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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

Incompressible Viscous Flows

Two-Dimensional Plane Flows

For two dimensional flows in xy-plane as shown in Figure 1, let

Figure 1. Schematics of plane flows in a Cartesian coordinate system.

That is

and Equation (1) is satisfied.

The nonzero element of

Equation (7) in two-dimensional case reduces to

Using (10), Equation (11) may be restated as

or

Equation (13) is the equivalent to the Navier-Stokes equation and contains a single unknown .



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