How High Does Water Rise in a Diving Bell?

[Fizzicist]

Homework Statement

During a test dive in 1939, prior to being accepted by the U.S. Navy, the submarine Squalus sank at a point where the depth of water was 73.0 m. The temperature at the surface was 27.0 C and at the bottom it was 7.0 C. The density of seawater is 1030 kg./m^3. A diving bell was used to rescue 33 trapped crewmen from the Squalus. The diving bell was in the form of a circular cylinder 2.30 m high, open at the bottom and closed at the top. When the diving bell was lowered to the bottom of the sea, to what height did water rise within the diving bell? (Hint: You may ignore the relatively small variation in water pressure between the bottom of the bell and the surface of the water within the bell.)

Homework Equations

p = $$\rho$$gh + pa? I really don't know...

The Attempt at a Solution

I don't even know how to approach this. I suppose I'd want to find the pressure at the bottom of the sea. This would be the pressure exerted on the gas (the air inside the bell). Then I could use the ideal gas law to solve for the change in volume, which would then give me the change in height? Am I approaching this correctly?

 

[Fizzicist]

nm...I solved it because I am a physics badass...


not really, but I solved it. :)

 

[Moetasim]

I would approach this problem by first understanding the basic principles involved. The diving bell is essentially a gas-filled chamber submerged in water. The pressure exerted on the gas inside the bell is equal to the pressure exerted by the column of water above it, according to Pascal's law. This means that as the diving bell descends to the bottom of the sea, the pressure on the gas inside the bell increases.

To solve for the height of water rising inside the bell, we can use the formula for hydrostatic pressure: P = ρgh, where P is pressure, ρ is density, g is the acceleration due to gravity, and h is the height of the water column. In this case, we can assume that the pressure at the surface of the water within the bell is equal to the atmospheric pressure, so we can ignore the term for atmospheric pressure in the equation.

Using the given values, we can calculate the pressure at the bottom of the sea: P = (1030 kg/m^3)(9.8 m/s^2)(73.0 m) = 758,420 Pa. This is the pressure exerted on the gas inside the diving bell at the bottom of the sea.

To find the height of water rising inside the bell, we can rearrange the equation to solve for h: h = P/(ρg). Substituting in the values, we get h = (758,420 Pa)/[(1030 kg/m^3)(9.8 m/s^2)] = 0.073 m. This means that the water would rise to a height of 0.073 m inside the diving bell when it is lowered to the bottom of the sea.

In conclusion, the height of water rising inside the diving bell is 0.073 m. This information can be used to ensure the safety of the trapped crewmen during the rescue operation.