIC VISCOUS FLUID MOTIONS AROUND CONICAL SURFACES
NAVAL WEAPONS LAB DAHLGREN VA
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The introduction of complex Navier-Stokes equations shows that steady axisymmetric motions of viscous incompressible fluids around conical surfaces can be expressed in terms of the corresponding general solution of the Stokes equations of slow motions. The latter integration is accomplished with the aid of slow-motion eigenfunctions with integral eigenvalues for infinite plates and semi-infinite needles and with generally complex eigenvalues for cones and conical corners. The eigenvalues and eigenmotions obtained resemble the corresponding eigenvalues and eigenmotions of the analogous flows past dihedral angles. In particular, the existence of critical and branching eigenvalues reveals that laminar flows past conical surfaces depend on the cone angle in a nonanalytic manner. The investigations include a note on diffusor and jet flows.
- Fluid Mechanics