Fluid mechanics
The Navier–Stokes equations
Illustrate Couette flow — an analytic solution of the Navier–Stokes equations for a viscous fluid between two flat plates with no pressure gradient. Vary the top-plate speed U and the gap H to verify the linear profile and shear rate .
Equipment
- Two parallel flat plates with a virtual viscous fluid layer
- Top-plate speed slider U (0.02–0.20 m/s)
- Gap slider H (20–100 mm)
- Draggable 3D canvas and shear-rate U/H readout
Procedure
Set up the Couette flow
Set the top-plate speed to about 0.10 m/s and the gap to about 60 mm with the sliders. Watch the velocity arrows: the bottom plate is at rest and the speed grows linearly up to U at the top — the no-slip boundary condition.
Verify the linear profile
Read the shear rate in s⁻¹. Double U while holding H and check that the rate doubles; each fluid layer slides over its neighbor with viscous stress .
Change the gap and compare
Hold U fixed and raise H from 20 mm to 100 mm: the profile stays linear but the shear rate U/H drops inversely with the gap. Drag the canvas to rotate the view and inspect arrows at every height.