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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

Elliptical Pipes

Consider an elliptical cross-section pipe shown in Figure 7 with its boundary given as

(62)

We assume that the velocity field is given by

(63)

Figure 7. Elliptical cross-section pipe subject to a constant pressure gradient.

(64)

Hence

(65)

The flow rate is given as

(66)

After integration, it follows that

(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