Sinking a cylinder with varying hole sizes

[haruspex]

In #75, how would you integrate the equation you substitute in for u when you are integrating with respect to y and there aren't any y terms?

I apologise if I've totally misunderstood.

Did you mean post #73?
You don't need y terms in order to integrate wrt y; you just need that the only variable present is y. In this case, the integrand is constant.

 

[cwinqi]

Did you mean post #73?
You don't need y terms in order to integrate wrt y; you just need that the only variable present is y. In this case, the integrand is constant.

I missed that part, thank you. I need to get my eyes checked. All makes sense now.

 

[Finder]

Feel free to repeat the analysis taking drag into account. You may find it cannot be solved analytically, though. As I recall, it can be modeled as a reduced hole size, but that could be wrong.

h will only diminish when the water outside reaches the top of the cylinder and flows in. Total submersion will follow swiftly, so the time taken for it to reduce to zero can be ignored.
There are three phases:
1. On placing the cylinder on the surface of the water and releasing, it quickly sinks to the point where its weight is balanced by the buoyancy.
2. It sinks slowly, limited by the rate at which water can flow through the hole. In this phase, h is nearly constant.
3. The water outside reaches the top and flows in, quickly reducing the airspace inside to zero.
For the purposes of the time to sink, only the second phase is interesting. The others are too brief.

Aside these three phases, is there a chance that in the process of sinking, the cylinder will attain equilibrium and therefore would not sink further to a complete submersion?

 

[haruspex]

Aside these three phases, is there a chance that in the process of sinking, the cylinder will attain equilibrium and therefore would not sink further to a complete submersion?

Water will continue to flow into the cylinder through the hole until either the top of the cylinder falls below the water line (entering stage 3) or the water inside reaches the same level as the water outside. Either way, if the material of the cylinder is denser than water the cylinder will sink.

 

[Finder]

Water will continue to flow into the cylinder through the hole until either the top of the cylinder falls below the water line (entering stage 3) or the water inside reaches the same level as the water outside. Either way, if the material of the cylinder is denser than water the cylinder will sink.

Alright, great, thank you.

 

[Finder]

Alright, great, thank you.

Water will continue to flow into the cylinder through the hole until either the top of the cylinder falls below the water line (entering stage 3) or the water inside reaches the same level as the water outside. Either way, if the material of the cylinder is denser than water the cylinder will sink.

In this particular case, the material of the cylinder is not denser than water but a certain mass (load) is to be added to the cylinder to cause it to sink just a little below the outside water level. i.e to the point where the total weight (added mass+cylinder itself) balances the Buoyant force and from there it starts sinking slowly. will it continue to sink till the water inside the cylinder reaches the same level as the water outside?

NB: the cylinder's height is more than the entire column of water it is being submerged into so only the second situation you stated can occur. (the cylinder cannot fall below the outside water line)

 

[kuruman]

The original thread is more than 3 years old and the problem as @Finder defined it is not the original in which the cylinder is fully submerged. The current question should be in a separate thread. I have reported it.

 

[Finder]

The original thread is more than 3 years old and the problem as @Finder defined it is not the original in which the cylinder is fully submerged. The current question should be in a separate thread. I have reported it.

Well,yes, i will start a separate thread. I was trying to know if there can be another phase aside the three phases @haruspex stated for a sinking cylinder. either way, all the derivations for this thread applies to mine. the weight of the cylinder as used for this thread can be translated as the total weight for my question.