Force tractive

Schlepp-kraft /. tractive force, -miihle /. drag mill, drag-stone mill. 

The physical transport of particles in a river occurs by two primary modes bedload and suspended load. Bedload consists of material moved along the bed of the river by the tractive force exerted by flowing water. Bedload may roll or hop along the bottom, and individual particles may remain stationary for long periods of time between episodes of movement. Suspended load consists of material suspended within the flow and that is consequently advected by flowing water. Rivers and streams are naturally turbulent, and if the upward component of turbulence is sufficient to overcome the settling velocity of a particle, then it will tend to remain in suspension because the particles become resuspended before they can settle to the bottom of the flow. Suspended load consists of the finest particles transported by a river, and in general is composed of clay- and silt-sized... 

They also have an impact on runoff characteristics as well as many physical parameters of rivers and streams. For instance, hydraulic attributes (width of water level, flow velocity, depth, tractive force, or shear stress) and hence the bed-load regime and temperature can alter the natural state. 

By trapping the sediment from used alpine waters, reservoirs reduce the transport of suspended load to residual flow reaches. In these sections with a reduced channel flow, the tractive force and shear stress is drastically reduced. This additionally reduces the bed load transport, which may then result in solid matter originating from unaffected tributary streams remaiiung in the main channel, thus significantly increasing the debris-flow hazard for episodic high water discharge [36]. 

III) Kramer s Modulus—Kramer (1935), in studies on tractive forces involved in model channels, developed an expression for measuring uniformity which depends on the ratio of the areas above and below the 50 percent line, as indicated in Figure 13. Kramer s uniformity modulus is the ratio of the area below to the area above this line. The modu-... 

The second theory is called the tractive-force theory and utilizes the concept of current drag or Geschiebe required to move particles of a given size. Later we shall develop the underlying basis of tractive force, but for the moment we merely note that it is distinguishable from the velocity theory in that the movement of a particle by a stream varies as the depth and slope of the stream. 

In the velocity theory above developed it is apparent that while fundamentally sound, the chief difficulty in practice concerns the measurement of bed velocities. This has been overcome in part by Rubey s analysis of the subject, and By the general theory of Kennedy and Lacey. However, in recent years studies of silt movement have utilized DuBoys (1879) expression of tractive force. This expression is simple and convenient and involves the basic elements of channel hydrology depth and slope. Tractive force means the force activity on the bed causing movement of the particulate material. The force required to impart initial motion to the bed material is called the critical tractive force. General movement is defined as the condition where particles up to and including the largest composing the bed are in motion. 

DuBoys expression for the tractive force may be derived iti the following manner Consider a channel with a uniform flow of water of depth L if no resistance is offered to the flow the kinetic energy of a... 

This is DuBoys equation for tractive force. The equation makes no allowance for internal friction and turbulence, bed friction, or movement of bed load. However, in spite of these omissions, it has been found that for a given bed material, the movement is proportional to the tractive force. DuBoys equation for the rate of movement of silt was of the form... 

Kramer s Equation—Kramer (1935) made a series of measurements of flume traction in which the important variables (including particle-size) were carefully controlled. Kramer s equation of the critical tractive force was as follows ... 

Work of U. S. Waterways Experiment Station—The most comprehensive study of silt movement in recent years is that by the Corps of Engineers (1935a), published by the U. S. Waterways Experiment Station. To some extent this study followed the pattern used by Kramer, but included more different kinds of material. The mean sizes for eight of the sands composing the beds ranged from 0.205 to 0.586 mm for one other sand the mean size was 4.08 mm. The sand, having a mean diameter of 0.586 mm, had a uniformity modulus of 0.280 all the others had moduli of approximately 0.5. The critical tractive-force equation obtained was... 

Calculate the critical tractive force on a flume bed of sand whose average diameter is 0.033 in. and Kramer s modulus 0.44. Take the specific gravity of sand as 2.65. 

Using the data of Problem 1 and assuming the particles to be spherical, compute the critical tractive force by means of Chang s equation. 

Fig. 2.31 Schematic illustration of cantilever torsion while (a) sliding up and (b) sliding down on a sloped surface (in the x direction). While sliding across a sloped surface with angle 6, the acting forces (the applied load L, the horizontal tractive force T, the adhesion force A, the reaction force from the surface acting on the tip with a component N in the surface normal direction and a component/(friction force) parallel to the surface) and the torsion momentum M are in equilibrium and depend on the direction of motion - uphill and downhill, denoted here with subscripts u and d, respectively, cp represents the torsion angle of the cantilever, which is proportional to the friction force h and t stand for tip height and cantilever thickness, respectively (reproduced with permission from [18]. Copyright 2006 American Chemical Society)...

Figure 7-11. Dead-weight tractive force method for measurement of friction, (a) Schematic diagram of apparatus. A Plate. B Block. T Telescope. W Loading weight. (b) Displacement as a function of time steel on indium load 2.94 N tractive force 1.96 N. After Burwell and Rabinowicz [10].

Tangential force coefficients can be determined by direct measurement of the tangential tractive force and the normal loading force of the system, but the ratio A /A is usually obtained by indirect methods. McFarlane and Tabor [9] found that the adhesion of indium to steel under the influence of a normal preload was so strong that the tractive force to initiate sliding after removal of the preload was essentially a measure of the shear force in indium. From this measurement they calculated a value of a =3.3 for indium. Courtney-Pratt and Eisner [10] evaluated A /A by electrical resistance and obtained a value of a = 11.66 for platinum. 

Figure 8-12 shows some typical results for platinum against platinum and for steel against steel. The tangential traction coefficient ((i = T/N, where T is the tangential tractive force and N is the normal loading force. The displacements at low values of T are almost entirely irreversible when T is relaxed and hence are due to the plastic shear of asperity junctions. The tangential traction coefficient approaches the coefficient of friction (as measured in the usual way) while the dis-... 

Let us consider the behavior depicted in Fig. 7-5b in terms of the asperity-junction mechanism for the boundary-lubricated case. The asperities actively in contact are classified into two categories bare asperities, and asperities protected by a film of lubricant. The junction strength concept gives the expression below for the tangential tractive force required for sliding ... 

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