Module 6: Navier-Stokes Equation
  Lecture 18: Macroscopic momentum balance for pressure-drop in a tubular flow
 
 

If the flow is laminar, the velocity profile is parabolic near the walls and is uniform in the central core of the tube. Shear-stress in such fluid also varies linearly with r:

 
(Fig. 18c)

 

   

Equation (1) can be integrated with to obtain:

 

 

Therefore,