|MadSci Network: Physics|
To come up with an analytical answer to the problem is really difficult. The mechanics of a splash are best understood by experimentation, or numerical simulation (by a computer model), as the paths and forces operating on gazzillions of particles have to be traced for a good understanding of what's going on. This is all beyond capabilities... However, we can still answer the question: "would the splash be unaffected by the force of gravity" by looking at how the various relevant parameters of a splash are affected by gravity. The change in density for water under gravity at 1G or 2G is probably not significant. Water at 0G (in a free fall) does not appear signifficantly less dense than water sitting still. Neither does water sitting in a container being accelerated (shaking a plastic bottle does not show evidence of a significant change in water density because of the accelerations, i.e., it does not dent inwards or explode) Water is a very hard fluid to compress so as long as the gravitational constant is kept within reasonable limits (I would imagine within one order of magnitude from 1G), the assumption is valid. We could hope for the height of the splash to be unchanged by gravity, if the mechanism for a splash was determined by two relevant parameters that were both affected by the force of gravity in exactly opposing ways. Let's look at the various relevant parameters in a splash: Speed of impact Rate of energy disipation in the water Surface tension When the surface of water splashes due to an object suddenly penetrating it, the splash is a result of a ripple that could not propagate away from the penetration point fast enough. A secondary splash happens when the water surrounding the hole left by the impact, rushes to fill the hole. The acceleration of the ball is affected positively with increased G, and the speed of waves in water (its ability to disipate the impact) is also increased with increased G. So far so good... However, surface tension, another relevant parameter of a water splash, is not affected by the force of gravity. In fact, water in microgravity tries to maintain a spherical shape (as a unit) by its own surface tension, until disturbed. Simply knowing that there is one relevant parameter of the splash that is not affected by gravity, is enough to answer: the height of the splash will have to be different at different values of G. Hope this answer is satisfactory, Your mad scientist, -Aurelio R. Ramos
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