Frictional force total

The radioautographic work suggests another model illustrated in Fig. XII-11. The load is supported over area A, with metal contacts of shear strength s over a portion of the area ctA and film-film contacts of shear strength Sf over the rest of the area. In analogy to Eq. XII-9, one can write the total frictional force, F as... 

The total friction force, F, (lb) acting tangent to the sheave is fF ... 

For the flow of a fluid in a pipe of length / and diameter d, the total frictional force at the walls is the product of the shear stress R and the surface area of the pipe (Rndl). This frictional force results in a change in pressure A Pf so that for a horizontal pipe ... 

Equation 11.21 gives the point values of R and R/pu2s at x = x. In order to calculate the total frictional force acting at the surface, it is necessary to multiply the average value of R between x = 0 and x = x by the area of the surface. 

Tire traction describes the force transmission between tire and road under aU eventualities. It is the prerequisite for controlled steering, acceleration, and braking of self-propelled vehicles on flat tracks. It finds its upper limit in the frictional force when total sliding occurs. Two aspects have therefore to be considered The mechanics of force transmission of elastic wheels and its relation to rubber friction. 

In the free-draining case sy/2 is also the relative velocity of the medium in the vicinity of a bead at a distance s from the center. Hence the frictional force acting on the bead is sy/2, and the rate of energy dissipation by the action of the bead is the product of the force and the velocity, or sy/2y. The total energy dissipated per unit time by the molecule will be given by the sum of such terms for each bead, or... 

In a fluidised bed the total frictional force must be equal to the effective weight of bed. Thus ... 

In a sedimenting suspension, however, the gravitational force on any individual particle is balanced by a combination of buoyancy and fluid friction forces, both of which are influenced by the flow field and pressure distribution in the vicinity of the particle. It is a somewhat academic exercise to apportion the total force between its two constituent parts, both of which are influenced by the presence of neighbouring particles, the concentration of which will determine the magnitude of their effect. 

In a fluidised bed, the total frictional force on the particles must equal the effective weight of the bed. Thus, in a bed of unit cross-sectional area, depth l, and porosity e, the additional pressure drop across the bed attributable to the layout weight of the particles is given by ... 

In simple terms, the onset of fluid motion may be qualitatively understood in terms of the sedimentation of an object in a fluid at unit gravity. The total force F acting on the object of critical volume Vc is equal to the sum of the buoyancy force and frictional force such that... 

Along with the frictional force on a bead, given by Eq. (9), there will be in general other forces F-, derived in part from the potential energy U that holds the polymer chain together, and in part from external sources, e.g., electric or centrifugal fields. The total force on the y th bead is thus Fj + F/. 

As the number of counter-ions exceeds the number of co-ions by far, the total electrical force exerted on the counter-ions is higher than that exerted on the co-ions. This gives rise to a resulting friction force on the solvent in the same direction as the flow of the counter-ions. 

Another questionable assumption is that of constant temperature. Frictional forces lead to surface-heat generation. The total power introduced through the shaft is partly dissipated into heat at the barrel, flights, and root of the screw surfaces, and is partly used to generate pressure. However, most of the power is dissipated into heat at the barrel surface (Fig. 9.30). This quantity is given by the product of the force F and the relative velocity between barrel surface and solid plug (35)... 

The proportionality between the area of real contact and the applied load supplies at last a rational explanation of the well-known Amontons 1 or Coulomb s2 law of friction, that the frictional force F is directly proportional to the total load P pressing the surfaces together. The meaning of this law has long been mysterious. Under ordinary circumstances the law holds fairly accurately, i.e. there exists a nearly constant coefficient of friction, /x = F/P. The frictional force is naturally proportional to the total area of these bridges consequently the frictional force should be proportional to the load. 

Equation (10) was shown to follow from a thermally activated model of Eyring s type, that is a stress-assisted thermally activated process for viscous flow [154]. For rough surfaces the area of true molecular contact is very small and, hence, the adhesion contribution to the total friction force is usually negligible, as manifested by a zero friction at zero load [148]. Yet in the microscopic limit of the SFM experiment employing a comparatively sharp... 

Where one or both of the contacting surfaces becomes permanently deformed during sliding, the energy required to produce the deformation represents an additional component of the friction force. For engineering surfaces the amount of permanent deformation which can be tolerated is very limited so that the deformation friction is small in comparison with the adhesive friction. Elastic deformation only makes a significant contribution to the total friction when there is a high level of hysteresis in the elastic recovery, such as in vehicle tyres, and this is not normally a consideration when molybdenum disulphide is used. For practical purposes it can therefore be assumed that adhesive friction is the only type of friction which needs to be considered. 

With a typical Ng value of 100, only very long grafted chains are in the regime with more them one entanglement per trapped P chain. In the simple regime with N < Ng2, the total friction force experienced by the N chain is... 

Once the average friction coefficient C is available, the drag (or friction) force over the surface can be determined from Rq. 7-1. In this case/1 is the surface area of the plate exposed to fluid flow. When both side.s of a thin plate are subjected to flow, A becomes the total area of the top and bottom surfaces. Note that the friction coefficient, in general, varies with location along the surface. 

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