Solid–fluid interaction: a continuum mechanics assessment

The dynamical interaction between solids and fluids is a subject of paramount importance in Mechanics with a wide range of applications to engineering problems. It is, however, still a challenging topic of theoretical investigation. With a view to case studies of dynamical behaviour of rockets, turbines, jets and sprinklers, we develop here a treatment that, in the full respect of the principle of conservation of mass and under suitable simplifying assumptions, leads to evaluate the thrusting force exerted by the fluid on the solid. The goal is reached by applying the Euler–d’Alembert law of continuum dynamics to the trajectory of a skeleton whose motion is an extension of the one of the solid. It is shown that the formulation in the context of continuum mechanics is essential to get a full understanding of the dynamical problem and for grasping the meaning and range of validity of the results. This is a distinctive feature from treatments in literature where particles or control windows with variable mass are considered. The statement of the von Buquoy–Meshchersky law as a governing principle in the dynamics of particles with variable mass, in substitution of Newton’s second law, is critically addressed. Under the assumption of low mass and high momentum time rate, the formula for the thrusting force is validated as a simplified expression fulfilling Galilei’s principle of relativity.