Proportional power index

Generally, the mean droplet size is proportional to liquid surface tension, and inversely proportional to liquid density and vibration frequency. The proportional power index is —1/3 for the surface tension, about -1/3 for the liquid density, and -2/3 for the vibration frequency. The mean droplet size may be influenced by two additional parameters, i.e., liquid viscosity and flow rate. As expected, increasing liquid viscosity, and/or flow rate leads to an increase in the mean droplet size,[13°h482] while the spray becomes more polydisperse at high flow rates.[482] The spray angle is also affected by the liquid flow rate, vibration frequency and amplitude. Moreover, the spray shape is greatly influenced by the direction of liquid flow (upwards, downwards, or horizontally).[482]... 

Notice that the carbon black hller reduces the rate of cut growth, but has only a small effect on the power index. Generally, it appears that abrasion occurs mainly in the third region, except when the abrasive track is very sharp. In this case the number of cycles to detach a small piece of rubber becomes small and the abrasion is proportional to the reciprocal of the energy density at break of the rubber compound. 

In the empirical correlation proposed by Kato et al.,[503] the mean droplet size is inversely proportional to the water pressure, with a power index of 0.5 for conical shaped annular-jet atomizers, and 0.7-1.0 for V-shaped flat-jet atomizers. This suggests a lower efficiency of the annular-jet atomizers in terms of spray fineness at high water pressures. The data of Kato et al.15031 were obtained for water pressures lower than 10 MPa. Seki et al.15021 observed the similar trend in the water atomization of nickel and various steels at higher water pressures (>10 MPa). Since k is dependent on both... 

If it is possible to assume that the maximum shear stress is proportional to the tip speed of the impeller, Eq. (18) has power index on the impeller diameter and rotation speed equivalent to those of Eq. (14). 

A number of models for the mechanical strength have been developed based on the concept of ionicity to predict the hardness of several compounds [35—38]. It is anticipated that covalent bonds take the responsibility for increasing the hardness. The hardness, or the activation energy required for plastic gliding, was related to the bandgap Eq, which is proportional to the inverse bond length in a fashion with the power index n varying from 2.5 to 5.0. 

Some properties, such as heat capacity, refractive index, and density, are not particularly sensitive to molecular weight but many important properties are related to chain length. Figure 3.2 lists three of these. The melt viscosity is typically proportional to the 3.4 power of the average chain length so 17 is proportional to Thus, the melt viscosity increases rapidly... 

The intensity of scattered light or turbidity (t) is proportional to the square of the difference between the index of refraction (n) of the polymer solution and of the solvent ( o), to the molecular weight of the polymer (M ), and to the inverse fourth power of the wavelength of light used (A). Thus ... 

Forster149 calculated that the rate of energy transfer kt should be proportional to the rate of fluorescence fcf, to an orientation factor X2, to the spectral overlap interval /, to the inverse fourth power of the refractive index n, and to the inverse sixth power of the distance r separating the two chromophores. 

Since the concentration is proportional in many individual cases to an easily delermined physical constant, such as specific gravity (e.g.. of solutions), the index of refraction, specific rotatory power (e.g., sugar solutions, tcrpcncsi. such constants are frequently used to ascertain and express concentration data. 

The volume of entrained air was found to be proportional to the drop height raised to the power of approximately 5/3. This is in contrast to Eq. (1) where the expected index is 2/3 [3]. This is an important result and suggests that a better approach to modelling of the air entrainment process might come from the use of a modified plume theory. 

Comparison between Experimental Results and Model Predictions. As will be shown later, the important parameter e which represents the mechanism of radical entry into the micelles and particles in the water phase does not affect the steady-state values of monomer conversion and the number of polymer particles when the first reactor is operated at comparatively shorter or longer mean residence times, while the transient kinetic behavior at the start of polymerization or the steady-state values of monomer conversion and particle number at intermediate value of mean residence time depend on the form of e. However, the form of e influences significantly the polydispersity index M /M of the polymers produced at steady state. It is, therefore, preferable to determine the form of e from the examination of the experimental values of Mw/Mn The effect of radical capture mechanism on the value of M /M can be predicted theoretically as shown in Table II, provided that the polymers produced by chain transfer reaction to monomer molecules can be neglected compared to those formed by mutual termination. Degraff and Poehlein(2) reported that experimental values of M /M were between 2 and 3, rather close to 2, as shown in Figure 2. Comparing their experimental values with the theoretical values in Table II, it seems that the radicals in the water phase are not captured in proportion to the surface area of a micelle and a particle but are captured rather in proportion to the first power of the diameters of a micelle and a particle or less than the first power. This indicates that the form of e would be Case A or Case B. In this discussion, therefore, Case A will be used as the form of e for simplicity. 

The fc-dependence of e and V translate into the fact that both spectra are not exactly proportional to k 3. In general one can approximate the spectra (at least for a limited range of wavenumbers) as power laws close to fc-3, so that it is convenient to define the spectral index of the scalar and tensor perturbations... 

In 2003 the integral power generation in Russia made up 888.2-billion kilowatt-hour, the proportion of nuclear power being 16.7% that was above that of 2002 by 6.3%. The capacity factor of all operating Russian Nuclear Power Plants (NPP) equaled 76.3% that was also above that of 2002 (by 4.6%). In 2002 the capacity factor at Volgodonsk NPP reached an unprecedently high index of 83.3% [2]. 

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