Series parallelism

Double-pipe exchangers are often piped in complex series-parallel arrangements on both sides. The MTD to be used has been derived for some of these arrangements and is reported in Kern (Process Heat Transfer, McGraw-Hill, New York, 1950). More complex cases may require trial-and-error balancing of the heat loads ana rate equations for subsections or even for individual exchangers in the bank. 

Tubular Tubular membranes (Fig. 22-51) are supported by a pressure vessel, iisiiallv perForated or porous. It can be as simple as a wrapped nonw oven Fabric, or as robust as a stainless-steel tube. All rim with tube-side Feed. Thev are rnainlv used For UF, with some RO applications, particularly For Food and daiiw. The primary diameters available are 12 and 25 mm. Tubes are oFten connected in series parallel bundles, gasketed or potted, are also common. 

These are unidirectional and uncontrollablet static electronic devices and used as static switches and shown in Figure 6.14. A diode turns ON at the instant it becomes forward biased and OFF when it becomes reverse biased. By connecting them in series parallel combinations, they can be made suitable for any desired voltage and current ratings. Whether it is a transistor scheme or a thyristor scheme, they are used extensively where a forward conduction alone is necessary and the scheme calls for only a simple switching, without any control over the switching operation. They are used extensively in a rectifier circuit to convert a fixed a.c. supply to a fixed d.c. supply. 

The triac may, however, have some limitations in handling frequencies higher than normal. In such cases, they can be simulated by using two SCRs in inverse parallel combinations as illustrated in Figure 6.22(b). Now it is known as a reverse conducting thyristor. An SCR has no frequency limitations at least up to ten times the normal. The required voltage and current ratings are obtained by series-parallel connections of more than one thyristor unit. 

These ratings can be enhanced by connecting them in series-parallel combinations. In scries to enhance the voltage rating and in parallel to enhance the cuiTcnl rating. Bui the controls may not be so accurate as with a single device. 

Restriction in series-parallel combinations of capacitor elements 25/814... 

For-della connected capacitor units In (his case, it will establish a line-to-line fault with a heavy fault current. Protection by HRC fuses would be more appropriate than for a grounded star or using an MCCB. For series-parallel connected units I his is applicable in HT capacitor banks comprising a number of small units arranged in series and parallel combinations. The fault current in such cases for an isolated neutral can be expressed by... 

This is applicable to both LT and HT capacitors. But it is more important in HT banks, which are relatively much larger and are built of a number of single units eonnected in series-parallel. These may encounter much higher fault currents in the event of a severe internal fault, even in one unit and are thus rendered more vulnerable to such ruptures. This phenomenon is more applicable to units that are externally protected w here (he intensity of fault may be more severe, than internally protected units. 

Amster and Hooper, 1986). Other formulations exist for eomponents in parallel with equal reliability values, as shown in equation 4.69, and for eombinations of series, parallel and redundant eomponents in a system (Smith, 1997). The eomplexity of the equations to find the system reliability further inereases with redundaney of eomponents in the system and the number of parallel paths (Burns, 1994) ... 

Surface per Unit sq ft Shells per Unit Series Parallel Surface per Shell sq. ft. ... 

Many systems consisting of several components can be classified as series, parallel, or a combination of both. However, llie majority of industrial and process plants (units and systems) have series of parallel configurations. 

In the parallel configuration, the same potential difference occurs across each and every element with the total current being the algebraic sum of the current flowing through each individual circuit element. Table 2-35 summarizes the equivalent resistance, conductance, capacitance, and inductance of series-parallel configurations of resistors, capacitors, and inductors. 

A series of four papers by G. W. Ford and others [ForG56,56a,56b, 57] amplified this work by using Polya s Theorem to enumerate a variety of graphs on both labelled and unlabelled vertices. These included connected graphs, stars (blocks) of given homeomorphic type, and star trees. In addition many asymptotic results were derived. The enumeration of series-parallel graphs followed in 1956 [CarL56], and in that and subsequent years Harary produced... 

CarL56 Carlitz, L., Riordan, J. The number of labeled two terminal series-parallel networks. Duke Math. J. 23 (1956) 435-445. 

The ACS Symposium Series was founded in 1974 to provide a medium for publishing symposia quickly in book form. The format of the Series parallels that of the continuing Advances in Chemistry Series except that in order to save time the papers are not typeset but are reproduced as they are submitted by the authors in camera-ready form. Papers are reviewed under the supervision of the Editors with the assistance of the Series Advisory Board and are selected to maintain the integrity of the symposia however, verbatim reproductions of previously published papers are not accepted. Both reviews and reports of research are acceptable since symposia may embrace both types of presentation. 

Figure 5.24. Stirred tank with series-parallel reaction.

In some heterogeneous reactions, for instance, in noncatalytic fluid-solid reactions, the resistances to the reaction may be taken to occur in series. However, in some other reactions, such as catalytic solid-solid reactions, more complicated series-parallel relationships among the resistances must be considered. 

Another interesting method of amperometric detection for LC is dualelectrode electrochemical detection. Instead of a single WE, one can place two WEs in series, parallel to or opposite each other. The series configuration is mostly used, mainly in the collection mode, i.e., the electroactive substance entering the detector is converted at the upstream (generator) electrode into a product that either is or is not detected at the downstream (indicator) electrode, depending on the potential of the latter. Hoogvliet et al.137,162 were easily able... 

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