[bigfans]

I am doing a project very simple in physics but with complicated geometry. So I try to simplify my question here: suppose a very simple pipe flow from left to right. The inlet velocity is not uniform (parabolic, x is flow direction and y is vertical axis), so how can I get the distribution of residence time of the system? Apparently, particles released from different positions (y) at the inlet will have different residence times when they exit the outlet.

Anybody can give me suggestions on that? Thanks a lot.