Frictional resistive force

Similarly, for the frictional resistive force, Ff, lumping the geometry factors into a constant, c, and letting a = friction coefficient ... 

Pzd = dynamic frictional resisting force based on the friction foi ce generated at the mean diameter of the raised area of the thrust washer, lb. 

Due to a nonzero acceleration [flflz/Af 0), the velocity of the particle increases the frictional resistive force (the drag force) also increases. In many systems, after some time the particle acceleration in the stagnant fluid becomes zero and the particle velocity becomes constant This velocity is called the terminal velocity. We express the resistive force vector on the particle as -/ Up-, when Up is the terminal velocity, for the z-component. 

Vf = frictional resistance force In order to avoid shear loading on the anchor holts ... 

Another parameter that plays an important role in unifying viscosity, diffusion, and sedimentation is the friction factor. This proportionality factor between velocity and the force of frictional resistance was introduced in Chap. 2, and its role in interrelating the topics of this chapter is reflected in the title of the chapter. 

Power. The power requited to drive a belt conveyor is derived from the tensile forces requited to propel or restrain the belt at the design speed. These include the tensile forces produced by the frictional resistance of the drive, conveyor components, and material the acceleration of the material and the gravitational forces requited to lift or lower the material. Detailed information and methods of calculation can be found in belt conveyor design handbooks and in Reference 9. 

Bending or torsional flexibihty may be provided by bends, loops, or offsets by corrugated pipe or expansion joints of the bellows type or by other devices permitting rotational movement. These devices must be anchored or otherwise suitably connected to resist end forces from fluid pressure, frictional resistance to pipe movement, and other causes. 

The total resistance is the sum of friction and eddy resistances. Both factors act simultaneously, but their contribution in the total resistance depends on the conditions of the flow in the vicinity of the particle. Hence, for the most general case the resistance force is a function of velocity, w, density, p, viscosity, the linear size of a particle, C, and its shape, ijr. Thus,... 

A fluid can be considered as being liquid, which is incompressible, or a gas, which is easily compressible. When a force of sufficient magnitude is applied to a fluid, motion will occur provided the frictional resistance within an open system is overcome. 

Pumping The act of forcing a fluid along a conduit by overcoming frictional resistance. 

Liquids in motion have characteristics different from liquids at rest. Frictional resistances within the fluid, viscosity, and inertia contribute to these differences. Inertia, which means the resistance a mass offers to being set in motion, will be discussed later in this section. Other relationships of liquids in motion you must be familiar with. Among these are volume and velocity of flow flow rate, and speed laminar and turbulent flow and more importantly, the force and energy changes which occur in flow. 

Friction is the resistive force that we experience when we try to slide one object over the surface of another. The coefficient of friction is the ratio of the lateral force required to slide the surfaces past one another relative to the force holding them in contact. Polymers exhibit two coefficients of friction the static coefficient of friction is a measure of the force required to initiate movement, the dynamic coefficient of friction is a measure of the force required to sustain movement at a constant rate. In general, the force required to initiate sliding is somewhat greater than that required to maintain a constant rate of movement. 

A typical piping application starts with a specified flow rate for a given fluid. The piping system is then designed with the necessary valves, fittings, etc. and should be sized for the most economical pipe size, as discussed in Chapter 7. Application of the energy balance (Bernoulli) equation to the entire system, from the upstream end (point 1) to the downstream end (point 2) determines the overall net driving force (DF) in the system required to overcome the frictional resistance ... 

This P -I type of response curve can also be easily shown to apply to a simple rigid-plastic mechanical system, in the manner shown in Figure 16 (see Refs. 15 and 22). Here, the spring in the system is replaced with a pure Coulomb friction element, with resisting force f, which is independent of displacement once the mass starts to move. All other symbols are defined above. 

Most sanitary and combined sewer networks consist of pipes designed to flow as open channels, i.e., with a free water surface. The wastewater flows downstream in such pipes by the force of gravity with a velocity of flow that depends principally on the pipe slope and frictional resistance. Typically, the design velocity is between 0.6 and 3 m s-1 to avoid blockage of the pipe by sewer solids accumulated at low flow conditions and to prevent damage of the sewer at a high flow. 

Friction resistance under the spread footings combined with passive resistance will be used to resist lateral forces, The following lateral forces are computed in terms of load per unit length of wall even though much of the toads will be resisted by individual spread footings. Frictional resistance is a function of vertical loads, not footing width. 

The electrophoretic driving force for a particle to move, depending on the electric held strength (E) and the net charge on the particle (z), is balanced by the frictional resistance if) which the particle must overcome to migrate. 

The velocity times the Stoke s friction factor gives the viscous resistive force ... 

The liquid state is a condensed state, so each molecule is always interacting with a group of neighbours although diffusing quite rapidly. As a result, although momentum through a shear plane still occurs, it is a small contribution when compared to the frictional resistance of the molecules in adjacent layers. It is the nature of this frictional resistance that we must now address and it will become clear that it arises from the intermolecular forces. The theories of the viscosity of liquids are still in an unfinished state but the physical ideas have been laid down. The first... 

Powder compaction may also be achieved in roll processes, including briquetting, in which compression takes place between two rollers rotating at the same speed—that is without producing any shearing action. In pellet mills, a moist feed is forced through die holes where the resistance force is attributable to the friction between the powder and the walls of the dies. 

The friction factor, which is plotted against the modified Reynolds number, is Pi/pu, where R is the component of the drag force per unit area of particle surface in the direction of motion. R can be related to the properties of the bed and pressure gradient as follows. Considering the forces acting on the fluid in a bed of unit cross-sectional area and thickness /, the volume of particles in the bed is /(I — e) and therefore the total surface is 5/(1 — e). Thus the resistance force is R SH — e). This force on the fluid must be equal to that produced by a pressure difference of AP across the bed. Then, since the free cross-section of fluid is equal to e ... 

The friction group resistance force per unit particle surface (Ri) and the interstitial velocity. 

A decrease in the amplitude of an oscillation as a result of energy loss from a system owing to frictional or other resistive forces. 

Capillary rheometers are used extensively to measure viscosity in the intermediate to high shear rate range. The rheometer has for all practical purposes a lower limit in viscosity measurement because of the plunger seals. These seals are shown on the bottom of the plunger in Fig. 3.16, and they induce a frictional resistance when they are pushed through the rheometer barrel. The piston force can be evaluated without polymer in the barrel, but it is always a source of error at low viscosities because of experimental variability. Moreover, barrel friction is one of the critical corrections that must be made when evaluating viscosity measurements... 

A measure of the frictional resistance that a fluid in motion offers to an apphed shearing force. Let F be the frictional force, and let S be the area of the interface between a stationary surface plane and a fluid with velocity dv/dr. Then the resisting or frictional force is given as ... 

---