In our gemara, we find it's forbidden to drink water located in a reshus haRabim unless one has his head and the majority of his body in the reshus from which he is drinking
In our shi'ur, we discussed (without resolution) a case of a drinking fountain, located in reshus haRabim, which is 10 tefachim high and 4 x 4 tefachim - a very ordinary looking fountain. If the fountain is a reshus haYachid, may one drink from it while standing in reshus haRabim?
The halachos of standing in one Reshus and drinking in another are discussed
in O.C Siman 350 and 351.
1) The drinker stands completely in Reshus haRabim:
In Siman 351 #1 we learn that one may not stand in Reshus HaRabim and place
his hand (or mouth M.B.) next to a pipe in order to drink the water as his
hand or mouth are in Reshus Harabim and the water is in Reshus haYachid and
so we have a simple case of Hotza'a.
2) The drinker's head is in Reshus haYachid:
mid'Oraisa this situation should be permitted as his mouth will be
considered a Mekom Petur. It does not have an area of 4x4 Tefachim. It is
not Batel to the Reshus haYachid as it is part of his body. On the other
hand it is not batel to the Reshus haRabim as it not in the same Reshus as
the rest of his body. (Aruch ha'Shulchan quoting the Rosh)
The water is transferred from the Reshus haYachid to the Stomach in the
Reshus haRabim via the mouth, a Mekom Petur. Even though we generally
enforce a Gezeirah not to transfer via a Mekom Petur, here it permitted as
there is no possibility of the water arriving in the stomach without passing
through the mouth.
Nevertheless, we find there is a Gezeirah in our Sugya that one should not do this unless the majority of the body is positioned in Reshus haYachid as well.
3) The drinker's head and majority of his body is in Reshus haYachid:
The reason for the Gezeirah is that one might bring the cup towards himself into the Reshus haRabim. The Shulchan Aruch rules that since you need the water where you are you might transfer it to the Reshus haRabim. The Mishnah Berurah #6 writes that there is no distinction between nice cups and ordinary cups. The source he quotes is the Avodas ha'Kodesh of the Rashba, and in the original it is clear that even if NO cup is used the Gezeirah still applies. In #8, the Mishnah Berurah writes that this is the accepted opinion.
The Shulchan Aruch quotes another opinion, that of the Rambam. According to
him the Gezeirah only applied to nice Keilim which one would come to take
into the Reshus haRabim. If the cup is not nice or if no cup was used then
the Gezeirah would not apply and one could drink as long as his head was in
the Reshus ha'Yachid. The Aruch ha'Shulchan #3 supports this opinion.
4) The drinker is in a Karmelis:
Since we do not make a Gezeirah on a Gezeirah, a person may stand in Reshus
haRabim and drink if his head is in a Karmelis.
Now, for your question:
(a) Is the drinker in a Reshus haYachid or a Karmelis? This is of course
dependent on the Machlokes of whether we require 600 000 people in addition
to a width of 16 Amos. If the Reshus in which the drinker stands is a
Karmelis then it would be sufficient to ensure that his head is over the
drinking fountain. In a number of questions of Gezeros of Hotza'a we find
that the Poskim are Mekil biZeman haZeh that we do not have a Reshus ha'Rabim d'Oraisa.
I would think that a combination of The Rambam's opinion together with the
questionable Reshus ha'Rabim would certainly permit drinking without a cup.
(b) Is the water in a Reshus haYachid?
The Chazon Ish O.C.104 #2 writes that a closed pipe which opens into a
Reshus ha'Yachid is a Makom Petur. If so, then drinking directly from the
pipe of the water fountain would not be a problem at all.
(c) Is turning on the water a ma'aseh or a Gerama? If it is a Gerama then it would not be forbidden from the Torah and the Gezera would not apply.
the Chazon Ish (above) suggests that turning on a tap is a Gerama and not a
Ma'aseh. A distinction should also be made between the initial flow of water as the a tap is opened (Koach Rishon) which is usually considered to be an action and the subsequent flow of water which is considered to be Gerama.
Incidentally, It would be extremely unlikely that an average person would
be able to get Rosho v'Rubo into 4x4 Tefachim. The Rashash in Succah is
puzzled by how a Sukah of the minimum shiur, which is 7x7 Tefachim is able to contain Rosho v'Rubo!
Kol Tuv
Ilan Segal