How High Did Water Rise in the Squalus Diving Bell?

[Jason Onwenu]

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/m³. 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 * g * height
PV = nRT
P1V1/T1 = P2V2/T2
V = pi * radius^2 * height

The Attempt at a Solution

P(bottom) = 101325 + (1030*9.8*73) = 838137 Pa
V2 = ? (The radius wasn't given...)
T2 = 280.15 K

P(top) = 101325
V1 = ? (The radius wasn't given...)
T1 = 303.15K

At this point, I couldn't really proceed with my calculations because a radius wasn't given. I'm wondering if I could solve for the radius with the information given or if the radius is even needed at all.

 

[SteamKing]

You should ask yourself this question: Why does the water stop rising inside the diving bell when it is lowered onto the submarine?

Once you answer this question, think about whether you need to know the radius of the cylinder.

 

[Jason Onwenu]

You should ask yourself this question: Why does the water stop rising inside the diving bell when it is lowered onto the submarine?

Once you answer this question, think about whether you need to know the radius of the cylinder.

I'm guessing it has something to do with (specific) gravity? Since there is a difference in temperature?

 

[SteamKing]

I'm thinking it has something to do with (specific) gravity?

Why would specific gravity stop water from rising inside the diving bell?

Isn't the specific gravity of the water inside the diving bell the same as the specific gravity of the water outside?

Hint: Think about what is changing inside the bell as the water rises.

 

[Jason Onwenu]

Why would specific gravity stop water from rising inside the diving bell?

Isn't the specific gravity of the water inside the diving bell the same as the specific gravity of the water outside?

Hint: Think about what is changing inside the bell as the water rises.

Pressure changes...

 

[Jason Onwenu]

Why would specific gravity stop water from rising inside the diving bell?

Isn't the specific gravity of the water inside the diving bell the same as the specific gravity of the water outside?

Hint: Think about what is changing inside the bell as the water rises.

Is specific gravity a constant value for a specific substance? Or does it vary with temperature?

 

[theodoros.mihos]

Do calculations until the end and then ask if you need the radius.