Answered by Shaykh Faraz Rabbani
I’ve been told by a reliable friend that when passing wind and intending to do wudu (as it has been broken), then washing below the abdomen (i.e. washing the private area with water) is not necessary as one has not excreted. one can begin the wudu from washing his hands, mouth nose.. and henceforth. Is this true?

Walaikum assalam wa rahmatullah,
The obligatory acts of wudu are only four (washing face, arms, and feet, and wiping a quarter of the head). It is also obligatory, with regards to the validity of one’s prayer, to remove any excessive filth on one’s body or clothes or place of prayer.
No filth normally comes out when passing wind. Thus, there is no need to wash one’s private parts after passing wind. Rather, the scholars have mentioned that doing so while thinking it to be necessary is a reprehensible innovation (bid`a).
And Allah alone gives success.
Wassalam,
Faraz Rabbani