;
Module 6: Navier-Stokes Equation
Lecture 16: Couette and Poiseuille flows
Apply NS in x-direction:
1
st
term is zero for SS
for fully developed flow;
. Horizontal
Therefore, the equation is simplified as
No external pressure was applied and in addition, it is a long plate
Integrate twice,
Apply BC (1)
(no slip condition)
BC (2)
Solve for
to obtain
This is the expression for velocity profiles in a Couette flow
(
Note:
at
).
(Fig. 16d)
for fully developed flow; 
. Horizontal
Therefore, the equation is simplified as 
(no slip condition) 
to obtain 
This is the expression for velocity profiles in a Couette flow 
). 
