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I am investigating the water-entry of a steel ball-bearing at different speeds. Ideally, I would like to model (to an extent) the forces experienced by the ball bearing as it transitions from air to water. For a free-falling ball-bearing, I would expect a sudden drop in its velocity as it transitions between fluids, before increasing (or decreasing) to reach its terminal velocity in the water.

In addition to surface tension, negligible or not, what other forces can I expect to be experienced by a sphere falling from air into water? I am aware of buoyancy and viscous drag (stokes' law and the drag equation), and air cavities which form behind the object at the boundary between fluids (which as far as I know are unpredictable mathematically). From my readings of other scientific research papers, I have become aware of specific gravity and the increase of the ball bearing's wetted area as it penetrates further below the surface of the water. What other considerations are there at the zone of transition between air and water?

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  • $\begingroup$ If your impact speeds are high enough, you might have to consider plastic deformation of your ball-bearing. I know this was a considerable factor in my childhood backyard gun experiments. $\endgroup$ – James Oct 9 '18 at 13:27
  • $\begingroup$ I think there is considerable literature on "water entry of projectiles". Don't they already tell you what the relevant factors are? $\endgroup$ – Deep Oct 10 '18 at 3:16
  • $\begingroup$ I have read a number of papers, but they all vary. I need clarification about the zone of transition. Wetted area and specific gravity are factors that I have read about, which some papers take into account at the fluid boundary, or when the sphere is completely submerged, or both. $\endgroup$ – Angellos Korsanos Oct 10 '18 at 5:34

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