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An inflated ballon will rise yo a definite height once it starts rise where as a submarine will always sink to bootom of ocean once it starts to sink, if no changes are made. How then can a submarine stay at a definite level under water.

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    $\begingroup$ I question the assertion of the first sentence... $\endgroup$ – DJohnM Sep 9 '19 at 3:31
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There's a few effects in play. What you've noticed is that floating level is an unstable equilibrium. Too light, and it rises uncontrollably. Too heavy, it sinks to the bottom.

  • As a general rule, submarines stay very close to neutrally buoyant. They tend not to go to the extremes. This is still unstable, as you noticed, but it means the instability is smaller
  • While moving, the submarine can stabilize with hydrodynamics. With the adjustable fins on the submarine, they can push water up or down as they move. We have control systems (or people) that oppose any such instability as it happens.
  • While not moving, they can pump water in and out of their ballast tanks. Again, the goal is to have a control loop which stabilizes the movement. If they're rising, they can pump more water in.
  • There are some interesting depths at which the thermoclines result in more dense water layered on top of less dense water. When this happens, this changes the buoyancy effects in a stabilizing fashion. This is a special case, of course, but its nice because it doesn't require the submariners to maintain a control system loop.
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submarines sink without limit for the following reason: As a submarine goes down, the pressure on its hull causes it to contract slightly. This decreases the displacement of its hull and thereby reduces its buoyancy, which makes it sink faster, which increases the pressure on the hull more, which makes it contract more, lose more buoyancy, and so on... until it reaches it crush depth.

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I think the main difference between a balloon's and a submarine's behavior is that air is quite compressible, while water is highly incompressible. The density of air therefore changes considerably with altitude, while the density of water is almost independent of depth. An object experiences neutral buoyancy when surrounded by a fluid of the same density. So there's a much wider range of object densities (basically any density less than that of the atmosphere at ground level) for which the object will equilibrate at a finite altitude, but there's only a tiny range of densities (just a hair above the standard density of water) for which an object will equilibrate at finite depth underwater.

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