Now applying Newton 's second law, the force balance equation can be written as,
                                                (2)
After simplification of above equation,
                                                (3)
For a fully developed flow, is constant and hence,
                                                (4)
where is a constant. At i.e. there is no shear stress at the centerline of the pipe. The shear stress at the pipe wall is maximum and is known as "wall shear stress" . Hence, . So, the shear stress distribution throughout the pipe is a linear function of radial coordinate and is given by,
                                                (5)
Substituting the value of from Eq. (5) and in Eq. (3), we get
                                                (6)
By definition, the wall shear stress for a laminar flow of a Newtonian fluid in a pipe is given by,
                                              (7)