Inclined plane

Summary

An inclined plane, also known as a ramp, is a flat supporting surface tilted at an angle from the vertical direction, with one end higher than the other, used as an aid for raising or lowering a load. The inclined plane is one of the six classical simple machines defined by Renaissance scientists. Inclined planes are used to move heavy loads over vertical obstacles. Examples vary from a ramp used to load goods into a truck, to a person walking up a pedestrian ramp, to an automobile or railroad train climbing a grade. Moving an object up an inclined plane requires less force than lifting it straight up, at a cost of an increase in the distance moved. The mechanical advantage of an inclined plane, the factor by which the force is reduced, is equal to the ratio of the length of the sloped surface to the height it spans. Owing to conservation of energy, the same amount of mechanical energy (work) is required to lift a given object by a given vertical distanc

Official source

https://en.wikipedia.org/wiki/Inclined_plane

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Simulating Viscoplastic Avalanches

Martin Rentschler

This is a numerical investigation of a yield-stress fluid flowing down an inclined plane. A three-dimensional, free-surface, two-phase incompressible Navier-Stokes solver is extended to handle generalized Newtonian fluids. Special attention is spent on the treatment of the non-Newtonian fluid close to the free-surface and on the boundaries, to get consistent values for the viscosity in those domains. The core of the solver is a projection method that is extended by an implicit solver for the stress terms in order to cope with high viscosities. This numerical tool is tested against experimental data of dam break experiments on an inclined plane, which were conducted in the Laboratoire d'hdraulique environnementale (LHE) at the École polytechnique fédérale de Lausanne (EPFL). After the numerical tool is validated by these experimental data, I investigate the flow structure of a yield-stress fluid inside unsteady flows on the inclined plane and inside the inclined channels. Some typical phenomena like the formation of levees and plug domains are reproduced. As in the numerical simulation all physical variables are accessible, the mechanisms inside these flows is analyzed. Looking at the energy dissipation process shows that for the Herschel-Bulkley fluids most of the energy is dissipated where the local Bingham number is close to one.

EPFL2010

The jamming transition is accompanied by a rich phenomenology such as hysteresis or nonlocal effects that is still not well understood. Here, we experimentally investigate a model frictionless granular layer flowing down an inclined plane as a way to disentangle generic collective effects from those arising from frictional interactions. We find that thin frictionless granular layers are devoid of hysteresis of the avalanche angle, yet the layer stability increases as it gets thinner. Steady rheological laws obtained for different layer thicknesses can be collapsed into a unique master curve, supporting the idea that nonlocal effects are the consequence of the usual finite-size effects associated with the presence of a critical point. This collapse indicates that the so-called isostatic length l*, the scale on which pinning a boundary freezes all remaining floppy modes, governs the effect of boundaries on flow and rules out other propositions made in the past.

AMER PHYSICAL SOC2021

Rayleigh-Taylor instability under an inclined plane

Gioele Mariano Nicolò Balestra, Pierre-Thomas Paul Brun, François Gallaire, Pierre Rieu

We revisit the canonical Rayleigh-Taylor instability and investigate the case of a thin film of fluid upon the underside of an inclined plane. The presence of a natural flow along the plane competes with the conventional droplet forming instability. In particular, experiments reveal that no drops form for inclinations greater than a critical value. These features are rationalized in the context of the absolute/convective analysis conducted in this article.

2015