upper plate velocity u2
1.0
lower plate velocity u1
-1.0
pressure gradient dp/dx
0.05

Directions

A fluid is located between two plates that move independently. Their velocities to the left or the right are changed with the two sliders. A pressure gradient can also be imposed on the fluid with a slider.

Details

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):

d²u / dy² = (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) = u1 (lower plate velocity),
u(h) = u2 (upper plate velocity).

This problem has an analytic solution:

ux(y) = [(y² − h²) / 2μ](dp/dx) + [(u2 − u1)/2](y/h + 1) + u1

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

About

This simulation was created in the Department of Chemical and Biological Engineering at University of Colorado Boulder for LearnChemE.com by John L. Falconer using Claude AI. It is a JavaScript/HTML5 implementation of a Mathematica simulation by David Gerhardinger. It was prepared with financial support from the National Science Foundation (DUE 2336987 and 2336988) in collaboration with Washington State University. Address any questions or comments to LearnChemE@gmail.com.