A Homogeneous Solution for Viscous Flow Around a Half Plane

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The present work develops a simple and concise form for the homogeneous solution to the problem of the two-dimensional steady flow of a viscous fluid in the presence of a half-plane, and some properties of this solution are discussed. The fluid motion described by the homogeneous solution is that of circulation around the half-plane. The streamlines form a family of parabolas. The means for generating this circulatory motion are discussed in terms of the asymptotic behavior of velocity and pressure at infinity. The flow produces no drag on the half-plane, but a jump in pressure does provide a net lift. The velocity components vanish on the half-plane and at infinity, attaining extremum values in the interior of the flow field. The critical points, determined from pressure and velocity gradients, are found to lie on the same streamline. Possible connection with the Navier-Stokes problem is also discussed.
Original languageEnglish
Pages (from-to)165-169
JournalQuarterly of Applied Mathematics
StatePublished - Jul 1975


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