3D Velocity Profile for Flow between Two Cylinders

This Demonstration simulates the solution of the Navier–Stokes equations for radially symmetric steady-state incompressible fluid flow between two long cylinders, with external constant pressure gradient. At the boundary conditions, the outer cylinder has zero velocity while the inner cylinder is moving with a constant velocity.


  • [Snapshot]
  • [Snapshot]
  • [Snapshot]


The Navier–Stokes equations for radially symmetric steady-state incompressible fluid flow between two long cylinders with external constant pressure gradient has the form
This can be solved analytically. The solution depends on the boundary conditions, which require the velocity of the fluid at the fluid and cylinder interface to match (the no-slip condition). Here the profile of the resulting velocity field is illustrated for boundary conditions in which the outer cylinder is fixed, and the inner cylinder is moving with velocity . If and are the inner and outer cylinder radii, respectively, those boundary conditions can be written
from which this solution can be found:
This Demonstration shows how the variation of the shape of this resulting velocity profile depends on both the inner cylinder velocity and the pressure gradient to viscosity () ratio.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.

Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2018 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+