Frictionally resisted

Note that the diffusion coefficient for a polymer through an environment of low molecular weight molecules is typically on the order of magnitude of 10"" m" sec". If the first subscript indicates the diffusing species, and the second the surrounding molecules, and P stands for polymer and S for small molecules, we see that the order of diffusion coefficients is Ds g > Dp g > Dp P sequence which makes sense in terms of relative frictional resistance. 

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. 

Fig. 7. (a) Configuration for flow turning. The frictional resistance resulting from the bend length must be added (b) pressure—loss coefficient, K, for 90°... 

Restraints ate provided to limit movements ia any number of directions (Fig. 7). For example, a siagle-directional arrangement uses a simple tie rod with pia connections (Fig. 7a). This type is favored because of low frictional resistance and positive action. Another simple arrangement utilizes a shoe and provides two functions at one poiat (Fig. 7b). Partial restraint along the pipe axis may be accompHshed as shown ia Figure 7c, and Figure 7d shows typical restraint perpendicular to the pipe axis. 

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. 

Hydraulic Gradient Hydraulic gradient, the head of hquid necessary to overcome the frictional resistance to hquid (froth) passage across the plate, is impoiTant for plate stabihty inasmuch as it is the only liquid head that varies across the length of passage. If the gradient is excessive, the upstream portion of the plate may be rendered inoperative because of increased resistance to gas flow caused by increased liqmd head (Fig. 14-34). In general the empirical criterion for stable operation is /j > 2.5/j/,g. 

As shown in Fig. 10, the nail solution applies to relatively weak interfaces, G c 1 J/m, where all the fracture events occur on one plane and the matrix holding the molecular nails does not deform but offers frictional resistance. In the next section, we explore how the fracture energy can increase by several orders of magnitude as we proceed from nails to nets. 

Viscosity and/or frictional resistance of the water, which is a function of temperature. 

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. 

Frictional resistance The resistance to fluid flow resulting from the friction between the fluid and the surrounding solid surface. 

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

The many empirical correlations advanced to represent the frictional resistance to flow vary from exact results because of the specific simplifying assumptions incorporated in each. Some relations agree in one region of flow and diverge in others. 

The resistance to flow through the various piping components that make up the. system (except vessels, tanks, pumps—items which do not necessarily provide frictional resistance to flow) such as valves, fittings, and connections into or out of equipment (not the loss through the equipment) are established by test and presented in the published literature, but do vary depending on the investigator. 

Friction resistance to flow inside tubes, flow rate into tubes (per tube) ... 

Note that for preliminary calculations, the frictional resistances in piping can be neglected but should be included in final calculations, particularly at high recirculation ratios. 

Start the mud pump, running as slowly as possible, to pump fluid at a rate of 1.5 to 2.0 bbl/min. This reduces fluid friction resistance pressures to a minimum and pumps at minimum standpipe pressure for circulation. The standpipe pressure (for 1.5 to 2.0 bbl/min) can be found from standard fluid hydraulic calculations. 

Table 22.9 Water-carrying capacity of pipes (SI units) (approximate frictional resistance in mbar per m of travel)...

Finally, the condensate is often pumped from the receiver to the boiler house. Pumped condensate lines carry only water, and rather higher water velocities can often be used to minimize pipe sizes. The extra friction losses entailed must not increase back pressures to the point where pump capacity is affected. Table 22.10 can be used to help estimate the frictional resistance presented by the pipe. 

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. 

Lubrication, in the generally accepted sense of the word, means keeping moving surfaces completely separated by means of a layer of some liquid. When this is satisfactorily achieved, the frictional resistance no longer depends on the solid surfaces but solely on the internal friction of the liquid, which, in turn, is directly related to its viscosity. The more viscous the fluid, the greater the resistance, but this is never comparable with that existing between non-lubricated surfaces. 

Boundary lubrication is perhaps best defined as the lubrication of surfaces by fluid films so thin that the friction coefficient is affected by both the type of lubricant and the nature of the surface, and is largely independent of viscosity. A fluid lubricant introduced between two surfaces may spread to a microscopically thin film that reduces the sliding friction between the surfaces. The peaks of the high spots may touch, but interlocking occurs only to a limited extent and frictional resistance will be relatively low. 

Receivers are commonly made of steel tuhe with welded dished ends, and are located horizontally. Small receivers may he vertical, for convenience of location. The liquid drain pipe from the condenser to the receiver should he amply sized, and any horizontal runs sloped to promote easy drainage. Shut-off valves in this line should not he in a horizontal outlet from the condenser, since their slight frictional resistance will cause liquid hack-up in the condenser. Oudet pipes from the receiver may he from the bottom or, by means of an internal standpipe, may leave at the top. A valve is invariably fitted at this point. 

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