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The problem how viscous flow enters a tube or a duct, how an initially uniform velocity distribution is transformed over the initial region of the duct with smooth walls has been known in engineering and computational fluid dynamics for a long time. Schiller [1] gave an engineering solution
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1. Ye.A. Gayev (ye_gayev@public.icyb.kiev.ua) (Institute of Hydromechanics of NASU, Kyiv, Ukraine)S.Z. Shikhaliev (sabir@shikh.pp.kiev.ua)(Institute of Energy Problem Modelling of NASU, Kyiv, Ukraine) Viscous flow through a duct with easily penetrable roughness modelled by Navier-Stokes equations