Multistage arrangement

A more economical alternative is found in a submersible pump where the pump, directly coupled with the prime mover, is slid into the tubewell through narrow pipes. Narrow pipes are easy to sink into rocky terrain or very deep water levels. They are less expensive and are easy to install due to the elimination of the need for a pump house. Once the unit is slid into the well it requires little maintenance. (See Figures 7.5-7.7.) Such pumps have a standard centrifugal multistage arrangement, and the motors are required to work under water or any other liquid. These motors have an exclusive application for submersible pumps. 

Integration of equation 21.5-8 from the inlet to the outlet of the ith stage of a multistage arrangement, again with the coefficient of dT constant, results in... 

Provided that the reaction kinetics are known, the available models can be used to determine optimal dosing profiles for single units and for multistage arrangements. Typical results that can be obtained by solving Eq. (48) numerically and applying a sequential quadratic programming (SQP) optimizer are shown in Fig. 12.18 [66]. 

On the other hand, a multistage arrangement may be considered for structural, operating technology, or kinetic reasons in the following cases ... 

A multistage arrangement of the basic diffusion still component (Figure 2) is possible, as shown schematically in Figure 6. 

Vortex dryers can be configured vertically or horizontally (Figure 21.42). The vertical configuration is widely known as a convex dryer. The horizontal vortex dryers are less popular, but they can easily be used in a multistage arrangement that allows for extended residence times, controlled temperature regimes, and intermittent operation, if necessary. 

Pressure losses at the feed side have to be reduced to a minimum in vapor permeation. Otherwise the process would no longer operate at constant pressure, but the feed vapor could reach a region where superheated conditions would exist. Consequently, pressure losses in vapor permeation modules have to be as low as several millibar only. In pervaporation the feed-side pressure losses are not that critical, but in multistage arrangements they will eventually limit the number of appHcable stages. 

These Roots vacuum pump combinations serve not only as boosters within the low pressure range where only a small pressure difference needs to be overcome, but also serve in multistage arrangements as a complete pumping unit, compressing from a few millibar abs. directly to atmospheric pressure. 

Often solvent extraction is carried out continuously in a countercurrent multistage device/cascade. The sieve-plate tower is an example of one multistage device, whereas Figure 8.1.37(a) illustrates a multistage arrangement of N mixer-settler devices (one such device is studied in Section 6.4.1.2). First, we analyze a dilute solution of solute i in a feed-extract phase system assumed to be essentially insoluble in each other (Cussler, 1997). Then we will analyze extraction systems with some mutual solubility of the feed and the extraction solvent. 

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