Stream function/velocity potential in fluid mechanics

Hi! When you are calculating ##\psi## or ##\phi## from the horizontal or vertical velocity components of a fluid's velocity, you end up with a constant ##C## carried along with the function. In my class, the professor just said something about them being arbitrary (I think..) and set them to zero.

Could somebody please explain to me exactly WHY we can just ignore them? Just a random guess: Does it have something to do with us being able to define origo of our coordinate systems anywhere we like, including at a point which makes ##C=0##?