Solve Diving Bell Problem: Find Height of Water Rise in Bell

[d_morales97]

A cylindrical diving bell 3.4 m in diameter
and 4.5 m tall with an open bottom is sub-
merged to a depth of 148 m in the ocean.
The temperature of the air at the surface is
22C, and the air’s temperature 148 m down
is 6.3C.
How high does the sea water rise in the bell
when the bell is submerged? The density of
sea water is 1025 kg/m3 and the acceleration
due to gravity is 9.81 m/s2 .



I've done the work while viewing at another post about this same type of problem, but keep coming up with an incorrect answer and it's frustrating... Wondering if anyone could help?



So to start, you need the height of the bell MINUS the height of the water inside the bell, I beleive? The height of the water inside the bell requires the volume of that space, and this is where I'm having problems. So to find the volume, I'm using the Combined Law P1V1/T1 = P2V2/T2. I just need to know how to start these types of problems and tips on how to work them.. Not looking for answers, I'm looking for procedures. Thanks in advance if anyone can help a struggling guy out!

~ Daniel

 

[SteamKing]

Why don't you start the problem this way: Assume the diving bell is lowered perfectly evenly so that at the surface, the open rim at the bottom makes contact at all points with the surface of the water. This traps a known volume of air having the stated surface conditions. Further, assume that this air trapped at the surface changes volume and temperature to keep the diving bell from flooding as it is lowered to its final depth.