Published in

Oxford Scholarship Online, 2018

DOI: 10.1093/oso/9780198805021.003.0005

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Viscous Flows

Book published in 2018 by S. G. Rajeev
This paper was not found in any repository, but could be made available legally by the author.
This paper was not found in any repository, but could be made available legally by the author.

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Abstract

Here some solutions of Navier–Stokes equations are found.The flow of a fluid along a pipe (Poisseuille flow) and that between two rotating cylinders (Couette flow) are the simplest. In the limit of large viscosity (small Reynolds number) the equations become linear: Stokes equations. Flow past a sphere is solved in detail. It is used to calculate the drag on a sphere, a classic formula of Stokes. An exact solution of the Navier–Stokes equation describing a dissipating vortex is also found. It is seen that viscosity cannot be ignored at the boundary or at the core of vortices.