Determination of the characteristic geometric parameter

We interrupt the procedure by asking an important question concerning the determination of the characteristic geometric parameter. 

It is obvious that we could name all the geometric parameters indicated in the sketch. They were all the geometric parameters of the stirrer and of the vessel, especially its diameter D and the liquid height H. In the case of complex geometry such a procedure would compulsorily divert from the problem. It is therefore advisable to introduce only one characteristic geometric parameter, knowing that all the others can be converted into dimensionless geometric numbers by division with it. 

As the characteristic geometric parameter in the above case the stirrer diameter 

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We interrupt the procedure to ask some important questions concerning (1) the determination of the characteristic geometric parameter, (2) the setting of all relevant material properties, and (3) the taking into account the gravitational acceleration. 

The Stlffness/Geometric parameter Y which defines the "severity" of the bending-wave dispersion characteristic between coupled and uncoupled conditions. Y and the loss factor T 2 of the viscoelastic layer determine the maximum system damping for the treatment. 

The characteristics of disperse systems (see Section 1.1.2) are determined by geometrical parameters, i.e. linear dimensions, projection areas, surfaces, volumes, and, sometimes, angular dimensions. In addition, other physical characteristics, which do not directly represent particle size, may be used for the determination of these parameters. In such cases, a mathematical conversion into the desired geometrical dimension takes place. The term particle size analysis defines the experimental determination of particle characteristics and the statistical treatment of results. 

On such a basis and by applying variational considerations, the equilibrium and stability properties of drops and bubbles have been widely investigated [13, 14,15]. Moreover, since the pioneering work of Bashforth and Adams [13], solutions of Eq. (5) provided in tabular form [16, 17, 18, 19, 20], have been used to infer the interfacial tension of drops and bubbles by measuring the characteristic geometrical quantities of the profile, arranged in non-dimensional parameters. Often the goal of these methods was the determination of p and b, which, once the density difference is known yields the surface tension. 

The present model takes into account how capillary, friction and gravity forces affect the flow development. The parameters which influence the flow mechanism are evaluated. In the frame of the quasi-one-dimensional model the theoretical description of the phenomena is based on the assumption of uniform parameter distribution over the cross-section of the liquid and vapor flows. With this approximation, the mass, thermal and momentum equations for the average parameters are used. These equations allow one to determine the velocity, pressure and temperature distributions along the capillary axis, the shape of the interface surface for various geometrical and regime parameters, as well as the influence of physical properties of the liquid and vapor, micro-channel size, initial temperature of the cooling liquid, wall heat flux and gravity on the flow and heat transfer characteristics. 

Effective Thermal Conductivities of Porous Catalysts. The effective thermal conductivity of a porous catalyst plays a key role in determining whether or not appreciable temperature gradients will exist within a given catalyst pellet. By the term effective thermal conductivity , we imply that it is a parameter characteristic of the porous solid structure that is based on the gross geometric area of the pellet perpendicular to the direction of heat transfer. For example, if one considers the radial heat flux in a spherical pellet one can say that... 

Conformational characteristics of PTFE chains are studied in detail, based upon ab initio electronic structure calculations on perfluorobutane, perfluoropentane, and perfluorohexane. The found conformational characteristics are fully represented by a six-state RIS model. This six-state model, with no adjustment of the geometric or energy parameters as determined from the ab initio calculations, predicts the unperturbed chain dimensions, and the fraction of gauche bonds as a function of temperature, in good agreement with available experimental values. 

Thus for a given reaction mass, the heat transfer coefficient of the internal film can be influenced by the stirrer speed and its diameter. The value of the equipment constant (z) can be calculated using the geometric characteristics of the reactor. The value of material constant for heat transfer (y) can either be calculated from the physical properties of the reactor contents-as far as they are known-or measured by the method of the Wilson plot in a reaction calorimeter [4, 5]. This parameter is independent of the geometry or size of the reactor. Thus, it can be determined at laboratory scale and used at industrial scale. The Wilson plot determines the overall heat transfer coefficient as a function of the agitator revolution speed in a reaction calorimeter ... 

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