Clarkson University
The CAMP building
Of Interest
CRCD Home
ME 437 Home
Syllabus
Assignments
Downloads
Site Map
Course Notes
Engineering Mathematics
Review of Viscous Flows
Review of Computational Fluid Mechanics

Particle Adhesion
Simulation Methods
Experimental Techniques
Applications
Search Powered by Google

The National Science Foundation
ME 437 The National Science Foundation
 Viscous Flows
Navier-Stokes Equation, Vorticity, Stream Function | Exact Solutions | Drag on Spherical Particles | Creeping Flows | Nonspherical Particles

Exact Solutions to the Navier-Stokes Equation

Oscillating Plate

Consider that case of a viscous fluid near an oscillating wall as shown in Figure 3. The unsteady Navier-Stokes reduces to

(25)

Figure 2. Schematics of flow near an oscillating wall.

The boundary conditions are:

, (26)

. (27)

Let

. (28)

Then

, (29)

, (30)

. (31)

Substituting (29)-(31) into Equation (25) it follows that

, (32)

or

, (33)

, (34)

, (35)

Thus, the velocity profile is given as

. (36)



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