Reciprocal systems

The principle of operation of the hydraulic reciprocating pump is similar to the beam pump, with a piston-like sub-surface pump action. The energy to drive the pump, however, is delivered through a hydraulic medium, the power fluid, commonly oil or water. The power fluid drives a downhole hydraulic motor which in turn drives the pump. A separate surface pump delivers the hydraulic power. The power fluid system can be of the closed loop or of the open type. In the latter case, the power fluids are mixed with the produced fluid stream. The performance of the hydraulic pump is primarily monitored by measuring the discharge pressures of both surface and sub-surface pumps. 

Iditional importance is that the vibrational modes are dependent upon the reciprocal e vector k. As with calculations of the electronic structure of periodic lattices these cal-ions are usually performed by selecting a suitable set of points from within the Brillouin. For periodic solids it is necessary to take this periodicity into account the effect on the id-derivative matrix is that each element x] needs to be multiplied by the phase factor k-r y). A phonon dispersion curve indicates how the phonon frequencies vary over tlie luin zone, an example being shown in Figure 5.37. The phonon density of states is ariation in the number of frequencies as a function of frequency. A purely transverse ition is one where the displacement of the atoms is perpendicular to the direction of on of the wave in a pmely longitudinal vibration tlie atomic displacements are in the ition of the wave motion. Such motions can be observed in simple systems (e.g. those contain just one or two atoms per unit cell) but for general three-dimensional lattices of the vibrations are a mixture of transverse and longitudinal motions, the exceptions... 

Of the adjustable parameters in the Eyring viscosity equation, kj is the most important. In Sec. 2.4 we discussed the desirability of having some sort of natural rate compared to which rates of shear could be described as large or small. This natural standard is provided by kj. The parameter kj entered our theory as the factor which described the frequency with which molecules passed from one equilibrium position to another in a flowing liquid. At this point we will find it more convenient to talk in terms of the period of this vibration rather than its frequency. We shall use r to symbolize this period and define it as the reciprocal of kj. In addition, we shall refer to this characteristic period as the relaxation time for the polymer. As its name implies, r measures the time over which the system relieves the applied stress by the relative slippage of the molecules past one another. In summary. 

The situation is not so simple when these various parameters are time dependent. In the latter case, the moduli, designated by E(t)and G(t), are evaluated by examining the (time dependent) value of o needed to maintain a constant strain 7o- By constrast, the time-dependent compliances D(t) and J(t)are determined by measuring the time-dependent strain associated with a constant stress Oq. Thus whether the deformation mode is tension or shear, the modulus is a measure of the stress required to produce a unit strain. Likewise, the compliance is a measure of the strain associated with a unit stress. As required by these definitions, the units of compliance are the reciprocals of the units of the moduli m in the SI system. 

The relaxation and creep experiments that were described in the preceding sections are known as transient experiments. They begin, run their course, and end. A different experimental approach, called a dynamic experiment, involves stresses and strains that vary periodically. Our concern will be with sinusoidal oscillations of frequency v in cycles per second (Hz) or co in radians per second. Remember that there are 2ir radians in a full cycle, so co = 2nv. The reciprocal of CO gives the period of the oscillation and defines the time scale of the experiment. In connection with the relaxation and creep experiments, we observed that the maximum viscoelastic effect was observed when the time scale of the experiment is close to r. At a fixed temperature and for a specific sample, r or the spectrum of r values is fixed. If it does not correspond to the time scale of a transient experiment, we will lose a considerable amount of information about the viscoelastic response of the system. In a dynamic experiment it may... 

Figure 9.38 Cavity ring-down absorption spectrum of the 0-0 band of the a Ag-X Z system of O2, where k is the reciprocal of the ring-down time. (Reproduced, with permission, from Newman, S. M., Lane, I. C., Orr-Ewing, A. J., Newnham, D. A. and Ballard, J., J. Chem. Phys., 110, 10749, 1999)...

The dimensionless quantities in brackets are, respectively, the reciprocal of the Froude number, the Euler number, and the reciprocal of the Reynolds number for the system. 

In 1840 a hydrauHc power network, which involved large reciprocating pumps that were driven by steam engines, suppHed fluid power to London. However, concurrent technology in steam (qv) turbines and the electric generators outmoded such networks until hydrauHc systems were improved with the use of rotary pumps and oil. The rotary piston pump marked the transition from use of water to oil as the hydrauHc fluid (4). The use of vacuum-distilled, refined mineral oils were instmmental in the success of rotary axial piston pumps and motors such as the Waterbury variable speed gear... 

The high solubility of the salt and resultant low water vapor pressure (58) of its aqueous solutions ate usehil ia absorption air conditioning (qv) systems. Lithium bromide absorption air conditioning technology efficiencies can surpass that of reciprocal technology usiag fluorochlorocarbon refrigerants. 

Motor-driven, multistage reciprocating compressors have reportedly been the most popular choice for aeroderivatives. Motor-driven, oil-fiooded screw compressors are also used in some cases. High horsepower, multistage centrifugal compressors, similar to those used at many pipeline compressor stations, may be required for the newer heavy-duty units if the distribution pipeline pressure is insufficient (see Pipelines). Gas turbines have more stringent fuel-gas specifications in terms of cleanliness than do gas-fired boilers. Thus oil- and water-knockout systems, coalescing filters, and fine-mesh filters are used. 

---