Technical Briefs

Flow Through a Lens-Shaped Duct

[+] Author and Article Information
C. Y. Wang

Departments of Mathematics and Mechanical Engineering, Michigan State University, East Lansing, MI 48824cywang@mth.msu.edu

J. Appl. Mech 75(3), 034503 (May 02, 2008) (4 pages) doi:10.1115/1.2840045 History: Received December 06, 2006; Revised August 27, 2007; Published May 02, 2008

The flow through a symmetric, lens-shaped duct is solved by accurate Ritz and perturbation methods. The flow rate (resistance) is found for various thickness ratios. The flow rate is much better than friction factor–Reynolds number product as an index for duct flows, especially for the lens duct studied in this paper. The results are also important for the torsion of lens-shaped bars.

Copyright © 2008 by American Society of Mechanical Engineers
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Grahic Jump Location
Figure 1

(a) Constant velocity lines for a lens duct with a thickness ratio of b=0.5. See the inset of Fig. 2 for dimensions. Values of constant velocity from the boundary: w=0, 0.02, 0.04, 0.06 and 0.08. (b) Velocity profiles w(x,0) along the x axis and w(0,y) along the y axis.

Grahic Jump Location
Figure 2

The normalized flow rate Q as a function of thickness ratio b. Dashed lines are approximations of Eq. 28 or Eq. 39. The small circle is the exact solution (Sokolnikoff and Sokolnikoff (7)). Small triangles are from Shah and Bhatti (3).




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