Submarines rely on three fundamental gas laws to dive, surface, breathe, and keep their crews alive. Boyle’s Law governs how ballast tanks control depth, Dalton’s Law and Henry’s Law explain the pressure-related dangers crews face, and the basic principles of buoyancy (Archimedes’ principle) make the whole concept of a submersible vessel possible in the first place. Understanding these connections turns abstract physics into something concrete: a 7,000-ton steel vessel that can vanish beneath the ocean and resurface on command.
Buoyancy: Why a Steel Vessel Can Float or Sink
Every submarine operates on the same principle that keeps a steel ship afloat. A solid block of iron sinks because it’s denser than the water it pushes aside. Reshape that same block into a hollow hull, and it displaces a much larger volume of water. The upward buoyant force equals the weight of the displaced water, so as long as the hull is large enough and light enough relative to the water it pushes out of the way, the vessel floats.
A submarine takes this a step further by making its overall density adjustable. When the sub’s total weight (hull, equipment, crew, and water inside it) is less than the weight of seawater it displaces, it’s positively buoyant and rises. When its weight exceeds the displaced water, it’s negatively buoyant and sinks. When the two are exactly equal, the sub is neutrally buoyant, hovering at a fixed depth without rising or falling. The trick to switching between these states is controlling how much seawater sits inside the hull, which is where ballast tanks and gas laws come in.
Boyle’s Law and the Ballast Tank System
Boyle’s Law states that the pressure and volume of a gas are inversely proportional at a constant temperature. Double the pressure, and the gas compresses to half its volume. Halve the pressure, and the gas expands to twice its volume. This relationship is the single most important gas law in submarine operations because it dictates how ballast tanks behave at every depth.
Ballast tanks are open to the ocean at the bottom and sealed with a vent valve at the top. To dive, the crew opens the vent valves, letting air escape from the top while seawater floods in through the bottom. The sub gets heavier and sinks. To surface, compressed air is forced into the tanks. Because the air pressure inside the tank exceeds the surrounding sea pressure, it pushes the water back out through the open bottom, making the sub lighter.
Boyle’s Law creates an accelerating effect during ascent. Deep underwater, sea pressure is high and the air inside ballast tanks is compressed into a smaller volume. As the submarine rises and external pressure drops, that same air expands, forcing out even more seawater. This lowers the sub’s density further, which accelerates it upward. The shallower it gets, the faster it rises. Submariners call this phenomenon “popping to the surface,” and it’s why careful depth management matters: once a sub starts rising with expanding air in its tanks, the process feeds on itself.
Emergency Blow
In a crisis, submarines carry banks of high-pressure compressed air, stored at 1,500 psi or more, specifically to blast water out of the main ballast tanks as fast as possible. Opening the emergency blow valves sends air at roughly 600 psi into the tanks in seconds, creating a rapid shift to positive buoyancy. The sub rockets toward the surface. Boyle’s Law amplifies the effect the whole way up, as the expanding air displaces progressively more water from the tanks during the ascent.
Pressure at Depth and Hull Limits
Water pressure increases by about one atmosphere for every 10 meters of depth. One atmosphere equals roughly 14.6 pounds per square inch (psi), the weight of the air above you at sea level. At 100 meters, a submarine’s hull faces about 10 atmospheres of external pressure, or 146 psi, pressing in from every direction. At 400 meters, that climbs to around 40 atmospheres, nearly 600 psi.
Military submarine hulls are built from high-yield steel alloys designed to resist this crushing force. HY-80 steel, a common choice, has a yield strength of about 615 megapascals after heat treatment. But externally pressurized cylinders don’t fail by simply being squeezed past their material strength. They buckle, collapsing inward at pressures well below what the raw steel could theoretically withstand. This is why submarines have ring-shaped internal stiffeners running the length of the hull, and why every class of submarine has a rated operating depth and a deeper “crush depth” that it must never approach. Corrosion thinning the hull by even a small fraction reduces those limits significantly.
Henry’s Law and Decompression Risk
Henry’s Law states that the amount of gas dissolved in a liquid is directly proportional to the pressure of that gas above the liquid. Increase the pressure, and more gas dissolves. Decrease the pressure quickly, and the dissolved gas comes out of solution as bubbles, the way carbonation fizzes when you open a soda bottle.
This matters for submarine crews primarily in scenarios involving pressure changes inside the vessel. Modern nuclear submarines maintain their internal atmosphere at roughly sea-level pressure regardless of depth, so the crew isn’t normally exposed to elevated pressures. But situations that compromise hull integrity, or operations involving divers leaving and reentering the sub through a lockout chamber, introduce pressure changes that push more nitrogen into the bloodstream.
If that pressure drops too quickly, the nitrogen forms bubbles in the blood and tissues. This causes decompression sickness, sometimes called “the bends,” which ranges from joint pain and skin rashes to life-threatening arterial gas embolisms, where gas bubbles block blood flow to vital organs. Treatment requires a hyperbaric chamber that re-pressurizes the surrounding air, forcing the nitrogen back into solution so the body can eliminate it gradually.
Breathing Underwater: Oxygen and CO2 Management
A submerged submarine is a sealed environment. The crew consumes oxygen and exhales carbon dioxide, so both gases need active management. Gas laws govern every step of this process.
Generating Oxygen
The primary method is electrolysis: passing an electric current through water to split H₂O into hydrogen gas and oxygen gas. The oxygen is released into the submarine’s atmosphere for the crew to breathe. Saltwater can’t be used directly because the sodium chloride in it would produce chlorine gas, which is lethal. Submarines first run seawater through reverse osmosis filters to remove the salt, producing pure freshwater. The salt brine goes back into the ocean, and the purified water feeds the electrolysis system.
As a backup, submarines carry canisters of sodium chlorate. When heated to extreme temperatures, this compound undergoes thermal decomposition, releasing oxygen along with ordinary table salt and iron oxide. These “oxygen candles” provide emergency breathing air if the electrolysis system fails.
Removing Carbon Dioxide
Dalton’s Law of partial pressures is relevant here. The total pressure of a gas mixture equals the sum of the partial pressures of each individual gas. In a sealed submarine, even though total air pressure stays normal, the partial pressure of CO₂ climbs steadily as the crew exhales. At concentrations above about 0.5%, carbon dioxide causes headaches, drowsiness, and impaired decision-making. Higher levels become dangerous.
Submarines use chemical scrubbers to pull CO₂ out of the air. One common approach uses monoethanolamine, a liquid solvent that absorbs carbon dioxide and can be regenerated by heating. Solid absorbents like zeolites and activated carbon also capture CO₂, though they tend to be less effective at the very low concentrations submarines aim to maintain. The goal is keeping CO₂ levels at or below 0.5%, with some systems pushing toward 0.2%.
How All Three Laws Work Together
A single dive-and-surface cycle puts all these gas laws into action simultaneously. As the submarine descends, rising external pressure (governed by the simple physics of water depth) compresses the air in its ballast tanks per Boyle’s Law, requiring the crew to fine-tune buoyancy with smaller trim tanks. Henry’s Law means any pressurized gas exposure dissolves more nitrogen into bodily fluids, a background risk the crew manages by keeping internal pressure stable. Dalton’s Law governs the partial pressures of every gas in the boat’s atmosphere, from the oxygen the electrolysis system produces to the CO₂ the scrubbers remove.
When the submarine surfaces, Boyle’s Law drives the expansion of air in the ballast tanks that pushes out seawater and accelerates the ascent. The same law applies to the high-pressure air flasks that store emergency breathing and ballast-blowing air: gas compressed into steel bottles at 1,500 psi expands enormously when released into the lower-pressure ballast tanks, delivering the force needed to bring thousands of tons of steel back to the surface in seconds.