Line Of Greatest Slope Research Articles

The dynamics of a disc on an inclined plane with friction in the dynamically consistent model of friction

The problem of the motion of a uniform circular disc of non-zero thickness on a fixed rough inclined plane is discussed. It is proved that, if the ratio of the coefficient of sliding friction to the slope of the plane is greater than unity, the disc comes to rest after a finite time. If this ratio is equal to unity, the limit motion of the disc is uniform slip along the line of greatest slope, and if this ratio is less than unity, the slip velocity of the disc increases without limit with time.

Risk assessment of major hazards: the effect of ground slope

Abstract Liquefied gases, such as chlorine and ammonia, are stored in large quantities at industrial sites. If released accidentally, they form a heavy gas cloud that has the potential to kill or injure large numbers of people. The dispersion of such a cloud is thus of interest to the risk assessment community [Nussey, Pantony, & Smallwood, 1992. HSE’s risk assessment tool, RISKAT. In: Major Hazards: Onshore and Offshore. pp. 607–638]. Little is understood about the effect of slope on risk. Here, the risk (probability) of being exposed to the gas cloud, given a release, is considered; probability language is needed because wind direction is assumed to be a random variable. This paper shows how the risk of being exposed to toxic gas released over a slope may be estimated using simple physical modelling. The physical model used is that of Tickle [J. Hazard. Mater. 49 (1996) 29], who showed that a finite-volume instantaneous release on an inclined plane can form a stable wedge-shaped cloud that moves down the line of greatest slope. Nonzero windspeeds are accounted for by following Tickle’s suggestion of vectorially adding windspeed to the advection induced by the slope. A range of windspeeds and slopes are considered. The slopes substantially affect the risk in the sense that the predicted risk contours are far from circularly symmetric.

Macroscopic aspects of Lüders band deformation in mild steel

Details are given of experiments on the propagation of single Lüders bands in mild steel. The results cover the effect of varying grain size on the appearance of the bands in specimens of differing cross-section, and concentrate on the macroscopic shape changes observed following the passage of the band. The results are generally consistent with a shear-flow concept [E. O. Hall, N. J. Carter and G. Vitullo, ICSMA 6, p. 393. Pergamon Press, Oxford (1983)], whereby the Lüders strain arises from a shear which creates both the macroscopic shape changes and sufficient free dislocation for the flow to continue at the lower yield stress. The shear component is strongly dependent on grain size, and at large grain sizes the Lüders band front becomes diffuse. The flow component is more nearly constant. However, the direction of shear is not in the line of greatest slope in the Lüders front, and this points to some other component, such as grip constraints or the bending moment of the specimen, as factors which may influence the shear direction. The same factors may be responsible for influencing the orientation of the Lüders band front.

Interesting results for rolling and slipping

Rolling with slipping of a uniform rigid body of revolution on a rough horizontal or inclined plane in two-dimensional motion is a standard problem in elementary dynamics; in such motion each cross section of the body of revolution remains parallel to a fixed vertical plane that is taken to contain the line of greatest slope in the case of motion on an inclined plane. Consider similar two-dimensional motion inside a fixed cylinder with general, rather than circular, cross-sectional curve C. This much more difficult problem is considerably simplified if there is no gravity force. The translational and rotational velocities of the body are then found to depend only on the change in direction of the tangent to the curve C up to the current point of contact during the motion and not on the curve itself.

Wind Regimes And Heat Exchange On Glacier De Saint-Sorlin

During the summers of 1969 and 1970, we recorded in the ablation zone of the Glacier de St-Sorlin (Massif des Grandes Rousses, France) temperature, air moisture, and wind profiles, as well as the radiation balance and the daily ablation. Numerous profiles characterize a katabatic flow following the line of greatest slope, and there appears to be a correlation between the speed of the “glacier wind” and the corresponding temperature gradients. Computed according to Prandtl’s theory of turbulent transfers, the flux of sensible and latent heat added to the radiation flux leads to theoretical values for the daily melting in good agreement with the measured values. The relative importance of the radiation balance on the melting of the snow is 57%; that of the sensible heat flux is 43%; the latent heat flux is very weak and negative.

Wind Regimes And Heat Exchange On Glacier De Saint-Sorlin

During the summers of 1969 and 1970, we recorded in the ablation zone of the Glacier de St-Sorlin (Massif des Grandes Rousses, France) temperature, air moisture, and wind profiles, as well as the radiation balance and the daily ablation. Numerous profiles characterize a katabatic flow following the line of greatest slope, and there appears to be a correlation between the speed of the “glacier wind” and the corresponding temperature gradients. Computed according to Prandtl’s theory of turbulent transfers, the flux of sensible and latent heat added to the radiation flux leads to theoretical values for the daily melting in good agreement with the measured values. The relative importance of the radiation balance on the melting of the snow is 57%; that of the sensible heat flux is 43%; the latent heat flux is very weak and negative.

The Rayleigh problem for a slightly diffusive density-stratified fluid

A doubly-infinite sloping flat plate, initially at rest in a slightly diffusive viscous density-stratified fluid, starts to move impulsively with a constant velocity along the line of greatest slope. The resulting flow is found to be an unsteady motion superimposed on a steady diffusion-induced flow, which is present throughout. Laplace transform methods give solutions which are valid either in an essentially non-diffusive outer layer or in a diffusive inner layer. The impulsive start sets up oscillations in the outer layer. These gradually die out, and a steady diffusive flow develops.A glass plate was towed vertically through stratified brine, into which aluminium particles were introduced. The flow velocities deduced from the particle motions confirmed the theoretical predictions.

Measurements of upper and lower tidal currents at Banc de la Chapelle

Measuring and analysis techniques are described for two sets of measurements of tidal currents near the surface and near the bottom at Banc de la Chapelle, a location 165 m. deep above the edge of the West European Continental Shelf. Reliable results are obtained for the semi-diurnal currents, but the scatter of the data is too great for consistent results to be extracted for the small diurnal and quarter-diurnal tidal constituents. The major axes of the mean semidiurnal current ellipses are aligned at about 30°. This direction is normal to the line of greatest slope of the shelf edge and to the main alignment of the large sand waves on the bank, which accords with a theory of formation of the latter. Bottom currents are on the average about 69% of the surface currents in magnitude. There is also some evidence for a residual drift of about 0·2 knot towards the West. An analysis is made of the errors involved in estimating the drift of a ship from Radar sights on moored buoys.

Effect of buoyancy forces on certain viscous flows with suction

In the first part of the paper the effect of gravity on the unsteady flow of a viscous incompressible fluid due to the motion of an inclined infinite porous flat plate along its line of greatest slope is discussed. The boundary layer equations are integrated for two cases: (1) when the suction velocity at the plate is constant; (2) when the suction velocity at the plate is inversely proportional to the square root of time. Explicit expressions for velocity and temperature distribution are given in both the cases for any σ (Prandtl number). In the case of a uniformly accelerated plate, it is found that for σ=1 and suction velocity proportional to t −1/2 the velocity increases with the non-dimensional parameter βg sin α. (T w−T ∞)/D and the skin friction at the plate is proportional to the square root of time. In the second part of the paper it is found that in the case of the free convection flow of a compressible fluid past an infinite flat plate subjected to suction the skin friction at the plate increases with gravity and decreases with suction.