Submarines and stuff

In our captivating introduction to pressure in fluids and buoyancy on the Friday before break, we discussed the forces responsible for objects floating or sinking. The buoyancy force, notated as Fb = ρVg (ρ = fluid density, V = volume of fluid displaced, g = acceleration due to gravity), is the force pushing an object up within a liquid, acting against the weight of that object pushing it down. If buoyancy force is greater than weight, then an object will float to the surface. If smaller, the object will sink. But wait, what if the buoyancy force and the weight of an object are the exact same??? Professor Metzler briefly mentioned this rare occasion in class, which got me thinking… how do submarines work?

Submarines are unique water-crafts capable of submersion and operation underneath the water’s surface. A key function of submarines is maintaining constant depth – often 100-200 meters below the surface – so that detection can be deterred. Naturally, submarines float. How, then, are they able to sink to (and stay at) such depths? The answer: ballast tanks, which are compartments designed to hold water (or air when empty) located around the outside of the ship. By allowing water into these tanks, the total mass of the submarine increases, allowing it to overcome the buoyancy force and sink. When the submarine reaches its cruising depth, the ballast tanks are filled with just enough water to make the density of the submarine equivalent to the density of the water. To return to the surface, compressed air is pumped into the tanks to force the water out.

Wow, very cool! Now, let’s crunch some numbers. The Virginia-class is the latest model of submarine produced by the US. Let’s find its buoyancy force! To begin, we know ρ and g (1000 kg/m3 and 9.8 m/s2, respectively). Then, all we need to find is volume! After conducting some research, I found that each submarine has a displacement of about 10,200 tons, which confused me at first because tons are a measurement of weight and displacement should be a volume. Then, I found out a ton of water is actually a volume measurement equivalent to 0.98 m3. Therefore, each submarine (when submerged) can be expected to displace 9,996 m3 of water. Boom, there is our V. So, if Fb = ρVg, then Fb = (1000 kg/m3)(9,996 m3)(9.8 m/s2) = 9.8 x 10^7 N! Very nice! 

I was planning on doing more calculations (such as finding what mass of water is required to be let into the ballast tanks at a given depth) but that seemed too hard. Anywho, Happy Thanksgiving!

Sources:

https://precollege.oregonstate.edu/sites/precollege.oregonstate.edu/files/cartesian_diver_lacuknos_10-15-20_-dc.pdf

https://science.howstuffworks.com/transport/engines-equipment/submarine1.htm

https://en.wikipedia.org/wiki/Virginia-class_submarine