Slow Viscous Flow
Many of the problems already presented dealt with situations where inertia forces were cither zero (parallel flow) or could be neglected because of some peculiarities, for example, flow in thin layers. A larger class of flows with negligible convective inertia forces was pointed out long ago by G.G. Stokes (1851): the slow viscous flows (often called Stokes flows or creeping flows). Among other results, Stokes obtained a formula expressing the drag of a sphere slowly moving in a viscous fluid; this represented one of the first approximate solutions of the Navier-Stokes equations for a flow past an immersed body. Slow viscous flow meaning small Reynolds numbers, some of the incrtialcss solutions presented so far can also be included in this class, such as flow through porous media (§4.5), flow in conical nozzles (§5.4), and even flows in narrow passages (lubrication. Chapter 9).
KeywordsStream Function Viscous Fluid Angular Speed Uniform Flow Stoke Flow
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