Effect of density of a sphere launched vertically in water on the water-surface behavior and sphere motion in air

Submerged solid spheres with specific gravities relative to water ranging from 1.36 to 7.93 were launched vertically upward toward the free surface of calm water. The motion of each sphere and the behavior of the water surface were investigated from the time the sphere passed through the calm water surface until it attained its maximum displacement position. The energy lost in the interaction between the sphere and the water surface (i.e., the interfacial containing energy Eo) was estimated from energy conservation. A larger Eo at the maximum displacement position of the sphere led to a larger increase in the height and width of the interfacial water sheet where the upper side of the sphere intersected with the free surface of calm water. This result corresponded to the result obtained by changing the submergence depth, as reported by Takamure and Uchiyama [“Air–water interface dynamics and energy transition in air of a sphere passed vertically upward through the interface,” Exp. Therm. Fluid Sci. 118, 110167 (2020)]. This aspect suggests that the characteristics of the interfacial water sheet are the dominant parameters influencing Eo. The presented findings can facilitate the determination of parameters to model the water exit problem.