# 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 : =, where is the dynamic viscosity of the fluid and is the pressure gradient.

u(y)

du

2

dy

2

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(y)=++1+u

x

y-h

2

2

2μ

dp

dx

(u-u)

2

1

2

y

h

1

that varies as a function of the pressure gradient and the upper and lower plate velocity.