Couette Flow
Couette Flow
The permanent laminar flow of an incompressible viscous fluid in the space between two parallel plates can be described by a linear ODE for :
u=u(y)
2
d
d
2
y
1
µ
dp
dx
where is the dynamic viscosity of the fluid and is the pressure gradient. The boundary conditions are:
µ
dp
dx
u(0)=0
u(h)=
U
0
This problem has an analytic solution:
u(y)=1+-1-
U
0
2
y
h
dp
dx
2
h
2μ
2
y
h
that varies as a function of the pressure gradient and the upper plate velocity.