By doing a force balance on a small volume element in the fully developed flow region in the pipe (Laminar Flow), we get velocity as function of radius only i.e. it does not depend upon the axial distance from the entry point. The velocity as the function of radius comes out to be:
  is constant.
By definition of average velocity is given by
where  is cross-sectional area.
Thus,
For fully developed flow, the maximum velocity will be at .<br>Thus,