Void calculations

Note that the local boiling void calculated this way is independent of channel length. The prediction of the point of bubble departure (void detachment) is, however, important in predicting the subcooled boiling void. Rouhani (1967) assumed... 

When considering a packed bed the interparticle or interstitial porosity amounts to approximately 40%. The average diameter of these interstitial voids calculates for a fairly regular packing to 0.4 times of the particle diameter, e.g. a regularly packed bed with 15 p,m particle creates interstitial pores of 6 pm. A bimodal particle size distribution of silicas employed for preparative columns can often be found, e.g. a major distribution around 15 pm and a minor peak at 4 pm. These small particles are thought to occupy the interstices between the 15 pm diameter particles and thus to stabilize the bed. 

Sample loses crystallinity upon desolvation and thus results are not comparable to others in the series Void calculated from crystal structures... 

The exchange of calculations showed that criticality is predicted by both Cadarache Karlsruhe with an accuracy of 1 to 2%. b the oise of Na-void calculations, discrepancies Iqr as much as a factor of 2 were found between the results of the two laboratories. The reasons for these are now being investigated by a thorough comparison of the calculaticms and the underlying data. 

T. A. PITTERLE et al., "Sodium Void Calculations, Analysis of Sodium Reactivity Measurements, Vol. II, APDA-216, Vol II, Atomic Power Development Assoc. 

Comparisons of experiments and calculations of the conventional cores with ENDF/B-IV data generally agreed with such comparisons for smaller cores, in spite of an increase in sensitivity of some parameters to nuclear data uncertainties. The csdculated keff for ZPPR-9 of 0.985 was essentially the same, power distributions were predicted to within 2% in core zones, and sodfum-void calculated-to-experimental ratios were similar to values observed before. Large control rod interactions were observed up to 50% for siz outer-ring rods compared with 20% in the smaller cores, but were calculated to within a few percent. Sensitivity analyses were made for 350-, 700-, and 1250-MW(e) core sizes. This has ted to a quantitative understanding of Ae way in which bias factors and uncertainties obtained from... 

The reflection tomograms (c) show the axial hole in the Plexiglas specimen, but also a real discontinuity in the A/5i -alloy. The internal discontinuity is located 6 mm from the edge, 50° from the axial hole and its dimension is about 1-2 mm. This may be an inclusion or a porosity (void). Multiple reflections from the measurement were ignored in the calculation of the Plexiglas tomogram (left). This is seen as a bright circle. 

Nelson et al. [34] determined from void shapes that the ratio 7100/7110 was 1.2, 0.98 and 1.14 for copper at 600°C, aluminum at 550°C, and molybdenum at 2000°C, respectively, and 1.03 for 7100/7111 for aluminum at 450°C. Metal tips in field emission studies (see Section VIII-2C) tend to take on an equilibrium faceting into shapes agreeing fairly well with calculations [133]. 

Covers theory and applications of ah initio quantum mechanics calculations. The discussions are useful for understanding the differences between ah initio and semi-empirical methods. Although both sections are valuable, the discussion of the applications oi ah initio theory fills a void. It includes comparisons between experiment and many types and levels of calculation. The material is helpful in determining strategies for, and the validity of. ah initio calculations. 

Czerminski R and R Elber 1990. Self-A voiding Walk Between 2 Fixed-Points as a Tool to Calculate Reaction Paths in Large Molecular Systems. International Journal of Quantum Chemistry 824 167-186. 

In a chromatographic analysis of low-molecular-weight acids, butyric acid elutes with a retention time of 7.63 min. The column s void time is 0.31 min. Calculate the capacity factor for butyric acid. 

First we must calculate the capacity factor for isobutyric acid. Using the void time from Example 12.2, this is... 

Solid Density. SoHds can be characterized by three densities bulk, skeletal, and particle. Bulk density is a measure of the weight of an assemblage of particles divided by the volume the particles occupy. This measurement includes the voids between the particles and the voids within porous particles. The skeletal, or tme soHd density, is the density of the soHd material if it had zero porosity. Fluid-bed calculations generally use the particle... 

Calculated assuming 65 vol % of methane ia product gas and 1.5 vol gas/culture void. 

Density. Although the polymer unit cell dimensions imply a calculated density of 1.33 g/cm at 20°C, and extrapolation of melt density data indicates a density of 1.13 g/cm at 20°C for the amorphous phase, the density actually measured is 1.15—1.26 g/cm, which indicates the presence of numerous voids in the stmcture. 

Because mass flow bins have stable flow patterns that mimic the shape of the bin, permeabihty values can be used to calculate critical, steady-state discharge rates from mass flow hoppers. Permeabihty values can also be used to calculate the time required for fine powders to settle in bins and silos. In general, permeabihty is affected by particle size and shape, ie, permeabihty decreases as particle size decreases and the better the fit between individual particles, the lower the permeabihty moisture content, ie, as moisture content increases, many materials tend to agglomerate which increases permeabihty and temperature, ie, because the permeabihty factor, K, is inversely proportional to the viscosity of the air or gas in the void spaces, heating causes the gas to become more viscous, making the sohd less permeable. 

When the void space in an agglomerate is completely filled with a Hquid (Fig. Ic), the capillary state of wetting is reached, and the tensile strength of the wet particle matrix arises from the pressure deficiency in the Hquid network owing to the concave Hquid interfaces at the agglomerate surface. This pressure deficiency can be calculated from the Laplace equation for chcular capillaries to yield, for Hquids which completely wet the particles ... 

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.

In (8.35) Y is the flow stress in simple tension (and may itself be a function of the temperature and strain rate) and is the critical volumetric strain at void coalescence (calculated within the model to equal 0.15 independent of material). Note that the ductile fragmentation energy depends directly on the fragment size s. With (8.35), (8.30) through (8.32) become, for ideal ductile spall fragmentation,... 

The concentration gradient normal to the outside of the catalyst particle. The rate is expressed on catalyst-filled reactor volume, with e void fraction for this smaller volume the rate must be higher to keep Vrr=Vcr< . This is calculated from the continuity requirement that was mentioned above ... 

A hand calculation method that can be used to take into account two-phase relief when the materials m the vessel are natural" surface active foamers. To account for disengagement, the vessel void fraction at disengagement should be evaluated (i.e.. the point at which the vent flow ceases to be two-phase and starts to be vapor only). ... 

It will be shown that a more elegant and more easily applicable solution of the problem is given by choosing another reference system. Both the dilute alloy and the unperturbed host can be described with respect to a common reference system, which consists of the unperturbed part of the alloy system and for obvious reasons is called void system. This void system allows for a single-site evaluation of the matrix element describing the wind force in electromigration and the t-matrix element required for the calculation of the residual resistivity due to a saddle-point defect. 

Particle Density —The actual density of the solid particles taking into account any volume due to voids (pores) within the structure of the solid particles. Particle density is calculated as follows ... 

At temperatures above or near the eutectic temperature of the polymer phase, CSEi values are typically in the range of 0.1-2 pFcm-2 [5], However, for stiff CPEs or below this temperature, CSEI can be as low as 0.001 pFcm 2 (Fig. 16). When a CPE is cooled from 100 °C to 50 °C, the CSE1 falls by a factor of 2-3, and on reheating to 100 °C it returns to its previous value. This is an indication of void formation at the Li/CPE interface. As a result, the apparent energy of activation for ionic conduction in the SEI cannot be calculated from Arrhenius plots of 1// sei but rather from Arrhenius plots of 7SE)... 

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