How Long Can One Stay Underwater?
Don't take the question in the title lightly. It has many halachic implications, even relating to releasing agunot...

One of the most sensitive and common questions throughout our people's turbulent history was the "question of agunot" (chained women). Many times husbands disappeared after fleeing from enemy fears, during wars, exile, and other events, and leading poskim (halachic authorities) had to determine in each case whether the husband of a particular agunah was still alive or not. The decision was seven times more difficult if witnesses saw the husband falling into the sea or drowning in a river, but no one saw him emerge. This question has many offshoots and related questions, the main one being: How long can a person stay underwater, after which halacha considers him dead?
The Gemara in Bava Kamma tells about a man named Nechunya, who was called "the well-digger" because he dug large, deep pits that collected water to quench the thirst of pilgrims on their way to Jerusalem. One day, Nechunya's daughter stumbled and fell into a large pit. Many people rushed to appeal to the Tanna Rabbi Chanina ben Dosa to pray for her rescue. The Gemara relates (see Rashi there) that "in the first hour" he told them "peace," meaning: even if she is still in the water pit, she is not dead. "In the second hour" he again told them "peace." And "in the third hour" he told them "she has come up," meaning: now too much time has passed for her to survive in the water pit, so she must have been saved miraculously. Indeed, afterward the girl related that an old man, Abraham our patriarch himself (Rashi s.v. "and an old man led her"), came to save her. It seems explicit in the Gemara that one cannot determine a person's death until after three hours of staying in water. Indeed, many Acharonim ("Torat Emet" section 1, "Eliyah Rabbah" section 12) explain that the Rivash (Responsa 377), who rules accordingly, relies on our sugya.
However, the Maharit (Responsa Even HaEzer section 26) raises the obvious question: is it possible for a human being to stay in water for more than two hours and survive without oxygen supply to the lungs? Therefore, Maharit wrote that when the Gemara counts the time of Nechunya's daughter's stay in the pit and says "first hour," "second hour," etc., it does not mean a period of 60 minutes, but rather the number of times people approached Rabbi Chanina ben Dosa, as if to say "the first time," "the second time," and so on.
As an additional explanation to this question, the Maharit says that it's possible that Nechunya's daughter did not fall into the water, but managed to grab onto projections in the pit walls with her remaining strength. However, if she had been drowning in water, she could not have survived for a long hour.
How much time is in an hour? Maharit brings a wonderful proof for his words, that one need not define "hour" as one twenty-fourth part of the day. The Mishnah (Sotah 9:2) says that Miriam waited one hour on the shore of the Nile for Moses, and in return she merited that the Israelites waited for her seven days when she became leprous. And in the Tosefta (Sotah chapter 1, halacha 4) it says that the measure of reward exceeds the measure of punishment by 500 times. A simple calculation shows that the Israelites should have waited for Miriam the prophetess 500 hours. However, the Israelites were delayed on her account for only a week, that is, 168 hours. It is proven, therefore, that the term "hour" can also indicate an undefined and unbounded period of time. Nevertheless, Rabbi Akiva Eiger wrote (Responsa Tinyana 47) that one should not be lenient regarding the words of the Rivash, but should rule according to their plain meaning, and only after three hours of staying in water can one decide that the husband is no longer alive.