Our lecturer said that velocity at any point in laminar flow is constant. But in another lecture slide (about flow velocity profiles), he also wrote that not all fluid particles travel at the same velocity and that in laminar flow, the velocity distribution at a cross-section will be parabolic in shape with the maximum velocity at the center being about twice the average velocity in the pipe. So how is the velocity then constant at any point in laminar flow? I'm sure I'm missing something but I can't make sense of the two statements together.
Edit: Thank you for the answer, I understand now what I wasn't seeing.