Open AccessThe steady flow of viscous fluid past a fixed spherical obstacle at small reynolds numbers
Author(s) -
S. Goldstein
Publication year - 1929
Publication title -
proceedings of the royal society of london. series a, containing papers of a mathematical and physical character
Language(s) - English
Resource type - Journals
eISSN - 2053-9150
pISSN - 0950-1207
DOI - 10.1098/rspa.1929.0067
Subject(s) - obstacle , reynolds number , mechanics , kinematics , radius , flow (mathematics) , mathematics , classical mechanics , viscous liquid , viscosity , physics , mathematical analysis , geometry , computer science , turbulence , computer security , quantum mechanics , political science , law
It was proposed by Oseen that, in considering the steady flow of a viscous fluid past a fixed obstacle, the velocity of disturbance should be considered small, and terms depending on its square neglected. This approximation is to be taken to hold not only at a great distance from the obstacle, but also right up to its surface; and involves the assumption that Ud/v is small, whered is some representative length of the obstacle, which in the case of a sphere is taken to be its diameter, U is the undisturbed velocity of the stream, andv the kinematic viscosity of the fluid. With this approximation, the equations of motion become linear, and can be solved; the condition of no slip at the boundary is then applied to complete the solution. We take the obstacle to be a sphere of radius and take the origin of coordinates at its centre.