Irregular Solid

Measuring To calculate density, you need to know both the mass and volume of an object. You can find the volume of an irregular solid by displacing water. 

Materials balance, graduated cylinder, water, washer or other small object 

Add about 15 ml of water to your graduated cylinder. Measure and record the volume. Because the surface of the water in the cylinder is curved, make volume readings at eye 

Carefully add the washer to the cylinder. Then measure and record the new volume. 

Use the initial and final volume readings to calculate the volume of the washer. 

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Wastewater pumps have anti-clog impellers to handle large irregular solids. 

Figure 8-5 The fluid mosaic model of Singer and Nicolson.61 Some integral membrane proteins, which are shown as irregular solids, are dissolved in the bilayer. Transmembrane proteins protrude from both sides. One of these is pictured as a seven-helix protein, a common type of receptor for hormones and for light absorption by visual pigments. Other proteins adhere to either the outer or the inner surface. Many membrane proteins carry complex oligosaccharide groups which protrude from the outer surface (Chapter 4). A few of these are indicated here as chains of sugar rings.

Modified Cross Sections. Nylon filaments are spun in a variety of cross-section shapes that include the conventional round to irregular solid and hollow shapes (Fig. 13). The cross-section shape is an important variant in designing the functionality and luster of fibers. The round cross section is used for strength in industrial applications and for subdued luster in apparel and upholstery. The multilobal cross sections are used to enhance bulk and for bright luster in both BCF and spun staple yams for carpets and upholstery. The grooves in the multilobal shapes also enhance moisture transport by wicking water through capillary action. Flat-sided ribbon-like cross sections provide cover in apparel applications. 

The determination of structure and bonding of polymer anchored catalysts is another area where the insolubility of the materials often precludes solution spectroscopic studies and one is limited to techniques that can be applied to irregular solids (57). In addition, combining oxygen plasma etching and surface analysis allows investigation of the depth of penetration of the metal into the polymer and allows detection of components that require concentration to allow detection. 

Solid-harmonic solutions J1/ and N j of the homogeneous Helmholtz equation in cell pi are products of spherical Bessel functions and spherical harmonics. Specific functional forms for the regular and irregular solid harmonics, respectively, are [188]... 

Table 41 which has been adsorbed at the temperature stipulated, and if we assume that the layer adsorbed is one molecule thick, we are in a position to compute the area of an irregular solid. 

In view of these complications, which are of extreme interest in themselves, it would seem that the adsorptive method of measuring the area of irregular solid surfaces must be trusted only as far as the order of magnitude of the surface is concerned and it would be well to use several different adsorbed substances and to compare the results for area given by each. 

This is an irregular solid so we use the information in the last entry of Table 7-1 in the absence of a specific correlation for this geometry. The properties were evaluated in Ex. 7-2 as... 

Volume Volume is the space occupied by an object. The derived unit for volume is the cubic meter, which is represented by a cube whose sides are all one meter in length. For measurements that you are likely to make, the more useful derived unit for volume is the cubic centimeter (cm ). The cubic centimeter works well for solid objects with regular dimensions, but not as well for liquids or for solids with irregular shapes. In the miniLAB on the next page, you will learn how to determine the volume of irregular solids. 

E. O. Steinbom, K. Ruedenberg, Rotation and Translation of Regular and Irregular Solid Spherical Harmonics, Adv. Quantum Chem. 7 (1973) 1-81. 

The utility of the above rules are numerous however, the reader may gain a better appreciation upon considering two brief examples. We can express the translation of a regular or irregular solid harmonic with a Taylor series expansion. 

Properties Nodular/irregular solid sp.gr. 2.57 oil absorp. 10-30 GE brightness 91-94 ref. index 1.52 hardness (Mohs) 6 noncombustible Toxicology Toxic as fine-ground powd. 

Despite these difficulties of definition and measurement it is most convenient for classification purposes, if a single-length parameter can be ascribed to an irregular solid particle. The most frequent expression used in connection with particle size is the equivalent diameter , i.e. the diameter of a sphere that behaves exactly like the given particle when submitted to the same experimental procedure. Several of these equivalent diameters are defined below. 

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