Philsom is right; everybody else is wrong. The hydrogen issue was a liberty taken by the writers. The longer you stay down, the more CO2 you get, not the more hydrogen. You get hydrogen while on the surface, because it is only on the surface where this type of submarine could charge its batteries. The release of hydrogen is a byproduct of the charging operation, which is true of any battery that uses a sulfuric acid electrolyte, including the humble and familiar battery under the hood of your car (unless you are British, in which case it is under the bonnet, and unless of course that the car is so small that the battery is in the trunk or boot or under a seat or something -- but I digress). As Philsom noted, this is supposed to be removed through ventilation, just as you advised to employ when charging your car battery.
Moreover, on a nuclear submarine you still get hydrogen, but not because of electrolysis in making oxygen from seawater. First of all, that hydrogen never gets into the boat in the first place because the O2 generating system vents it directly overboard without it ever getting into the atmosphere inside the pressure hull in the first place (unless there is a leak). Second, in my humble experience aboard 1960's-vintage U.S. ballistic missile submarines a submarine's O2 generators never work worth sh*t in the first place and are usually OOC (out-of-commission, for you non-quals) for repairs. Rather, you get hydrogen for the same reason you get it in a diesel boat -- from recharging the ship's battery which is used as the electricity supply when the reactor is scrammed below snorkeling depth, something which is done routinely for all sorts of training events. On nuke boats, however, we also have a catalytic converter system that removes hydrogen from the atmosphere (provided you get it adequately ventilated from the battery well into the general ventilation system of the ship).
Finally, if you have the bad luck to get seawater into the battery well to the extent that it comes in contact withe the sulfuric acid (which is most definitely not ever supposed to happen, but can as a result of battle damage or other damage to the hull), you will get chlorine gas, which is not explosive or flammable but which is highly toxic.
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