Calculation model for water mass entrained by the water exit of a particle using two projected images captured from orthogonal directions

Water exit is an extremely important phenomenon because it contributes to the development of physics and biology and its application in engineering. In particular, it is necessary to consider the spatiotemporal change in the water mass entrained around an object to correctly understand the scenario of water mass. In this study, a solid particle is launched vertically upward in water toward the surface. The volume of the water mass is estimated using images captured from two orthogonal directions while considering the spatiotemporal development of the water mass. In this study, two water mass estimation methods (Models 1 and 2) are constructed and applied to experimental results of the water exit reported in a previous study by the authors Takamure and Uchiyama (2020a). Model 1 considers the spatiotemporal development of the water mass and estimates the vertical motion of the particle under the influence of water mass with high accuracy when the water mass barely develops around the particle (i.e., submergence depth is small). However, when a large water mass entrains around the particle with an increase in the submergence depth, the estimation accuracy of the volume of the water mass decreases owing to the multilayer structure of the water mass. Model 2 improves the estimation accuracy of the volume of the water mass when the particle covers a large amount of water mass by considering the existence of the multilayer structure of the water mass. For the largest submergence depth in the experiment in this study on the water exit of the particle, the estimation accuracy of the volume of the water mass for Model 1 was approximately 50%, while that for Model 2 was over 80%. Further, the motion of the particle can be estimated with high accuracy even if the water mass is relatively complex and has a multilayer structure by incorporating the effects of the multilayer structure of the water mass into Model 1. This method enables us to estimate the water mass quantity easily and accurately by photographing an object from two orthogonal directions using two synchronized high-speed cameras. This water mass estimation technique is useful for understanding physical phenomena and for engineering applications. •Water mass estimation methods are applied to the water exit of the spherical particle.•The water mass volume is captured from two orthogonal directions.•Estimation accuracy decreases without consideration of multilayer structure.•Estimation accuracy is over 80% wi