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Engineering Mathematics
Review of Viscous Flows
Review of Computational Fluid Mechanics
Review of Turbulence and Turbulence Modeling

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The National Science Foundation
ME 637 The National Science Foundation
 Viscous Flows
Navier-Stokes Equation, Vorticity, Stream Function | Exact Solutions | Drag on Spherical Particles | Creeping Flows | Nonspherical Particles

Creeping Flow Past a Sphere

Pressure, Shear Stress and Drag Variations

Variation of the pressure filed is studied in this section. The Navier-Stokes equation under creeping motion assumption in spherical coordinate system is given as

Using the expression for the velocity components as given by Equations (15) and (16), after some algebra we find

Integrating (21) and (22), it follows that

The expression for shear stress is given by

The drag force acting on the sphere then is given by

After integration, the famous Stokes drag law follows. That is

The corresponding drag coefficient is given as

where the Reynolds number is defined as



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