Journal ArticleDOI
Sliding sheets: lubrication with comparable viscous and inertia forces
E. O. Tuck,M. Bentwich +1 more
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In this article, 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 h 0 [Lt ] L from the wall.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 e = 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.read more
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The transition between the Stokes equations and the Reynolds equation: a mathematical proof
Guy Bayada,Michèle Chambat +1 more
TL;DR: In this paper, it was shown that the Reynolds equation is an approximation of the Stokes equation and that the kind of convergence is strongly related with the boundary conditions on the velocity field.
Journal ArticleDOI
Air cushioning with a lubrication/ inviscid balance
Frank T. Smith,L. Li,Guoxiong Wu +2 more
TL;DR: In this paper, the air cushioning effect in the gap between an almost inviscid body of water and a nearby solid wall is studied theoretically and is found to depend on predominantly lubricating forces in the air, in certain applications.
Journal ArticleDOI
Core-annular oil/water flow: the turbulent-lubricating-film model and measurements in a 5 cm pipe loop
TL;DR: In this article, a model for steady core-annular flow in pipes has been extended by incorporating the effect of turbulence in the water film surrounding the oil core, which predicts the pressure-gradient increase with oil velocity correctly, provided that actual wave amplitudes and wavelengths observed during these tests are used as input data.
Journal ArticleDOI
The spreading of insoluble surfactant at the free surface of a deep fluid layer
TL;DR: In this article, the spreading of an insoluble monolayer containing a fixed mass of surfaceactive material over the initially horizontal free surface of a viscous fluid layer is investigated.
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The laser interferometer skin-friction meter: a numerical and experimental study
J. D. Murphy,R. V. Westphal +1 more
TL;DR: In this article, the applicability of thin-film lubrication theory to the measurement of instantaneous skin friction has been investigated, and it is shown that the observed surface waves are not the result of a hydrodynamic instability.
References
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Journal ArticleDOI
Numerical methods in boundary-layer theory
TL;DR: There is a large variety of numerical methods that are used to solve the many flow problems to which boundary-layer theory is applied Two particular methods, the Crank-Nicolson scheme and the Box scheme, seem to dominate in most practical applications.
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Flow Development in the Hydrodynamic Entrance Region of Tubes and Ducts
TL;DR: In this paper, a new method of analysis has been devised for determining the developing laminar flow and corresponding pressure drop in the entrance region of tubes and ducts, formulated in a general manner which applies to ducts of any cross section.
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Viscous compressible and incompressible flow in slender channels
TL;DR: In this paper, an analytical study is made of viscous flow in slender channels and similar solutions to the approximate equations of motion, valid for flow at moderate or high Reynolds numbers, are found for incompressible two-dimensional and axisymmetric flows and for compressible flows through twoodimensional channels with adiabatic walls.
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A nonlinear unsteady one-dimensional theory for wings in extreme ground effect
TL;DR: In this paper, the gap-flow problem in the case of unsteady motion is reduced to a nonlinear first-order ordinary differential equation in the time variable, and some known results are recovered and generalized.
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Steady flow and static stability of airfoils in extreme ground effect
TL;DR: In this paper, a thin airfoil-like body in close proximity to a plane ground surface is analyzed on the basis of a one-dimensional, but non-linear, gap-region flow, matched to the outside via a trailing edge which may possess significant flap-like appendages.