Module 6: Navier-Stokes Equation
  Lecture 17: Tubular laminar flow and Hagen-Poiseuille equation
 
 
Steady-state, laminar flow through a horizontal circular pipe

(Fig. 17a)

Assumptions:   (no swirling, circulation)

We are interested in solving   

Continuity:    
 

Fully developed flow:  

Therefore, r

But
 (No-slip condition)
  everywhere.
So, the problem is reduced to solving .