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Engineering Mathematics
Review of Viscous Flows
Review of Computational Fluid Mechanics

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The National Science Foundation
ME 537 The National Science Foundation
 Viscous Flows
Navier-Stokes Equation, Vorticity, Stream Function | Exact Solutions | Drag on Spherical Particles | Creeping Flows | Nonspherical Particles

Creeping Flows

General Solution in Spherical Coordinate

In the absence of body force the general solution for creeping motion in spherical coordinates was given by Lamb. From (3) it follows that

(14)

where

(15)

with

 

are spherical harmonics. The corresponding expression for the velocity field is given as

(16)

where  are also spherical harmonics similar to those given by (14).

Expressions for the stress field and the corresponding drag and torque were given by Happel and Brenner (pages 66-67).



Dr. Goodarz Ahmadi | Turbulence & Multiphase Fluid Flow Laboratory | Department of Mechanical & Aeronautical Engineering
Copyright © 2002-2005 Dr. Goodarz Ahmadi. All rights reserved.
Potsdam, New York, 13699
ahmadi@clarkson.edu