Impact of two circular plates one of which is floating on a thin layer of liquid

The paper deals with the axisymmetric unsteady problem of the collision of two circular plates, one of which is located initially on the surface of a shallow liquid layer and another is falling down on it. The presence of air between the colliding plates is taken into account. Both the air and the liquid are assumed ideal and incompressible and their flows potential. The flows in the liquid layer and between the plates are assumed one-dimensional with corrections for three-dimensional effects close to the plate edges. The present study is focused on the stage of strong interaction between the plates, during which the floating plate is accelerated and the hydrodynamic pressure in the liquid layer takes its maximum value. A simplified model of this interaction is suggested. Velocities of the plates and the hydrodynamic pressure on the bottom of the liquid layer are analytically estimated and compared with experimental results. The model provides the maximum of the hydrodynamic pressure, which can be used at the design stage. It is shown that the air flow between the moving plates is of major importance to explain the low amplitude of the measured hydrodynamic pressures.