A rigid sphere of radius moves through water ( , ) at speed .

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 rigid sphere of radius a=0.10 mma=0.10\,\mathrm{mm} moves through water (ρ=998 kg m−3\rho=998\,\mathrm{kg\,m^{-3}}, μ=1.00×10−3 Pa s\mu=1.00\times10^{-3}\,\mathrm{Pa\,s}) at speed U=1.0 cm s−1U=1.0\,\mathrm{cm\,s^{-1}}. ((a)) Find the Reynolds number based on the sphere's diameter. ((b)) Compute the drag coefficient CDC_D from Stokes's law, CD=24/ReC_D = 24/Re, and from Oseen's correction, CD=(24/Re)(1+316Re)C_D = (24/Re)(1+\tfrac{3}{16}Re), and state by what percentage they differ.

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