I need to find the circulation for a flow in a pipe. I'm using the velocity in the angular direction (cylindrical coordinate system). Am I right in thinking that an ideal vortex is one where there is no vorticity? That would mean there is no circulation. It's strange, because the velocity is written in terms of circulation, and its circulation is constant. So that can't be correct. I'm trying to write the circulation in the forms of a surface integral and a line integral. The surface integral contains vorticity, which shows up as zero when I compute it. Say if the velocity is gamma/(2*pi*r) gamma = circulation The line integral of the circulation is: gamma = integral (velocity) ds If I write ds = 2*pi*r, then I get gamma = v*2*pi*r, which just gives me gamma = gamma. Any help in my thought process please?