Viscous, laminar, gravitationally-driven flow of a thin film over a round-crested weir is analyzed for moderate Reynolds numbers. A previous analysis of this flow utilized a momentum integral approach with a semiparabolic velocity profile to obtain an equation for the film thickness (Ruschak, K. J., and Weinstein, S. J., 1999, “Viscous Thin-Film Flow Over a Round-Crested Weir,” ASME J. Fluids Eng., 121, pp. 673–677). In this work, a viscous boundary layer is introduced in the manner of Haugen (Haugen, R., 1968, “Laminar Flow Around a Vertical Wall,” ASME J. Appl. Mech. 35, pp. 631–633). As in the previous analysis of Ruschak and Weinstein, the approximate equations have a critical point that provides an internal boundary condition for a bounded solution. The complication of a boundary layer is found to have little effect on the thickness profile while introducing a weak singularity at its beginning. The thickness of the boundary layer grows rapidly, and there is little cumulative effect of the increased wall friction. Regardless of whether a boundary layer is incorporated, the approximate free-surface profiles are close to profiles from finite-element solutions of the Navier-Stokes equation. Similar results are obtained for the related problem of developing flow on a vertical wall (Cerro, R. L., and Whitaker, S., 1971, “Entrance Region Flows With a Free Surface: the Falling Liquid Film,” Chem. Eng. Sci., 26, pp. 785–798). Less accurate results are obtained for decelerating flow on a horizontal wall (Watson, E. J., 1964, “The Radial Spread of a Liquid Jet Over a Horizontal Plane,” J. Fluid Mech. 20, pp. 481–499) where the flow is not gravitationally driven. [S0098-2202(00)01904-0]
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December 2000
Technical Papers
Thin-Film Flow at Moderate Reynolds Number
Kenneth J. Ruschak, Senior Research Associate,
e-mail: kenneth.ruschak@kodak.com
Kenneth J. Ruschak, Senior Research Associate
Manufacturing Research and Engineering Organization, Eastman Kodak Company, Rochester, NY 14752-3701
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Steven J. Weinstein, Research Associate
Steven J. Weinstein, Research Associate
Manufacturing Research and Engineering Organization, Eastman Kodak Company, Rochester, NY 14752-3701
Search for other works by this author on:
Kenneth J. Ruschak, Senior Research Associate
Manufacturing Research and Engineering Organization, Eastman Kodak Company, Rochester, NY 14752-3701
e-mail: kenneth.ruschak@kodak.com
Steven J. Weinstein, Research Associate
Manufacturing Research and Engineering Organization, Eastman Kodak Company, Rochester, NY 14752-3701
Contributed by the Fluids Engineering Division for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received by the Fluids Engineering Division December 20, 1999; revised manuscript received July 5, 2000. Associate Technical Editor: D. Williams.
J. Fluids Eng. Dec 2000, 122(4): 774-778 (5 pages)
Published Online: July 5, 2000
Article history
Received:
December 20, 1999
Revised:
July 5, 2000
Citation
Ruschak, K. J., and Weinstein, S. J. (July 5, 2000). "Thin-Film Flow at Moderate Reynolds Number ." ASME. J. Fluids Eng. December 2000; 122(4): 774–778. https://doi.org/10.1115/1.1319499
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