WOLFRAM NOTEBOOK

WOLFRAM|DEMONSTRATIONS PROJECT

Double-Sided Couette Flow

​
upper plate velocity
u
2
1
lower plate velocity
u
1
-1
pressure gradient
dp/dx
0.05
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(y)
:
2
d
u
d
2
y
=
1
μ
dp
dx
, where
μ
is the dynamic viscosity of the fluid and
dp
dx
is the pressure gradient.
The boundary conditions are:
u(-h)=
u
1
(lower plate velocity),
u(h)=
u
2
(upper plate velocity).
This problem has an analytic solution:
u
x
(y)=
2
y
-
2
h
2μ
dp
dx
+
(
u
2
-
u
1
)
2
y
h
+1+
u
1
that varies as a function of the pressure gradient and the upper and lower plate velocity.
Wolfram Cloud

You are using a browser not supported by the Wolfram Cloud

Supported browsers include recent versions of Chrome, Edge, Firefox and Safari.


I understand and wish to continue anyway »

You are using a browser not supported by the Wolfram Cloud. Supported browsers include recent versions of Chrome, Edge, Firefox and Safari.