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On the force and moment on a body in an incompressible fluid, with application to rigid bodies and bubbles at high and low Reynolds numbers. (English) Zbl 0836.76028
The force and moment exerted on a rigid body in an unsteady uniform flow of an incompressible viscous or inviscid fluid are analysed. Integral formulae are derived which express the force and moment in terms of the velocity and vorticity of the fluid and the velocity of the body. The results obtained earlier by the author are now extended to take into account the influence of added mass, normal stresses induced by free vorticity, and viscous skin friction. As illustrative applications, the induced drag of a vortex on airfoil, the force on a cylinder moving in a slowly varying rotational mean flow, and the viscous drag on solid spheres and bubbles are determined. The author claims that the drag on a bubble in high Reynolds number motion can be predicted directly by the developed theory, in contrasts to usual approach in which the drag can by determined by equating the viscous dissipation to the work done by the drag force.

MSC:
76D99 Incompressible viscous fluids
76B10 Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and hydrofoil theory, sloshing
76B99 Incompressible inviscid fluids
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