Double-Sided Couette Flow
Double-Sided 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=, where is the dynamic viscosity of the fluid and is the pressure gradient.
u(y)
2
d
d
2
y
1
μ
dp
dx
μ
dp
dx
The boundary conditions are:
u(-h)=
u
1
u(h)=
u
2
This problem has an analytic solution:
u
x
-
2
y
2
h
2μ
dp
dx
(-)
u
2
u
1
2
y
h
u
1
that varies as a function of the pressure gradient and the upper and lower plate velocity.