CP 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 was 27.0o C at the surface and 7.0o C at the bottom. The density of seawater is 1030 kg/m3. (a) 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: Ignore the relatively small variation in water pressure between the bottom of the bell and the surface of the water within the bell.) (b) At what gauge pressure must compressed air have been supplied to the bell while on the bottom to expel all the water from it?
Solution to 58P Step 1 0 Temperature at the surface T =27 C=300.11 0 Temperature at the bottom T =7 V =280.12 Depth, y =73m Height of diving bell h =2.3m 1 3 Density at the bottom =1030kg/m Pressure at the surface=P =1.013x10 Pa 5 atm Step 2 (a)Height to which water raises=h 2 V=Ah………………………………………………………………………(1) Thus volume and height are proportional to each other V1h 1 V2h 2 From ideal gas equation, V /V =P T /P T 1 2 2 1 1 2 P =P +gy 2 atm Therefore, h2h1P atmT 2P 2 )1 5 5 3 h22.3(1.013x10 PaX280.15K)/(1.013x10 Pa+1030kg/m X9.8X73)300.15K h20.26m
