This simulation calculates the thickness of a boundary layer for flow between stationary parallel plates as a function of distance down the plates. Use sliders to vary the distance between the plates, the fluid velocity and the kinematic viscosity of the fluid. The boundary layer (shaded light blue region) represents the region where viscous forces must be taken into account due to the no-slip condition. Outside of the boundary layer (white region), viscous forces are negligible. Once the two boundary layers meet midway between the plates, the fluid flow is fully developed.
The Prandtl–Blasius boundary layer solution is used:
where \(\delta_L\) and \(\delta_T\) are boundary layer thickness for laminar and turbulent flow (cm), \(x\) is length down the plates (cm), \(Re\) is the Reynolds number (dimensionless), \(u\) is fluid velocity (cm/s) and \(\nu\) is kinematic viscosity (cm²/s).
Fluid flow is laminar for \(Re < 2\times10^{5}\) and turbulent for \(Re > 3\times10^{6}\). The boundary layer thickness for the transition region \(\delta_R\) (\(2\times10^{5} \le Re \le 3\times10^{6}\)) is calculated from:
where \(f\) is the fraction of flow in the transition region that is turbulent, and \(x_L\) and \(x_T\) are the boundaries of the laminar and turbulent regions (cm).
[1] B. R. Munson, T. H. Okiishi, and W. W. Huebsch, Fundamentals of Fluid Mechanics, 6th ed., Hoboken, NJ: John Wiley & Sons, 2010.
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 Jaeda C. Sichel and Rachael L. Baumann. It was prepared with financial support from the National Science Foundation (DUE 2336987 and 2336988). Address any questions or comments to LearnChemE@gmail.com.