What Happens to a Punctured Pressurized Canister as It Sinks in the Ocean?

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When a punctured pressurized canister is dropped into the ocean, the air inside, which is at twice the atmospheric pressure, will initially bubble out as it seeks to equalize with the external pressure. As the canister sinks deeper, the increasing water pressure will eventually exceed the internal air pressure, leading to water leaking into the canister. This process will continue until the pressures equalize, causing the canister to fill with water. The behavior of the canister changes as it descends due to the increasing external pressure. Ultimately, the canister will fill with water and sink fully.
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Homework Statement


A pressurized canister of air is punctured and then dropped into the ocean where it quickly sinks. The pressure of the air inside the canister is two times greater than atmospheric pressure. Describe what will happen to the canister as it sinks. In particular, will the air bubble out of the canister or will water leak into the canister? Or will this behavior change as the canister sinks?

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The Attempt at a Solution


I have a hard time visualizing these types of questions. But here's what I was thinking - that the air inside the canister would bubble out until the pressure in the inside was equalized with the outside; then water would start leaking into the canister, causing it to begin sinking? Am I on the right path?
 
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The question says the canister starts sinking immediately. You are along the right lines however. Just take the initial sinking into account.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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