Packing symbols

Figure 4-9. Comparison of liquid hold-up hi, calc calculated acc. to Eq. (4-34) with experimentally determined values hp expi vahd for Rep > 5 and Fv/Fv,f1< 0.65, for various packings. Symbols can be found in Table 4-5 in the annex to this chapter...

Fig. 16. Plots showing (a) variation of (c F/2)J. / ) with 1 for O2 (left plot, X, 0.84- 0.72 mm = 20-25 mesh Q 0.42-0.29 mm = 40-50 mesh) and N2 (right plot, on 3.2-mm pellets) in Bergbau-Forschung carbon molecular sieve and (b) variation of HETP with Hquid velocity (interstitial) for fmctose (soHd symbols), and glucose (open symbols) in a column packed with KX 2eoHte crystals. From refs. 22 and 23.

On this table, the Arrhenius number E/RT was designated by e, but this symbol is already used in this book for the empty fraction in a packed bed. The correct symbol for E/RT = y is used here. On the last line in this table the derivative of the heat removal rate is given ... 

FIG. 5 Adsorption isotherms for a hard sphere fluid from the ROZ-PY and ROZ-HNC theory (solid and dashed lines, respectively) and GCMC simulations (symbols). Three pairs of curves from top to bottom correspond to matrix packing fraction = 0.052, 0.126, and 0.25, respectively. The matrix in simulations has been made of four beads (m = M = 4). 

FiG. 7 The same as in Fig. 6, for the matrix made of chains with four beads (m = Af = 4) at packing fraction 0.126. The nomenclature of lines and symbols and their location are similar to those of Fig. 6. 

Li and Hsiao [143] provide a useful approach to the environmental problem of removing (by stripping) volatile organics from solution in a contaminated water stream by using fresh air as the stripping medium. It should be noted that a number of industrial firms perform this stripping with steam. The mass balance on the VOC component around the column (trayed or packed) as shown in Figure 8-55 uses the symbols of Reference 143. 

Because the packed tower is a continuous contacting device as compared to the step-wise plate tower, performance capacity is expressed as the number of transfer units, N, the height of the transfer unit, H.T.U., and mass transfer coefficients K a and Kj a. Figure 9-68 identifies the key symbols and constant flow material balance. 

Figure 9-68. Counter-current packed tower symbols.

Figure 10-173. Direct contact tray column for heat transfer. This could be a baffle tray, sieve type tray, bubble or other contact device, or open spray or random packed column. (Symbols only used by permission Smith, J. H. Hydrocarbon Processing, Jan. 1979, p. 147. Gulf Publishing Company. All rights reserved.)...

The symbols Al, A2, and A3 represent the three simple metal structures cubic closest packed, body centered, and hexagonal closest packed, respectively. 

FIG. 4 Nomialized concentration distribution of a 0.1 molar 1 1 electrolyte in an uncharged cylindrical pore of radius five times the diameter of the ions. The dashed line, solid up-triangles, and solid down-triangles are the neutral solvent particles, cations, and anions, respectively, in an SPM model with 0.3 solvent packing fraction. The open symbols are for the cations and anions in the RPM model. 

FIG. 9 Salt exclusion as a function of surface charge in a cylindrical pore in equilibrium with an SPM electrolyte of 0.1 solvent packing fraction. The open sqnares and circles are results of a 0.4 molar 1 2 electrolyte in a pore off = S.OrfandiJ = l.Od, respectively. The open np-triangles and down-triangles are results of a 0.4 molar 2 2 electrolyte in a pore of R = 5.0d and R = l.Od, respectively. The corresponding solid symbols are resnlts under the same conditions, bnt with a 0.1 molar electrolyte. 

FIG. 14 Comparison of total pressure between two charged surfaces in 1 1, 2 1, and 2 2 electrolytes. The open squares, up-triangles, and down-triangles are results of 1 1, 2 1, and 2 2, respectively, for the SPM model of 0.3 packing fraction. The corresponding solid symbols are for the RPM model. 

Figure 3.10 Illustrative example of linear regression between two artificial variables for six experimental units. For each unit, denoted by a different graphical symbol, a closely packed set of five observations with negative slope is measured. The whole data set, if fitted naively, would show a very significant positive slope.

Lot number, control number, or batch number means any distinctive combination of letters, numbers, or combination of letters, numbers, or symbols, or nay combination of them, from which the complete history of the manufacture, processing, packing, holding, and distribution of a batch or lot of drug product or other material can be determined. 

February, and beef is sold de-boned and vacuum packed and cut to the customer s specifications, all certified and labelled with the Organic Trust symbol. 

For additional symbols of further packings cf. [38, 156], T (triangular) refers to hexagonal layers, Q to layers with a periodic pattern of squares. The packing Qs yields a primitive cubic lattice (Fig. 2.4), Qf a body-centered cubic lattice (cf. Fig. 14.3, p. 153). Sometimes the symbols are set as superscripts without the angular brackets, for example Ti[Ca03]c. 

State the Jagondzinski and the Zhdanov symbols for the closest-packings of spheres with the following stacking sequences ... 

Fig. 9 shows comparisons of CFD results with experimental data at a Reynolds number of 986 at three of the different bed depths at which experiments were conducted. The profiles are plotted as dimensionless temperature versus dimensionless radial position. The open symbols represent points from CFD simulation the closed symbols represent the points obtained from experiment. It can be seen that the CFD simulation reproduces the magnitude and trend of the experimental data very well. There is some under-prediction in the center of the bed however, the shapes of the profiles and the temperature drops in the vicinity of the wall are very similar to the experimental case. More extensive comparisons at different Reynolds numbers may be found in the original reference. This comparison gives confidence in interstitial CFD as a tool for studying heat transfer in packed tubes. 

Fig. 34. Comparison of radial temperature profiles for WS packed with full cylinders, with and without heat sinks solid symbols are for temperatures averaged over fluid and solid, open symbols for temperatures averaged over fluid alone.

First tabulate the isotopes symbols, the mass of isotope and its associated packing fraction. 

Isotope Symbol Mass of Isotope (u) Packing Fraction... 

The symbol X in this case was first introduced by Van Deemter to account for packing inhomogeneity. 

Figure 3.20. A lateral view of different stacking sequences of triangular nets. They correspond to some typical close-packed structures. The first layer sequence shown corresponds to a superimposition according to the scheme ABABAB... (equivalent to BCBCBC... or CACACA... descriptions) characteristic of the hexagonal close-packed, Mg-type, structure. With reference to the usual description of its unit cell, the full stacking symbol indicating the element, the relative position of the superimposed layers and their distance is Mg Mg. The other sequences correspond to the schemes ABC.ABC. (Cu, cubic), ABAC.ABAC. (La, hexagonal), ACACBCBAB. (Sm, hexagonal). For Cu the constant ch of the (equivalent, non-conventional) hexagonal cell is shown which may be obtained by a convenient re-description of the standard cubic cell (see 3.6.1.3). ch = cV 3, body diagonal of the cubic cell.

Another common notation for describing stacking of close-packed 36 nets (T nets) is that devised by Zhdanov (1945) (a number notation equivalent to Jagodzinski s notation). A short description of the Zhdanov symbol is the following a + is assigned if the order between a layer and its previous partner follows the... 

Their polytypic nature may be represented by a series of close-packed stacking variants of similar triangular atomic nets (A, B, C nets) corresponding to the following symbols ... 

In the Mg structure the atoms are arranged in close-packed layers stacked in the sequence ABAB... (equivalent to BCBC..., etc) the corresponding layer symbol (triangular nets) is Mgo.25Mgo.75. Compare this symbol with those relevant to Cu, La, Sm. 

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