Scaling physical arrangement

Figure 2. Physical arrangement of a metal (M) undergoing scaling (39)...

For purposes of data correlation, model studies, and scale-up, it is useful to arrange variables into dimensionless groups. Table 6-7 lists many of the dimensionless groups commonly founa in fluid mechanics problems, along with their physical interpretations and areas of application. More extensive tabulations may oe found in Catchpole and Fulford (Ind. Eng. Chem., 58[3], 46-60 [1966]) and Fulford and Catchpole (Ind. Eng. Chem., 60[3], 71-78 [1968]). 

Molecular modeling helps students understand physical and chemical properties by providing a way to visualize the three-dimensional arrangement of atoms. This model set uses polyhedra to represent atoms, and plastic connectors to represent bonds (scaled to correct bond length). Plastic plates representing orbital lobes are included for indicating lone pairs of electrons, radicals, and multiple bonds—a feature unique to this set. 

When interaction and physical phenomena length scales become comparable to or larger than the size of the structure, as, for example, with polymer contour chain length, the system may exhibit unusual behavior and generate novel arrangements not accessible in bulk. 

Chemical flowshops are widely used in industry for the medium-scale synthesis of chemicals. In a flowshop, a number of different physical units, such as reactor vessels, ovens, dryers, and distillation columns are placed in a serial, or largely serial, arrangement. Rather than being devoted to the preparation of a single chemical, many different chemicals are synthesized one after another in a flowshop by feeding in the appropriate precursors and reagents as the intermediates pass through most or all of the units. This mode of operation is an effective use of the physical plant because no part... 

This statement is supported by the results shown in Fig. 1. The researchers carried out their measurements in smooth pipes with diameters d = 0.36 - 12.63 cm, thereby changing the scale in the range of 1 35. Furthermore, the physical properties of the fluid tested (water or air) varied widely. Nevertheless, the relationship i (Re) did not display this change Every numerical value of Re still corresponded to a specific numerical value of The pi-space is scale-independent, it is scale invariant The pi-relationship presented is therefore valid not only for the examined laboratory devices but also for any other geometrically similar arrangement ... 

---