# 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.