Gemara

Mishnah: One who drinks Malei Lugmav (is liable).

Shmuel: 'Malei Lugmav' does not literally mean his full mouth. Rather, it is enough that if he would tilt his head to one side his cheek will appear full.

Question: The Mishnah says 'Malei Lugmav' (presumably it is precise)!

Answer: It means like Malei Lugmav.

Question (Beraisa) Question: What is the Shi'ur to be is liable for drinking on Yom Kipur?

Answer #1 (Beis Shamai): It is a Revi'is;

Answer #2 (Beis Hillel): It is Malei Lugmav;

Answer #3 (R. Yehudah): It is like Malei Lugmav;

Answer #4 (R. Yehudah ben Beseira): It is Kedai Gemi'ah (the amount a person can swallow at once. It is less than Malei Lugmav (Magid Mishnah Shabbos 18:2).)

Answer: We can answer just like we answered the Mishnah - Beis Hillel mean like Malei Lugmav.

Question: If so, this is like R. Yehudah!

Answer: They argue about Malei Lugmav Dachuk (R. Yehudah is Mechayev even if there is just enough to make his cheek look full).

Question (R. Hoshaya): If so, this should have been taught in Maseches Eduyos, with all the Halachos in which Beis Shamai is more lenient than Beis Hillel!

Answer: The question was asked regarding a giant (his Malei Lugmav is more than a Revi'is), so Beis Shamai is more stringent.

Question (R. Zeira): Regarding eating there is one Shi'ur for everyone (the volume of a big date). Why does the Shi'ur for drinking vary according to the person?

Answer (Abaye): Chachamim know that the volume of a big date of food relieves anyone who is fasting, but drinking gives relief only if it is his Malei Lugmav.

Objection (R. Zeira): Surely Og Melech ha'Bashan is not relieved by the same amount of food as normal sized people!

Answer (Abaye): Indeed, Og is relieved by the same amount, just not as much as normal sized people.

Kerisus 12b - Mishnah: If one drank (a Revi'is of) Tamei liquids or a Revi'is of wine, and entered the Mikdash:

If the delay was bi'Chdei Achilas Pras (the time to eat half a loaf), he is liable (regarding wine this is mid'Oraisa).

R. Eliezer says, if he paused while drinking the wine, or added any water to it, he is exempt.

13a - Beraisa: All (Tamei) drinks join to the Shi'ur of a Revi'is to Metamei (mid'Rabanan) one who drinks them bi'Chdei Achilas Pras.

Rishonim

Rambam (Hilchos Shevisas Asor 2:1): If one drinks liquids fitting for people and they are the volume of Malei Lugmav, he is liable. This is the amount that when he puts it in one side of his mouth it looks like his mouth is full. In an average person this is less than a Revi'is.

Rambam (ibid. 4): If one drank intermittently over the time needed to drink a Revi'is, the amounts he drank can join to the Shi'ur of Malei Lugmav.

Source #1 (Ran DH ul'Inyan Tzirufan Shel Mashkin): The Rambam learns from the Tosefta (Pesachim 1:10) which says that regarding Chametz, liquids join to the Shi'ur within the time to drink a Revi'is.

Hagahos ha'Gra (on Tosefta Pesachim 1:10): The text should say that they join within Kdei Achilas Pras.

Question Ran (ibid.): Tamei liquids join to Metamei one who drank them within Kdei Achilas Pras!

Source #2 (Magid Mishnah): The Rambam learns from the Tosefta (Yoma 4:4); the same Shi'ur applies to other Isurim. Some say that they join within Kdei Achilas Pras, the Shi'ur for Tamei liquids. It is better to say that Chachamim were more stringent regarding Tum'ah mid'Rabanan, for then we need not reject the Tosefta.

Question: The Gemara (80b) says that we are more lenient and require a shorter Tziruf (than usual) for Tum'ah mid'Rabanan for eating Tamei food!

Answer (Lechem Mishneh): Regarding Tamei food Chachamim were lenient to require Tziruf within the same Shi'ur allotted for a smaller quantity of Isurim. They were stringent to equate the Shi'ur for Tamei liquids to that of food, lest people treat both Tum'os lightly.

R. Mano'ach: Drinking a Shi'ur on Yom Kipur brings relief only if it was within the time to drink a Revi'is. For a Zar to be liable for drinking Terumah he must drink a k'Zayis, like the Shi'ur for eating, within the time to drink a Revi'is (Tosefta Terumah 7:3). One becomes Tamei for ingesting the same amount of Tamei food or drink (half a Pras, which equals a Revi'is), therefore the Shi'ur of time is the same (Kdei Achilas Pras).

Minchas Bikurim (on Tosefta Yoma 4:4 DH Kedai): The Halachah is that we join what one drinks within Kdei Achilas Pras (Rambam - three k'Beitzim; Rashi - four k'Beitzim).

Poskim

Shulchan Aruch (OC 612:9,10): If on Yom Kipur one drinks Malei Lugmav he is liable. We measure according to the person himself. It is not really his mouthful. Rather, when he puts it in one side of his mouth it looks like his mouth is full. In an average person this is less than a Revi'is.

Mishnah Berurah (25): When he fills one cheek it looks like both are full.

Kaf ha'Chayim (42): 'Less than a Revi'is' connotes slightly less. However, Sefer ha'Chinuch says that the Shi'ur is k'Beitzah. The Shulchan Aruch (271:3) says that it is the majority of a Revi'is, so one should give an (average size) Choleh at most half a Revi'is at once.

Note: The Shulchan Aruch (618:7) says that we measure the person's Malei Lugmav. Perhaps the Kaf ha'Chayim discusses when we cannot do so because he is too weak.

Shulchan Aruch (ibid.): If one paused in the middle of drinking, if the total time from beginning to end was at most the time to drink a Revi'is we join what he drank for a Shi'ur. Some say that the Shi'ur to join drinking is the same as for eating, Kdei Achilas Pras.

Gra (DH v'Yesh Omrim): The Mishnah and Beraisa (Kerisus 12b and 13a) clearly refute the first opinion (the Rambam)! Perhaps the Rambam learns from R. Elazar, who exempts if one paused while drinking the Revi'is. The Gemara rules like R. Elazar that if he paused, he is exempt. This is wrong. R. Elazar learns from "v'Shechar" (do not drink in an intoxicating way), we do not learn to other cases.

Shulchan Aruch (OC 618:7) When we feed a pregnant woman or Choleh on Yom Kipur, we give less than the amount which joins to a Shi'ur. The Choleh should measure how much he can put in one side of his mouth to make it look full. He should not drink this amount at once. Before drinking again he should wait the time to eat four k'Beitzim (of bread), or at least the time to drink a Revi'is. If even though is not enough, he eats as much as necessary.

Mishnah Berurah (21,22): The Choleh should measure before Yom Kipur. He should also time how long he takes to eat four k'Beitzim. If this is too long, he should try to wait the time to eat three k'Beitzim. The Chasam Sofer says that Kdei Achilas Pras is nine minutes.