Sea water has a pressure of .44psi per ft. or 4.4psi per 10'. Therefore at a dpth of 300' there would be 132psi correct? At 200' feet down there would be 88psi yes?

Now the question (please don't laugh)

If I had a tube with a metal ball in it, sealed at one end like a test tube, that was 100 feet long and I placed the bottom of it at 300' down, leaving the top (open) at 200' down - Would the pressure on the the ball at the bottom of the tube be the same as if I had just placed the ball in the open on the ocean floor?

There would be the weight of 300' of water pushing down on the ball in the tube, but there would not be the SURROUNDING pressure on it because THAT pressure would be on the tube... maybe

What if the tube was full of water but ran all the way to the surface?

Would ball A (the one in the tube) have less pressure on it than ball B (the one in the open on the seafloor) ?

 

If the tube that is open at 200 feet is then filled with water all the way down to the bottom of the tube then the pressure on the ball in the tube will be the same as the ball on the sea floor outside.
If the tube went all the way to the surface But it was filled up only to the the 200 foot level (from300 feet at the bottom) then the pressure on the ball at the bottom of the tube would be 100 feet of water + 200 feet of air. the second term is negligible.

 

We're missing part of the design here

If the tube was open to pressure of 200' then it would fill with water and the ball at the bottom would see 100' of head at first and would increase as the tube filled, ending at 300' of head.

If the tube had a flexible barrier at the top, then depending on the characteristics ofthe barrier, the 200' water column would push the barrier down until the combination of internal air pressure plus the tension of the barrier (if there is any) balances the weight of water above (now greater than 200' since the barrier that began at 200' has now descended, compressing the air as it goes). The pressure would be due to the original 100' head plus the weight of water that fill the tube above the barrier minus the tension of the barrier itself. The limiting boundary condition for a very light weight stiff barrier that is free to move down the tube but separate the internal air from the external water would be where the air compresses to the point that it balances the weight of water above it. The ball would now have its maximum force, but would still be less than the ball outside the tube sincethe head would be 100' plus something less than 200'.

 

The pressure seen by the ball would be the same in both examples as the head of water above the ball is the same in both cases.

 

Answer to question-1: I suppose you have fixed a piston type of thing on the top of the tube. In such case, the air inside the tube will be compressing until the pressure balances the weight of the water column over the piston. In this circumstance, the pressure on the ball will be equal to Water Column + Weight of Compressed Air –Pressure due to Buoyant Force.

Answer to question-2: Pressure of 100 feet of water will act on the ball.

Answer to question-3: Same