Force tangential

The boundary conditions at the z=0 surface arise from the mechanical equilibrium, which implies that both the nonnal and tangential forces are balanced there. This leads to... 

Tangential forces from air compression act on the blades and are transmitted through the fan hub to the shaft ia the form of a resisting torque. 

Figure 5-22b shows this phenomenon. When contact is made between the surface and the rotating shaft, the coulomb friction will induce a tangential force on the rotor. This friction force is approximately proportional to the... 

Since/is a tangential force, only the vector projection of the area is effective. Integrating these forces from 0 to Ti/2,f s given by equation 9.1-1 which is more easily done by a change of variables giving/= p r, and the stress is j Equation 9.1-2 gives... 

Viscosity is the shear resistance between adjacent fluid layers. Consider in Fig. 4.1 the shearing action between two parallel planes, each of area A, separated by a distance Y. The tangential force F for a given area required to slide one plate over the other at a velocity (v) parallel to each other is... 

To force the air to flow through the impeller blades of a centrifugal fan, a tangential force is needed. According to the momentum law this force is... 

There are two possible kinds of force acting on a fluid cell internal stresses, by which an element of fluid is acted on by forces across its surface by the rest of the fluid, and external forces, such as gravity, that exert a force per unit volume on the entire volume of fluid. We define an ideal fluid to be a fluid such that for any motion of the fluid there exists a pressure p(x, t) such that if 5 is a surface in the fluid with unit normal vector n, the stress force that is exerted across S per unit area at x at time t is equal to —p x,t)h. An ideal fluid is therefore one for which the only forces are internal ones, and are orthogonal to 5 i.e. there are no tangential forces. ... 

The surface force apparatus (SFA) is a device that detects the variations of normal and tangential forces resulting from the molecule interactions, as a function of normal distance between two curved surfaces in relative motion. SFA has been successfully used over the past years for investigating various surface phenomena, such as adhesion, rheology of confined liquid and polymers, colloid stability, and boundary friction. The first SFA was invented in 1969 by Tabor and Winterton [23] and was further developed in 1972 by Israela-chivili and Tabor [24]. The device was employed for direct measurement of the van der Waals forces in the air or vacuum between molecularly smooth mica surfaces in the distance range of 1.5-130 nm. The results confirmed the prediction of the Lifshitz theory on van der Waals interactions down to the separations as small as 1.5 nm. 

Fig. 33—Typical scratch curve of Sample 4, Fn is the normal load. Ft is the measured tangential force, Pd is the penetration depth, Rd is the residual depth. The critical load is 86.63 mN.

Figure 33 shows a typical scratch test curve of Sample 4. Both the penetration depth and the residual depth as well as the tangential force can be obtained from this curve. The critical load can be found from the transition stages plotted in the three curves. The critical load (L ) of Sample 4 is 86.63 mN. 

The friction coefficient is defined as the tangential force acting on a sliding body to the ground reaction force. For rubbers this is a function of the ground pressure. Its dependence has been discussed sufficiently in the literature where it was shown that this is important for soft rubbers on smooth surfaces [2,3], but is of little influence for tire compounds on roads which are always sufficiently rough for the load dependence to be small if not completely absent [4,5]. 

The dynamic (absolute) viscosity is the tangential force per unit area required to move one horizontal plane with respect to the other at a unit velocity when maintained at a unit distance apart by the fluid. The readers are referred to Equations 18.1 and 18.2 for the dynamic viscosity. 

Visser uses the preceding equation for the tangential force, and makes the additional assumption of laminar flow near the wall to arrive at the following equation ... 

That is, the removal of spherical particles from a flat surface is determined by the magnitude of the wall shear stress, x0. Visser (1) also claims that since the removal mechanism is unknown, it is not possible to relate the Fh (tangential force) to the Fa (adhesive force) on theoretical grounds. Therefore, he assumes that the tangential force required for particle release is proportional to the adhesive force. 

The most useful method of measuring surface tension is by the well-known Wilhelmy plate method. If a plate-shaped metal is dipped in a liquid, the surface tension forces will be found to produce a tangential force (Figure 2.13). This is because a new contact phase is created between the plate and the liquid. 

Tangential force per centimeter of surface = qs x (rate of strain) (4.5)... 

The geometrical force balance is considered only in the X-Y plane. This assumes that the liquid does not affect the solid surface (in any physical sense). This assumption is safe in most cases. However, only in very special cases, if the solid surface is soft (such as with contact lens), then tangential forces will also need to be included in this equation (as extensively described in the literature). There exists extensive data that convincingly support the equation for liquids and solids. 

When there is no tangential force (or no transmission of angular momentum) across the liquid—sphere interface, the sphere slips within the liquid. Within the hydrodynamic theory, the rotational relaxation time is negligible for an inertialess slippery sphere. A variable coefficient of slip (or stick), j3, may be introduced. As 3 tends from 0 to 00 the rotational relaxation time increases from 0 to r)V/kT [221, 222]. 

Some investigators believe that the best course to follow in scratch hardness determination is to find the tangential force acting on the surface of material under test required to obtain a scratch of width b. In this case, hardness is expressed as the ratio of that force to the scratch cross-section or a magnitude proportional to it, or else as a quotient of the work necessary to produce the scratch and its volume. Proponents of this method (Yushkin, 1971) consider that scratch hardness tests in the present form play only a marginal role. Unlike Shreyner (1949), who contended that the results obtained under these methods are less accurate than those for mineral-bymineral scratch after Mohs, they accept that these tests have certain usefulness, but only of a complementary nature. The differences of opinion arise from the different approach to the question of accuracy of the method of determination itself, since as can readily be proved, a strict relationship exists between hardness defined as the ratio of load P to square of... 

PRESSURE. If a body of fluid is at rest, the forces are in equilibrium or the fluid is in static equilibrium. The types of force that may aci on a body are shear or tangential force, tensile force, and compressive force. Fluids move continuously under the action of shear or tangential forces. Thus, a fluid at rest is free in each part from shear forces one fluid layer does not slide relative to an adjacent layer. Fluids can be subjected to a compressive stress, which is commonly called pressure. The term may be defined as force per unit area. The pressure units may be dynes per square centimeter, pounds per square foot, torr. mega-Pascals, etc. Atmospheric pressure is the force acting upon a unit area due to the weight of the atmosphere. Gage pressure is the difference between the pressure of the fluid measured (at some point) and atmospheric pressure. Absolute pressure, which can be measured by a mercury barometer, is the sum of gage pressure plus atmospheric pressure. 

In the previous sections, only the normal contact of two elastic spheres with perfect smooth surfaces (i.e., no tangential force) is considered. However, for oblique contact between two frictional spheres, tangential forces are encountered, and, consequently,... 

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