The significance of negative sign is that the velocity decreases from the pipe centerline to the pipe wall. Substitution of the value from Eq. (7) in Eq. (6) yields,
                                              (8)
Now, integrating Eq. (8), the velocity profile is as follows;
                                              (9)
where is a constant. Applying "no-slip boundary condition", i.e. at . Hence,
The velocity profile can now be written as,
                                              (10)
where is the centerline velocity.