# Peeter Joot's (OLD) Blog.

• ## Recent Comments

 Somebody is there on avoiding gdb signal noise… peeterjoot on Derivative recurrence relation… Mike on Derivative recurrence relation… gerry on Just Energy Canada nasty busin… Bo Chen Hsu. on PHY354H1S. Advanced Classical…

• 251,828

# Archive for April 16th, 2012

## Flow between infinite moving inner cylinder and outer cylinder (3D visualizations).

Posted by peeterjoot on April 16, 2012

[Click here for a PDF of this post with nicer formatting.]

We previously looked at the problem of an infinite cylinder of radius $R_1$ is moving with velocity $v$ parallel to its axis. It is places inside another cylinder of radius $R_2$. The axes of the two cylinders coincide. The fluid is incompressible, with viscosity $\mu$ and density $\rho$, the flow is assumed to be stationary, and no external pressure gradient is applied, and found the solution to have the form

\begin{aligned}\boxed{w = \frac{G}{4 \mu} (R_2^2 - r^2) + \left(v - \frac{G}{4 \mu} (R_2^2 - R_1^2)\right)\frac{\ln r/R_2}{\ln R_1/R_2}.}\end{aligned} \hspace{\stretch{1}}(3.27)

This system with such simple geometry lends itself well to 3D visualization of the velocity profiles

An animation of this can be found at http://youtu.be/OiJTopWx7L8. The Mathematica notebook that generated this is available at phy454/twoCylinders3D.cdf. The 3D visualization portion of that notebook has also been made available as part of the wolfram demonstrations project.