It is permissible to wash one’s hands for the sake of a mitzvah, because it is not for pleasure purposes. Therefore, kohanim (“priests”) may wash their hands fully, in preparation for the priestly blessings (Rama 613:3, Sh.A. 128:6). However, one is not permitted to immerse in a mikveh on Tish’a B’Av.
Upon awakening in the morning, everyone is obligated to wash his or her hands up until the joints connecting the fingers to the palm of the hand, because an evil spirit rests on one’s hands after a night’s sleep, and it can cause harm to the orifices of the body. In order to remove this spirit, one must wash each hand three times, alternately. After using the bathroom, one should wash his hands again, once, and recite the blessing Al netillat yadayim, because the Sages instituted a mitzvah to wash one’s hands, with a blessing, in preparation for the morning prayers (Shacharit). And even though we are usually careful to wash the entire hand, on Tish’a B’Av one should wash only up to the joints connecting the fingers to the palm, because according to the letter of the law, that is sufficient both in terms of preparing for Shacharit and in order to remove the evil spirit (Sh.A. 613:2).
Throughout the year, one should preferably wash his hands three times before every prayer service. Nevertheless, on Tish’a B’Av, one should not wash his hands before praying, because doing so is not obligatory. However, one who touched filthy parts of his body and wants to recite holy words should wash his hands, because he is doing so for the sake of a mitzvah, not in order to derive pleasure (M.B. 613:5-6, K.H.C. 6).
There is uncertainty regarding the law of someone who relieves himself without touching any part of the body that is usually covered, for perhaps he does not need to wash, seeing that he did not touch any filth. In order to avoid the quandary, it is best to touch a usually-covered part of the body – which have flecks of sweat – when using the bathroom. This way, everyone would agree that one may wash his hands until the upper knuckles, in order to say the blessing of Asher Yatzar in cleanliness (Sh.A. 613:3, M.B. 4).
The mitzvah for a niddah (menstrual woman) to immerse herself in a mikveh at the first halachically-acceptable opportunity does not override the prohibition against washing on Tish’a B’Av. Similarly, a man who is accustomed to immersing in a mikveh in order to remove keri defilement (caused by the emission of semen) may not immerse on Tish’a B’Av, because a pious custom does not override the prohibition against washing (B.Y., Sh.A. 554:8, 613:11).
According to most poskim, one need not wash one’s hands more than once after using the bathroom; but some people are accustomed to washing three times (see M.B. 4:39). Those who always wash three times may do so on Tish’a B’Av, as well, because this washing is for the sake of purification and a mitzvah, not pleasure. (See Peninei Halachah, Tefillah 8.3-5. Also see note 2, where R. Ovadyah Yosef is quoted as saying that there is no need to hurry and wash one’s hands three times before relieving oneself in the morning. According to him, one washes three times and recites the blessing only after relieving oneself.)
Some say that a person who touches a covered part of the body with one finger should wash only that hand until the upper knuckles (Ch.A. 40:18, M.B. 613:6). Others hold that he must wash both hands (Shelah, Yafeh LaLev; see also K.H.C. 4:86). The same authorities dispute a case in which someone touches his shoe – even if it is made of cloth – with one finger. There are many other uncertainties regarding these laws. For example, does someone who touches a normally-covered area that [nonetheless] has no sweat particles need to wash his hands (see Peninei Halachah, Tefillah 5, note 2)? Furthermore, according to the letter of the law, one who touches body parts that are usually covered may [simply] rub his hands [on anything that cleans] and then say words of holiness (Sh.A. 4:23, M.B. 61). Why, then, do we not do so on Yom Kippur and Tish’a B’Av? In practice, it appears that if, in a specific situation, one generally acts strictly throughout the year and washes his hands, he should also wash them on Tish’a B’Av, for he is doing so for the sake of a mitzvah. If, however, he sometimes makes do with rubbing his hands on his clothing [or the like], he should do the same on Tish’a B’Av. If someone touches a normally-covered area of his body and now wants to pray, he should wash his hands, because that is the halachah, as explained in Peninei Halachah, Tefillah 5.2. One who touches a usually-covered area [of the body] with one finger while using the facilities should wash both hands; and it seems that everyone would agree with this. After all, many authorities hold that one must wash both hands upon leaving a bathroom, even if he did not relieve himself or touch a normally-covered body part (see B.H. 613:3). One who touches mud with his finger should wash only the soiled area, because there is no evil spirit here that spreads to the rest of the hand. See Piskei Teshuvot 613:2.