Module 6: Navier-Stokes Equation
  Lecture 16: Couette and Poiseuille flows
 
 
Example 2: Suppose that an external pressure-drop along x-direction is applied across the channel, in addition to the conditions mentioned in example 1. Now, calculate the velocity profiles in the channel.
  • X-momentum balance is now modified to
     

Y–momentum balance:

 
  •   
    But is a function of y only. This implies that  (constant)
Integrating twice,
Apply BCs to obtain

You should check the two BCs.

Special case  

  1. (Same as in example 1)

 

,    where,