Example 2-15 Parallel System Fraction Paralleled

Determine the portion of a 30-mile, 18-in. (17.124-in. I.D.) line which must be paralleled with 20-in. (19.00-in. I.D.) pipe to raise the total system capacity 1.5 times the existing rate, keeping the system inlet and outlet conditions the same. 

Pressure-Base Multipliers For Quantity Temperature-Base Multipliers For Quantity  

New Pressure Base, Lbs./sq.in. abs. Multiplier New Temperature Base, 0 F. Multiplier 

Through High Pressure Transmission Lines, Monograph No. 6, U.S. Dept, of Interior, Bureau of Mines, Washington, DC. 100 1.0769 

Applied Process Design for Chemical and Petrochemical Plants 

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There are six KBIs for each ternary system that could be presented in a three-dimensional triangular prism. It was expedient, however, to show the results in terms of sections parallel to a side of the triangular base. In such sections, for example, the mole fraction Xq is kept constant and is varied between 0 and 1 - Xc while Xg =... 

Both types of detector systems can be used in two modes of applications, i.e., on-line and off-line. In the on-line mode the fractionation and detection systems are directly coupM. It is possible to use more than one detector either in series or in parallel. Examples of this mode of detection will be given in the section dealing with combined techniques. The off-line mode involves the collection of the fractions with subsequent determination of the constituents. The advantage of this approach is that further sample pretreatment procedures could be applied where necessary before the constituents are detected. In addition, quantitative estimates of the recoveries can be made. 

The commercial composite materials being marketed today are optimized in order to make the interfacial properties acceptable in the sense that they will not fail at such low levels as to detract from the overall composite behavior. Considering a unidirectional specimen, where the fibers are all aligned parallel to each other, commercial systems can be described by a rule of mixtures661 relationship (Fig. 10). Properties of the matrix and fiber can be linearly combined based on the volume fraction of each constituent. For example, the longitudinal tensile modulus is the sum of the proportion of each component. The interface in these systems is considered ideal in that it efficiently transmits forces between fiber and matrix without failure. Using this model as a basis for micromechanical analysis and discussion, the magnitude of the forces present at the interface can be predicted. 

Note that a Miller index of zero implies that the plane is parallel to that axis, since it is assumed that the plane will intersect the axis at 1 /oo. A complete set of equivalent planes is denoted by enclosing the Miller indices in curly brackets as hkl. For example, in cubic systems (1 0 0), (1 0 0), (0 1 0), (0 1 0), (001), and (0 01) are equivalent and the set is denoted in braces as 1 0 0. The maximum possible number of (h k 1) combinations that are equivalent occurs for cubic symmetry and is equal to 48. In hexagonal cells, four indices are sometimes used, h k i 1), where the relation i = —(h + k) always holds. The value of the i index is the reciprocal of the fractional intercept of the plane on the axis, as illustrated in Figure 1.10. It is derived in exactly the same way as the others. Sometimes, hexagonal indices are written with the i index as a dot and, in other cases, it is omitted entirely. 

If, as in the above example, some of the receptors can be inactivated without a decrease in the maximal effect, the dis-pensble receptor fraction is commonly referred to as spare receptors . Despite its widespread use in the literature, the term is not very precisely defined, and some argument exists about its proper use. Some authors consider a parallel shift of the dose-effect curve in response to an irreversible inhibitor (as for curves 1 and 2 in Figure 3.9) sufficient evidence of spare receptors. Using this interpretation, it would seem that any system with an initial gap between dose-effect and dose-receptor occupancy curves would qualify. Others insist that not only should there be a gap between dose-effect and dose-receptor occupancy curves, but that also the dose-effect curve should be steeper than the dose-receptor occupancy curve. 

When a system of interest is a mixture of two states that have each been characterized spectroscopically, then it is possible to calculate the fraction of each state within the mixture. As an example, let the system of interest be a protein comprised of a-helix and parallel -pleated sheet and let the observable be the molar ellipticity at a specified wavelength, [0]obs- Taking the characteristic molar ellipticities at the specified wavelength to be [0] and [0] p for the a-helix and the parallel 8-pleated sheet, respectively, the observed molar ellipticity may be expressed in terms of the mole fractions Xi of each of the conformations, i.e.,... 

At the same time the market expansion must allow for an increased technical learning and must support as quickly as possible the development and market introduction of (energy) efficient systems. On the one hand this is necessary to allow the limited and valuable biomass to be used as efficiently as possible and on the other hand the cost reduction potentials can be exploited immediately. In parallel the development of a broad basis of the used biomass fractions is necessary to compensate possible price fluctuations of individual biomass fractions, for example as a result of climatically indicated yield variations. 

Another example of a similar situation is one of a parallel system consisting of a large number of identical components. A certain fraction of the total number of components is allowed to fail before they... 

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