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  • Print publication year: 2011
  • Online publication date: February 2012

8 - Viscous Incompressible Flow


External aerodynamics was a disturbingly mysterious subject before Prandtl solved the mystery with his work on boundary layer theory from 1904 onwards.

L. Rosenhead, Laminar Boundary Layers, Oxford 1963


This chapter examines the role of viscosity in the flow of fluids and gases. Although the viscosity of air is small, it must be included in a flow model if we are to explain wing stall and frictional drag, for example. The four preceding chapters are concerned with the analysis of airfoils, wings, and bodies of revolution based on an assumption of inviscid flow (i.e., negligible viscous effects). The inviscid-flow model allowed analytical solutions to be developed for predicting, with satisfactory accuracy, the pressure distribution on bodies of small-thickness ratio at a modest (or zero) angle of attack. However, the inviscid-flow model leads to results that are at odds with experience, such as the prediction that the drag of two-dimensional airfoils and right-circular cylinders is zero. This contradiction is resolved by realizing that actual flows exhibit viscous effects.

Viscosity is discussed from a physical viewpoint in Chapter 2. In Chapters 5, 6, and 7, the existence of viscosity is acknowledged when it is necessary to advance an analytical derivation for an inviscid flow. Also, viscous effects are called on, with words like viscous drag and separation, when comparing the predicted and observed behavior of airfoils and wings. However, no analysis in this textbook has been developed thus far that provides the required detailed physical basis for these effects.

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References and Suggested Reading
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Gad-El-Hak, M. 1989
Hiemenz, K. 1911
Holmes, B. J.Croom, C. C.Hastings, E. C.Obara, C. J.Van Dam, C. P. 1988
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Howarth, L. 1938
Lauchle, G. C. 1991
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Pohlhausen, E. 1921
Raymer, D. P.Aircraft Design, A Conceptual ApproachAmerican Institute of Aeronautics and AstronauticsWashington, DC 1989
Roach, R. L.Nelson, C.Sakowski, B. A.Darling, D. D.van de Wall, A. G. 1992
Schlichting, E. H.Gersten, E. H.Boundary Layer TheorySpringer-VerlagBerlin 2003
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Thwaites, B. 1949
White, F. M.Fluid MechanicsMcGraw-Hill Book CompanyNew York 1986
White, F. M.Viscous Fluid FlowMcGraw Hill Book CompanyNew York 1974