Answer: In the matter of purifying oneself for salaah, one is required to clean himself from two types of impurities. The first is that of the visible impurity which is an impurity that one can see and he is required to remove it from his body and clothing when he wishes to perform the prayer. Included under this impurity would be urine, stool, blood and other similar impurities. When a person goes to the washroom to ease himself, he is required to clean himself properly and in doing so he has removed the visible impurity from himself.

However, by easing himself, another type of impurity comes over him which is known as the ritual impurity and this is the second type of impurity. This form of impurity cannot be seen, however it exists on a person and hence, he is required to remove it by performing wudhu. As for the act of passing wind, this brings about the ritual impurity and there is no visible impurity. As such, it would be required for one to perform wudhu in order to free himself from the ritual impurity but since there is no visible impurity there will be no need to wash one's private parts.

And Allah knows best.
Mufti Waseem Khan