I need help determining the forces, and the direction of them in this fluid statics problem.
A hollow cylinder with closed ends is $300\,\rm mm$ in diameter and $450\,\rm mm$ tall. It has a mass of $27\,\rm kg$ and a tiny hole at the bottom. It is lowered slowly into water and then released. Calculate:
a. The pressure of the air inside the cylinder.
b. The height to which the water will rise.
c. The depth to which the cylinder will sink.
I was already given the answers to these problems for clarification, but I think I'm going to start with the free body diagram (FBD) to part c.
Now I know there is a weight from the cylinder going down and a buoyant force going up because of the water and the submerged volume of the cylinder. Now, does the air trapped in the cylinder also create a buoyant force, or some kind of force also pushing up? And how would I calculate this force if there is one? After that, I'm sure I can get the rest of the calculations.