Skip to main content Accessibility help

Sliding sheets: lubrication with comparable viscous and inertia forces

  • E. O. Tuck (a1) and M. Bentwich (a2)


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 = Uh20L. 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.



Hide All
Bentwich, M. 1978 Semi-bounded slow viscous flow past a cylinder Q. J. Mech. Appl. Maths 31, 445459.
Blottner, F. G. 1975 AGARD Lecture Series no. 73, pp. 3.13.51.
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, 417433.
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, 338347.
Tuck, E. O. 1980 A nonlinear unsteady one-dimensional theory for wings in extreme ground effect J. Fluid Mech. 98, 3347.
Tuck, E. O. 1981 Steady flow and static stability of airfoils in extreme ground effect J. Engng Maths 15, 89102.
Tuck, E. O. 1982 An inviscid theory for sliding flexible sheets. J. Austral. Math. Soc. (Ser. B) 23, 403415.
Williams, J. C. 1963 Viscous compressible and incompressible flow in slender channels AIAA J. 1, 186195.
MathJax is a JavaScript display engine for mathematics. For more information see

Sliding sheets: lubrication with comparable viscous and inertia forces

  • E. O. Tuck (a1) and M. Bentwich (a2)


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed