This equation obtains its leading coefficient of the negative of the streamwise pressure gradient by application of the no-slip boundary condition at the outer radius.  
This equation obtains its leading coefficient of the negative of the streamwise pressure gradient by application of the no-slip boundary condition at the outer radius.  Easily giving rise to a D'Arcy friction of 64 divided by the Reynolds number, it is not strictly applicable to the situation for which it was originally developed, since it applies only to steady, fully developed, purely axial laminar flow of an incompressible Newtonian fluid in circular pipes.  FTP, identify this exact solution of the Navier-Stokes equation stating that the flow velocity is parabolic with centerline velocity equal to the pressure gradient divided by four times the dynamic viscosity, which is named for a Frenchman and designed to model flow in blood vessels.
This equation obtains its leading coefficient of the negative of the streamwise pressure gradient by application of the no-slip boundary condition at the outer radius.  
Hagen-Poiseuille equation