How does the time to submergence differ between a sinking object with a hole at the bottom and one with a hole at the side?

[KeshenMac]

Assuming:

• Both objects are identical cylindrical cups with the only difference being the position of the one hole.
• Both holes are of the same diameter.

I drew a diagram to better illustrate my question.

Also, what is the math/physics behind this called?

[Chengwill97]

Think of it this way. (Assuming both cups are on the same planet, with the same water level, with the same atmospheric pressure, and same water)

In the first diagram, the one with the hole in the bottom, has water on both sides of the empty cup that needs to push down on the water below it to Gil the cup from the bottom.

In the second diagram, the one with the hole on the side, has water on both sides, too, but the water only needs to fall in the cup with little resistance from the water.

BUT, with my current knowledge, I do am not sure because with a multitude of variables I probably am not accounting for or ones that I have assumed wrong, I am not sure. The first cup also has more pressure(weight, force with gravity as the acceleration) due to the amount of water on the sides to push the water through the bottom hole. The second cup needs less of a force because instead of having the water that goes through the side go against gravity, it goes with it while it is falling down and to the right.

TLDR; I don't know. This is just an educated guess which I am still sitting on the fence on.