One of the thirty-nine categories of Melacha (activity forbidden on Shabbat) is repairing, fixing something that is not working properly. Hacham Ovadia Yosef ruled that this prohibition of Tikkun (fixing) applies to a clogged drain. If a sink is completely clogged, such that the water is not going down at all, it would be forbidden to open the drain with a plunger, as this constitutes "repairing" a malfunctioning pipe. However, given that one would likely need to use the sink on Shabbat, it would be permissible to ask a gentile to open the drain. Preferably, Hacham Ovadia adds, one should have a gentile ask another gentile, as asking a gentile to ask a gentile to perform Melacha is treated more leniently in Halacha than asking a gentile directly. However, if it would be too difficult to find two non-Jews for this purpose, one would be allowed to ask a non-Jew directly to open the drain.
Rav Moshe Feinstein (Russia-New York, 1895-1986) issued a similar ruling concerning a clogged toilet. If the toilet is completely clogged, it is forbidden to open the clog on Shabbat, but it is permissible to ask a non-Jew to do so.
This does not apply, however, to the case of a partially-clogged drain, where the water is going down slowly. In such a case, it would be permissible on Shabbat to open the drain to allow the water to flow freely, as this does not constitute "Tikkun." Since the pipe is already functional, one would be allowed to open the drain more fully. Likewise, Hacham Ovadia writes, in such a situation it would be permissible to pour boiling hot water down the drain on Shabbat to open the partially-clogged pipe. (This obviously assumes that the water had been boiled before Shabbat, such as in an urn, and one fills a pitcher with hot water from the urn and pours it down the drain.) Although there might be raw food in the pipe that might be technically "cooked" by the hot water, Hacham Ovadia notes that such "cooking" would not violate the Shabbat prohibition of Bishul (cooking). He cites the Hatam Sofer (Rav Moshe Sofer of Pressburg, 1762-1839) as asserting that the prohibition of Bishul applies only to cooking that prepares food for consumption. If one cooks food that is inedible as is the case of food being "cooked" inside a drainage pipe this does not violate the prohibition of Bishul. Therefore, one may pour boiling water down the drain to open a clog.
Summary: If a sink or toilet is completely clogged, such that the water is not going down at all, it is forbidden to open the clog on Shabbat, but one may ask a gentile to do so. In the case of a partial clog, it is permissible to open the clog on Shabbat. In such a situation, one may pour hot water down a drain to open a clog on Shabbat.
