Hostname: page-component-745bb68f8f-5r2nc Total loading time: 0 Render date: 2025-02-12T01:47:40.477Z Has data issue: false hasContentIssue false
  • English
  • Français

Sliding sheets: lubrication with comparable viscous and inertia forces

Published online by Cambridge University Press:  20 April 2006

E. O. Tuck  and
M. Bentwich
E. O. Tuck
Affiliation:
Applied Mathematics Department, University of Adelaide
M. Bentwich
Affiliation:
Department of Fluid Mechanics and Heat Transfer, Tel Aviv University
Get access Rights & Permissions [Opens in a new window]

Abstract

A rigid plane thin sheet is sliding steadily at speed U close to a plane wall, in a fluid of kinematic viscosity v. The sheet is infinitely wide and is of length L in the direction of motion, and its leading edge is a distance h0 [Lt ] L from the wall. A solution is sought for arbitrary finite values of R = Uh20/νL. In the limit as ε = h0/L→0, the problem reduces to that of solving the boundary-layer equation in the gap region between sheet and wall, and this is done here both by an empirical linearization, and by direct numerical methods. The solutions have the property that they reduce to those predicted by lubrication theory when R is small, and to those predicted by an inviscid small-gap theory when R is large. Special attention is paid to the correct entrance and exit conditions, and to the location of the centre of pressure.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 135 , October 1983 , pp. 51 - 69
Copyright
© 1983 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bentwich, M. 1978 Semi-bounded slow viscous flow past a cylinder Q. J. Mech. Appl. Maths 31, 445–459.Google Scholar
Blottner, F. G. 1975 AGARD Lecture Series no. 73, pp. 3.1–3.51.
Cameron, A. 1966 Principles of Lubrication. Longmans.
Keller, H. B. 1975 Some computational problems in boundary-layer flows. In Proc. 4th Intl Conf. Numer. Meth. Fluid Dyn. (ed. R. D. Richtmyer). Lecture Notes in Physics, vol. 35, pp. 1–21. Springer.
Keller, H. B. 1978 Numerical methods in boundary layer theory Ann. Rev. Fluid Mech. 10, 417–433.Google Scholar
Michell, A. G. M. 1950 Lubrication. Blackie.
Newman, J. N. 1977 Marine Hydrodynamics. M.I.T. Press.
Schlichting, H. 1960 Boundary Layer Theory, 4th edn. McGraw-Hill.
Sparrow, E. M., Lin, S. H. & Lundgren, T. S. 1964 Flow development in the hydrodynamic entrance region of tubes and ducts Phys. Fluids 7, 338–347.Google Scholar
Tuck, E. O. 1980 A nonlinear unsteady one-dimensional theory for wings in extreme ground effect J. Fluid Mech. 98, 33–47.Google Scholar
Tuck, E. O. 1981 Steady flow and static stability of airfoils in extreme ground effect J. Engng Maths 15, 89–102.Google Scholar
Tuck, E. O. 1982 An inviscid theory for sliding flexible sheets. J. Austral. Math. Soc. (Ser. B) 23, 403–415.Google Scholar
Williams, J. C. 1963 Viscous compressible and incompressible flow in slender channels AIAA J. 1, 186–195.Google Scholar