Air at rest fills a narrow duct

PHYSICS · Subjective · Fermi University Physics · Fluids & Continuum Physics · Viscous flow and dynamical similarity · Viscous flow and dynamical similarity

Fluid Dynamics, Ch The Navier-Stokes equations and unsteady exact solutions

Problem

Air at rest fills a narrow duct. A wall suddenly starts moving parallel to itself, generating vorticity at that wall. Using the kinematic viscosity of air, ν=1.51×10−5 m2 s−1\nu = 1.51\times10^{-5}\,\mathrm{m^2\,s^{-1}}, estimate the time for vorticity to diffuse a distance L=2 mmL = 2\,\mathrm{mm} across the duct, using the diffusion-time estimate t∼L2/νt \sim L^2/\nu that follows from the viscous vorticity equation.

Browse the problem library