A small glass sphere of radius and density falls through castor oil of density and…

PHYSICS · Multi-part · Fermi University Physics · Fluids & Continuum Physics · Viscous flow and dynamical similarity · Viscous flow and dynamical similarity

Fluid Dynamics, Ch Stokes flow, lubrication and viscous wetting

Problem

A small glass sphere of radius a=0.50 mma = 0.50\,\mathrm{mm} and density ρs=2500 kg m−3\rho_s = 2500\,\mathrm{kg\,m^{-3}} falls through castor oil of density ρf=960 kg m−3\rho_f = 960\,\mathrm{kg\,m^{-3}} and viscosity μ=0.65 Pa s\mu = 0.65\,\mathrm{Pa\,s}. ((a)) Find the terminal speed UtU_t, assuming Stokes drag applies. ((b)) Check the Reynolds number (based on the sphere diameter) to confirm that Stokes flow is a good approximation.

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