Let's say we have a horizontal pipe with steady, incompressible, two dimensional flow. There is friction at the top and bottom of the pipe which causes viscous effects. The flow is fully developed. The velocity profile is parabolic. Obviously there is an x-component (u) of velocity. Is there also a y-component of velocity (v), in this fully developed region? My intuition says no, but from reading my book it implies that there is, although it is not very well explained. Thanks!