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Steady Stokes flow past dumbbell shaped axially symmetric body of revolution-an analytic approach. (English) Zbl 1299.76044
Summary: The problem of steady Stokes flow past dumbbell-shaped axially symmetric isolated body of revolution about its axis of symmetry is considered by utilizing a method [S. Datta and K. Srivastava, Proc. Indian Acad. Sci., Math. Sci. 109, No. 4, 441–452 (1999; Zbl 0962.76024)] based on body geometry under the restrictions of continuously turning tangent on the boundary. The relationship between drag and moment is established in transverse flow situation. The closed form expression of Stokes drag is then calculated for dumbbell-shaped body in terms of geometric parameters $$b$$, $$c$$, $$d$$ and $$a$$ with the aid of this linear relation and the formula of torque obtained by A. T. Chwang and T. Y. T. Wu [J. Fluid Mech. 63, 607–622 (1974; Zbl 0293.76014)] with the use of singularity distribution along axis of symmetry. Drag coefficient and moment coefficient are defined in various forms in terms of dumbbell parameters. Their numerical values are calculated and depicted in respective graphs and compared with some known values.
##### MSC:
 76D05 Navier-Stokes equations for incompressible viscous fluids
drag; torque
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