When gunfire hits the surface of a pond, the water seems to always splash directly upwards, in 90° to the surface of the water, no matter at which angle the gun is fired. The angle is usually very small, but most of the water still seems to splash upwards, instead of away from the shooter at nearly the same angle the shot was fired at. I wonder why it happens like this.
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$\begingroup$ I think this is like when a comet hits earth... doesn't matter what the angle of imact is - always get a circular crater as the kinetic energy gets dumped into the ground and causes an explosion - expect the same with bullet hitting water. - heats water put energy in and the result is a whole volume gets heated and 'explodes' upwards. $\endgroup$– tomCommented Dec 6, 2014 at 18:57
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1$\begingroup$ The initial "ripple" will be forward-scattered, but the main splash is a result of water rushing in from all directions to fill the subsurface void. The net momentum is just about purely vertical. $\endgroup$– Carl WitthoftCommented Dec 6, 2014 at 19:46
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3 Answers
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Water does not compress easily in liquid (or solid) form. Keep that in mind.
When the bullet hits, it transfers momentum to the water molecules. Momentum is a vector, and you can break it into vertical and horizontal components, and consider them separately.
First, consider the vertical momentum. That's the component that is parallel to the force of gravity. The vertical momentum is transferred to ("pushes") the water molecules out of the way. So there is a void, and then the water rushes back in because of the water pressure. The upward splash occurs because of the net upward momentum of the water as it fills the void. Gravity slows down the splashing water.
Second, consider the horizontal momentum. Since gravity does not act horizontally, the only horizontal force on the water molecules is their resistance to compression and the force of the bullet (horizontally). The horizontal momentum of the bullet is transferred to water molecules. Since the water molecules resist compression strongly, the horizontal momentum is spread throughout the water on the pond surface. The mass of water is huge compared to the mass of the bullet, so the resulting horizontal momentum for the individual water molecules is tiny. They just don't move horizontally very much.
So the end result is that the splashing water has very little motion in the horizontal direction, and it basically goes straight up (and then down).
(I considered the pond as having no external horizontal forces, but the banks would exert a horizontal force. The effect would be tiny, however, and you can treat the water molecules are "free bodies" in the horizontal direction.
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This can be answered using Pascal's law which states that in a fluid, pressure is equal in all directions. When the bullet hits the water surface, because of friction and momentum transfer, a depression is created. Now for the sake of convenience, consider a small volume of water at the bottom of the depression. There is equal pressure in all directions. But horizontally, the pressure force is balanced by adjoining water. Vertically in the downward direction, the pressure force is balanced in a similar way. But in the upward direction, there is nothing to balance the pressure force. Due to this force exerted on the water, it rises upwards. A simpler way of saying the same thing is using the Archimede's principle. The depression created in water will experience an upward force equal to the weight of volume of water displaced. When the water riing upward comes to the height of the surface, it doesn't stop there due to inertia and goes yet higher seen as the splash. Hence the splash is observed and only in the upward direction.
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Hardly any of the bullet's energy is transferred into forward momentum of the liquid; at high velocities almost all of its energy is lost to cavitation. When a bullet enters a liquid it creates a cavity. The splash that you observe is the result of the initial displacement of water near the surface caused by the creation of that cavity. This is very easy to see in high-speed videos.
I.e., you could say that the water doesn't really "know" which way the bullet is traveling. An instantaneous view of cavitation is an explosion from the point of the bullet: the water's momentum vectors radiate out equally in every direction. The net result at the surface is a virtually vertical splash, just like you would get detonating an explosive along the path of the bullet.
Interestingly, the collapse of the cavity results in momentum vectors radiating roughly equally from the center of collapse. If that center is near the surface than you will observe more water ejected by the vectors that cross the surface of the water. If the cavity's center is deeper then a cycle of cavities can be observed as the cavitation energy dissipates.
