# Water Rising in a Diving Bell.

• Fizzicist
In summary, during a test dive in 1939, the submarine Squalus sank at a depth of 73.0 m in seawater with a temperature difference of 20.0 C between the surface and bottom. Using a diving bell, the 33 trapped crewmen were rescued from the submarine. The diving bell, shaped like a circular cylinder, was 2.30 m high and open at the bottom. To determine the height of water within the diving bell, the pressure at the bottom of the sea and the ideal gas law were used. Ultimately, the problem was successfully solved.
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?

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

not really, but I solved it. :)

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.

## 1. Can water really rise in a diving bell?

Yes, water can indeed rise in a diving bell. This is due to the principles of buoyancy and pressure, which cause the water level inside the bell to equalize with the surrounding water.

## 2. Why does the water rise in a diving bell?

The water rises in a diving bell because of the weight of the bell itself. As the bell is lowered into the water, the displaced water creates a downward force, causing the water level to rise inside the bell.

## 3. How does this phenomenon affect divers inside the bell?

The rising water inside the diving bell can be dangerous for divers, as it can cause them to lose buoyancy and potentially get trapped or injured. Divers must carefully monitor the water level and manage their air supply as the water rises.

## 4. Can the water level in a diving bell be controlled?

Yes, the water level in a diving bell can be controlled by adjusting the amount of air inside the bell. By adding or releasing air, divers can control the buoyancy of the bell and maintain a safe water level.

## 5. Are there any safety precautions that should be taken when using a diving bell?

Yes, there are several safety precautions that should be taken when using a diving bell. These include proper training for divers, regular maintenance and inspection of the bell, and following proper procedures for monitoring and controlling the water level.

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