Effect of Froude number on the motion of a spherical particle launched vertically upward in water

A spherical particle with a diameter of 25.4 mm and density of 2640 kg/m3 was launched vertically upward toward the free surface of calm water. The Froude number of the particle passing through the water surface was varied. The dependence of the Froude number on the particle motion and water surface behavior was investigated from the instant the particle crossed the water surface until it attained its maximum displacement position. Based on the classical energy conservation law, the energy lost in the interaction between the particle and water surface (i.e., interface containing energy, Eo) was estimated. Eo was found to increase with the increase in the Froude number when the particle crossed the water surface. In addition, owing to Eo at the maximum displacement position of the spherical particle, the height and width of the interfacial water sheet changed by the same ratio at the point of intersection of the upper side of the particle with the calm water surface. This result was in agreement with that obtained by changing the submergence depth, as reported by Takamure and Uchiyama (2020). This finding suggests that the characteristics of the interfacial water sheet are the dominant parameters influencing the interface containing energy. The presented findings can help determine the parameters to model the water exit problem. •A spherical particle is launched vertically upward in water.•Investigation of the Froude number effect on the water surface behavior.•Interfacial water sheets have a self-similar property.•The thickness and width of the interfacial water sheet are the dominant parameters.•The present findings can help determine the parameters to model the water exit problem.