Slimness ratio

Table 7.13 shows cross sections of the three common slender column configurations. Formulas for each respective moment of inertia I and radius of gyration k are given. With the above formulas buckling force F can be calculated for a column configuration. Table 7.14 lists values of slim ratios (I/k) for small-nominal-diameter column lengths. 

The particle-size distribution and the shape of the particles also influence the ratio of length-to-diameter of the extractor. As the costs for extractors depend not only on volume, but mainly on the diameter, the proper selection of the extractor height/diameter ratio must be made, with a preference for slim vessels. So far, only for the decaffeination of coffee beans with a particle size of about 7 mm can large ratios of 9 1 (length to diameter) be applied. For large particle sizes it is of advantage to feed the solvent from top to bottom, in order to avoid back-mixing. For the usual particle-size-distribution, ratios of 6 1 should be used. For raw material which tends to swell, like black tea or paprika, the ratio should be only 3 1, or if the extractor is equipped with baskets, the baskets should be equipped with multiple distribution. 

The reciprocating bioreactor is a slim cylindrical vessel with a height/ diameter ratio of the order of 4 to 5 (Brauer and Sucker, 1979). The reactor contains a package of sieve plates attached to five rods. In the reactor of Brauer and Sucker (1979), the plate spacing is 42 mm, the diameter of the holes in the plates is 12 mm, and the hole spacing is 29 mm. This element undergoes a reciprocating motion up and down the reactor with an amplitude of 100 mm. 

Injection of 0.6 PV of carbon dioxide produced only 6% of a pore volume of additional oil. Linear laboratory miscible floods normally produce over 10% additional oil. The lower value of oil recovery reflects the inefficient macroscopic oil displacement induced by an unfavorable mobility ratio that exists between carbon dioxide and the oil. This phenomenon has not been reported for experiments conducted in long, slim tube models, where their smaller diameter, 0.2 in. vs. 1.6 in., masks the effect. 

When the slenderness ratio exceeds a value of 100 for a strong slim column, failure by buckling can be expected. Coliunns of stiflfer and more brittle materials will buckle at lower slenderness ratios. The constant factor m in Euler s critical-load formula clearly shows that the failure of a column depends on the configuration of the column ends. The basic four types with their respective m are ... 

Wlien the slenderness ratio exceeds a value of 100 for a strong slim column, failure by buckling can be expected. Columns of stiffer and... 

The key features of liquid crystal displays (LCDs) are low-voltage driving, low power consumption, and a slim profile. Thus LCDs are used in a variety of applications. Research and development is being carried out to increase contrast ratio, viewing angle, screen size, etc. So far, those challenges have been overcome, and R+D has produced results that started with the TN mode and led to the VA and IPS modes. 

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