Constant over

Oxygen occurs free in the atmosphere (21% by volume. 23 by weight). The proportion is constant over the earth s surtace it is also constant for many miles upwards, because the turbulence of the atmosphere prevents the tendency for the lighter gases, for example helium, to increase in amount at higher altitudes. 

A number of simulation methods based on Equation (7.115) have been described. Thess differ in the assumptions that are made about the nature of frictional and random forces A common simplifying assumption is that the collision frequency 7 is independent o time and position. The random force R(f) is often assumed to be uncorrelated with th particle velocities, positions and the forces acting on them, and to obey a Gaussiar distribution with zero mean. The force F, is assumed to be constant over the time step o the integration. 

In the region where > 1 then if the interparticle force is assumed to be constant over thi integration time step the following result is obtained [van Gunsteren et al. 1981] ... 

Dg remains constant over a wide range of resin to liquid ratios. In a relatively short time, by simple equilibration of small known amounts of resin and solution followed by analysis of the phases, the distribution of solutes may be followed under many different sets of experimental conditions. Variables requiring investigation include the capacity and percent cross-linkage of resin, the type of resin itself, the temperature, and the concentration and pH of electrolyte in the equilibrating solution. 

The foregoing conclusion does not mean that the rate of the reaction proceeds through Table 5.1 at a constant value. The rate of reaction depends on the concentrations of reactive groups, as well as on the reactivities of the latter. Accordingly, the rate of the reaction decreases as the extent of reaction progresses. When the rate law for the reaction is extracted from proper kinetic experiments, specific reactions are found to be characterized by fixed rate constants over a range of n values. 

The assumption that k values are constant over the entire duration of the reaction breaks down for termination reactions in bulk polymerizations. Here, as in Sec. 5.2, we can consider the termination process—whether by combination or disproportionation to depend on the rates at which polymer molecules can diffuse into (characterized by kj) or out of (characterized by k ) the same solvent cage and the rate at which chemical reaction between them (characterized by kj.) occurs in that cage. In Chap. 5 we saw that two limiting cases of Eq. (5.8) could be readily identified ... 

Capacitors. The outstandingly low dielectric loss of parylenes make them superior candidates for dielectrics in high quality capacitors. Furthermore, their dielectric constant and loss remain constant over a wide temperature range. In addition, they can be easily formed as thin, pinhole-free films. Kemet Flatkaps are fabricated by coating thin aluminum foil with Parylene N on both sides and winding the coated foils in pairs (62). 

Electrical properties of acetal resin are collected in Table 3. The dielectric constant is constant over the temperature range of most interest (—40 to 50°C). Table 3. Electrical Properties of Acetal Resins... 

Most glass-ceramics have low dielectric constants, typically 6—7 at 1 MHz and 20°C. Glass-ceramics comprised primarily of network formers can have dielectric constants as low as 4, with even lower values (K < 3) possible in microporous glass-ceramics (13). On the other hand, very high dielectric constants (over 1000) can be obtained from relatively depolymerized glasses with crystals of high dielectric constant, such as lead or alkaline earth titanate (11,14). 

Properties. Xanthan gum is a cream-colored powder that dissolves in either hot or cold water to produce solutions with high viscosity at low concentration. These solutions exhibit pseudoplasticity, ie, the viscosity decreases as the shear rate increases. This decrease is instantaneous and reversible. Solutions, particularly in the presence of small amounts of electrolyte, have exceUent thermal stabiHty, and their viscosity is essentially constant over the range 0 to 80°C. They are not affected by changes in pH ranging from 2 to 10. 

The prefactor M(T), also called a frequency factor, has units of inverse seconds. It may have a weak dependence on temperature. Some theoretical models predict a variation with, but such variation is frequently ignored and M is taken as constant over limited temperature ranges. The prefactor M is often... 

Electrical Properties. AH polyolefins have low dielectric constants and can be used as insulators in particular, PMP has the lowest dielectric constant among all synthetic resins. As a result, PMP has excellent dielectric properties and alow dielectric loss factor, surpassing those of other polyolefin resins and polytetrafluoroethylene (Teflon). These properties remain nearly constant over a wide temperature range. The dielectric characteristics of poly(vinylcyclohexane) are especially attractive its dielectric loss remains constant between —180 and 160°C, which makes it a prospective high frequency dielectric material of high thermal stabiUty. 

Economic Aspects. The North American demand for anhydrous aluminum chloride, estimated to be from 25,000 to 30,000 metric tons per year (9), is divided among the appHcations shown in Figure 2. In 1984 the anhydrous aluminum chloride demand was estimated at 40,000 tons in Western Europe and 9,000 tons in Japan (10). Pricing is heavily dependent on the cost of aluminum metal. The deHvered price of aluminum chloride during the first quarter of 1989 ranged from 0.32/kg for bulk tmddoads to 0.35/kg for small dmms. The North American demand for this catalyst has remained relatively constant over the last 20 years (10). 

Other. Insoluble alkaline-earth metal and heavy metal stannates are prepared by the metathetic reaction of a soluble salt of the metal with a soluble alkah—metal stannate. They are used as additives to ceramic dielectric bodies (32). The use of bismuth stannate [12777-45-6] Bi2(Sn02)3 5H20, with barium titanate produces a ceramic capacitor body of uniform dielectric constant over a substantial temperature range (33). Ceramic and dielectric properties of individual stannates are given in Reference 34. Other typical commercially available stannates are barium stannate [12009-18-6] BaSnO calcium stannate [12013 6-6] CaSnO magnesium stannate [12032-29-0], MgSnO and strontium stannate [12143-34-9], SrSnO. ... 

The slope of the water solubiUty curves for fuels is about the same, and is constant over the 20—40°C temperature range. Each decrease of 1°C decreases water solubiUty about 3 ppm. The sensitivity of dissolved water to fuel temperature change is important. For example, the temperature of fuel generally drops as it is pumped iato an airport underground hydrant system because subsurface temperatures are about 10 °C lower than typical storage temperatures. This difference produces free water droplets, but these are removed by pumping fuel through a filter-coalescer and hydrophobic barrier before deUvery iato aircraft. 

Economic Aspects. The Dow Chemical Company and Aqualon Co. are the only hsted principal producers of EC and HEEC products woddwide. Consumption has remained constant over the past several years, and the products ate not expected to grow in the future. Production is estimated at 5000 t/yr, roughly equally divided between The Dow Chemical Company and Aqualon Co. As with other cellulose ethers, the price for EC and HEEC varies by grade. 

Process variables do not change G and, therefore, Mj- is constant over modest ranges of operating conditions. 

The Optimum Velocity Profile. The optimum velocity profile (41), that is the velocity profile that yields the maximum value for the flow pattern efficiency, is one in which the mass velocitypv is constant over the radius of the centrifuge except for a discontinuity at the wall of the centrifuge (r = rP). This optimum velocity profile is shown in Figure 14a. For this case the following values for the separation parameters of the centrifuge are obtained... 

If the latent heat of vaporization is then assumed to be constant over the temperature range of interest, equation 6 can be integrated to give the Clausius-Clapeyron expression ... 

Hibemia-Chemie has described a vapor-phase process that passes fresh and recycled 85 wt % phosphoric acid over a catalyst of hydrochloric acid-leached bentonite impregnated with phosphoric acid. Catalyst activity was claimed to remain constant over a period of one year at the following conditions (126) ... 

For flow past a cyhnder, the vortex street forms at Reynolds numbers above about 40. The vortices initially form in the wake, the point of formation moving closer to the cylinder as Re is increased. At a Reynolds number of 60 to 100, the vortices are formed from eddies attached to the cylinder surface. The vortices move at a velocity slightly less than V. The frequency of vortex shedding/is given in terms of the Strouhal number, which is approximately constant over a wide range of Reynolds numbers. 

Breakeven charts present a snapshot of the present situation by means of graphs which are generally drawn in the manner shown in Figs. 9-2, 9-3, and 9-4. Since the lines are straight, this implies that Cs, Cy , and Aee will remain constant over the range of variation of R, which is of interest. The values would be based on the production rate currently achieved (or scheduled), since all the data are available from... 

Rotameters require no straight runs of pipe before or after the point of installation. Pressure losses are substantially constant over the whole flow range. In experimental work, for greatest precision, a rotameter should be cahbrated with the flmd which is to be metered. However, most modern rotameters are precision-made so that their performance closely corresponds to a master cahbration plot for the type in question. Such a plot is supphed with the meter upon purchase. 

The fin efficiency is found from mathematically derived relations, in which the film heat-transfer coefficient is assumed to be constant over the entire fin and temperature gradients across the thickness of the fin have been neglected (see Kraus, Extended Suiface.s, Spartan Books, Baltimore, 1963). The efficiency cui ves for some common fin configurations are given in Figs. Il-3(k7 and 11-30 ,... 

Data for determining the size of natural-draft towers have been presented by Chilton [Proc. Inst. Elec. Eng., 99,440 (1952)] and Rish and Steel (ASCE Swuposium on Thermal Power Plants, October 19.58). Chilton showed that the duty coefficient Df of a tower is approximately constant over its normal range of operation and is related to tower size by an efficiency factor or performance coefficient as follows ... 

Equation (12-46) may be solved by trial and error or graphically to estimate the true values of H, and t and, hence, the ac tual drying rate. The values of X and depend on the value of but can generally be considered constant over the range of temperatures usu ly encountered in air diying. 

The effect of increasing gas rate is to increase /cg and decrease 0g, with the result that tends to be constant over a range of gas rates. 

If the oxidizing gas is pure oxygen, and iNi2+ remains approximately constant over the oxide thickness... 

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