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Engineering Mathematics
Review of Viscous Flows
Review of Computational Fluid Mechanics

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ME 537 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

Unsteady Parallel Flows (Plate Suddenly Set in Motion)

 Consider that special case of a viscous fluid near a wall that is set suddenly in motion as shown in Figure 1. The unsteady Navier-Stokes reduces to

(1)

Figure 1. Schematics of flow near a wall suddenly set in motion.

The boundary conditions are:

(2)

(3)

The corresponding initial condition for the fluid that starts from rest is given as
(4)



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