Irregular volume

Irregular Volumes To find the volume, replace the y s by cross-section areas Aj and use the results in the preceding equations. 

The greater the value of n, the greater the accuracy of approximation. Irregular volume... 

To find irregular volume, replace y s by cross-secfional area Ay, and use fhe results in the preceding equation. 

Because of the diversity of filler particle shapes, it is difficult to clearly express particle size values in terms of a particle dimension such as length or diameter. Therefore, the particle size of fillers is usually expressed as a theoretical dimension, the equivalent spherical diameter (esd), ie, the diameter of a sphere having the same volume as the particle. An estimate of regularity may be made by comparing the surface area of the equivalent sphere to the actual measured surface area of the particle. The greater the deviation, the more irregular the particle. 

True Density or Specific Gravity. The average mass per unit volume of the individual particles is called the tme density or specific gravity. This property is most important when volume or mass of the filled composition is a key performance variable. The tme density of fillers composed of relatively large, nonporous, spherical particles is usually determined by a simple Hquid displacement method. Finely divided, porous, or irregular fillers should be measured using a gas pycnometer to assure that all pores, cracks, and crevices are penetrated. 

A nonproportional sampler is suitable for near-constant flow conditions. The sample is simply drawn from the waste stream at a constant flow rate. Sampling lines should be as short as possible and free from sharp bends, which can lead to particle deposition. Proportional samplers are designed to collect either definite volumes at irregular time intervals or variable volumes at equal time intervals. Both types depend on flow rate. Examples of some of these are the vacuum and chain-driven wastewater samplers. Other types, which have cups mounted on motor driven wheels, vacuum suction samplers, and peristaltic pump samplers, are also available (26,27). 

Particle shape also affects the sintering of a powder compact. Jagged or irregular shaped particles, which have a high surface area to volume ratio, have a higher driving force for densification and sinter faster than equiaxed particles. High aspect ratio platey particles, whiskers, and fibers, which pack poorly, sinter poorly. 

Impression Plasters. Impression plasters are prepared by mixing with water. Types I and II plasters are weaker than dental stone (types III and IV) because of particle morphology and void content. There are two factors that contribute to the weakness of plaster compared to that of dental stone. First, the porosity of the particles makes it necessary to use more water for a mix, and second, the irregular shapes of the particles prevent them from fitting together tightly. Thus, for equally pourable consistencies, less gypsum per unit volume is present in plaster than in dental stone, and the plaster is considerably weaker. 

With closely screened material, the percentage of voids (usually 37 percent) is independent of particle size. With unscreened particles showing a wide variation in size, the void volume is decreaseci irregularity in gas flow results. 

Fig. 12-88. Curve A shows the calculated surface based on an assumed 50 percent void volume and cubical-shaped particles. The B set of cui ves applies to such unscreened irregularly shaped particles as are usually encountered in practice.

Particle diameter is a primary variable important to many chemical engineering calculations, including settling, slurry flow, fluidized beds, packed reactors, and packed distillation towers. Unfortunately, this dimension is usually difficult or impossible to measure, because the particles are small or irregular. Consequently, chemical engineers have become familiar with the notion of equivalent diameter of a partiele, which is the diameter of a sphere that has a volume equal to that of the particle. 

These two nomographs provide a convenient means of estimating the equivalent diameter of almost any type of particle Figure 1 of regular particles from their dimensions, and Figure 2 of irregular particles from fractional free volume, specific surface, and shape. 

Static test results may be evaluated by measurement of change of mass or section thickness, but metallographic and X-ray examination to determine the nature and extent of attack are of greater value because difficulty can be encountered in removing adherent layers of solidified corrodent from the surface of the specimen on completion of the exposure, particularly where irregular attack has occurred. Changes in the corrodent, ascertained by chemical analysis, are often of considerable value also. In view of the low solubility of many construction materials in liquid metals and salts, changes in mass or section thickness should be evaluated cautiously. A limited volume of liquid metal could become saturated early in the test and the reaction would thus be stifled when only a small corrosion loss... 

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