Cross section total

In the model results, translational factors have roughly been taken into account by application of the correction factor (37). For cross sections, the velocity v should be replaced by the effective radial velocity Vr averaged also over the impact parameter. With the reasonable choice of Rc for the mean impact parameter one obtains Vr = 0.7u from Eq. (39). However, it should be kept in mind that significant uncertainties may enter in this treatment of the translational factors. Thus, the good agreement between the model results and the experimental data might be accidental. 

For convenient evaluation of the total cross section one may use the simple formula 

The applicability of the simple formula (41) should not be overestimated for X-vacancy exchange. It applies favorably for processes taking place in a well-localized transition region. This is not the case for the vacancy exchange between inner shells. However, for rapid estimates, formula (41) may serve as a useful tool to determine total cross sections for inner-shell vacancy exchange.  

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Experimentally, it is these invariants (equation (B 1.3.17), equation (B 1.3.18) and equation (B 1.3.19)) that can be obtained by scattering intensity measurements, though clearly not by measuring the total cross-section only. 

Here z denotes distance measured along the tube from the injection point and f is the volume flow rate of carrier gas, per unit total cross-section. 

The enthalpy flux vector N per unit total cross section in the... 

The gradient, is often denoted i for simplicity. It is often convenient to analy2e the discharge for a unit area using the specific discharge, q. The specific discharge represents the volumetric discharge divided by the total cross-sectional area, ie,... 

The porosity appears in the denominator of the right-hand side of the equaUty owing to the dependence of velocity on the available flow area, which is reduced from the total cross-sectional area by the factor n. 

The downcomer zones generally occupy 10 to 30 percent of the total cross section. For segmental downcomers, weir length ranges from 60 to 80 percent of the column diameter, so that the downcomer zone on each end of the plate occupies from 5 to 15 percent of the total cross section. 

The peripheral stiffening zone (tray ring) is generally 25 to 50 mm (1 to 2 in) wide and occupies 2 to 5 percent of the cross section, the fraction decreasing with increase in plate diameter. Peripheiy waste (Fig. 14-28) occurs primarily with bubble-cap trays and results from the inabihty to fit the cap layout to the circular form of the plate. Valves and perforations can be located close to the wall and little dead area results. Typical values of the fraction of the total cross-sectional area available for vapor dispersion and contact with the liquid for cross-flow plates with a chord weir equal to 75 percent of the column diameter are given in Table 14-6. 

The open area for these plates ranges from 15 to 30 percent of the total cross section compared with 5 to 15 percent for sieve plates and 8 to 15 percent for bubble-cap plates. Hole sizes range from 6 to 25 mm (1/4 to 1 in), and slot widths from 6 to 12 mm (14 to V2 in). The Turbogrid and Ripple plates are proprietary devices. 

The standard velocity based on total cross section is defined as ... 

W = Maximum allowable mass velocity, lb/(fL total cross section) (hr)... 

Values of the total cross-section a a for A1 Ka, radiation, relative to the carbon Is level, have been calculated by Scofield [2.7], and of the asymmetry parameter /Ja by Redman et al. [2.8]. Seah and Dench [2.3] have compiled many measurements of the inelastic mean free path, and for elements the best-fit relationship they found was ... 

Mean airstream velocity diminishes as inspiratory flow moves toward the lung parenchyma because of the rapid increase in total cross-sectional area. The largest increases in area occur in the distal bronchioles and pulmonary airways, causing u to approach zero because... 

Ideally, the sample should be injected onto the column as an infinitely thin disc, which covers the total cross section of the column. Because this is impossible, PSS has injected finite volumes onto the columns. In theory, these injection volumes should be as low as possible. In order to be able to detect the sample with significance, a certain (high) concentration of the sample has to be injected. This concept works well for low molar mass compounds, which do not generate much sample viscosity. However, when working with samples... 

The three layers can be treated as an iso-strain parallel model in the flow direction. The total cross-section Atotai and the total tensile modulus totai E,) of a composite sample can be determined as follows ... 

Ax = Total cross-sectional area of tower diameter, ft ... 

These stress-strain diagrams may be applied, for example, to the investigation of a rod of which has its total volume is glass fiber and half plastic. If the glass fibers are laid parallel to the axis of the rod, at any cross-section, half the total cross-sectional area is glass and half plastic. If the rod is stretched 0.5%, reference to the stress-strain diagrams... 

Adding equations 5.26 and 5.27 and dividing by A, the total cross-section area of the pipe, then ... 

The energy required for conveying can conveniently be considered in two parts that required for the flow of the air alone, and the additional energy necessitated by the presence of the particles. It should be noted, however, that the fluid friction will itself be somewhat modified for the following reasons die total cross-sectional area will not be available for the flow of fluid the pattern of turbulence will be affected by the solids and the pressure distribution through the pipeline will be different, and hence the gas density at a given point will be affected by the solids. 

If the height of the column is Z, its total cross-sectional area is S, and a is the interfacial area between the two phases per unit volume of column, then the rate of transfer of a... 

Table II. Total Cross-Sections for Reactions of Ions with Ethylene...

The >eff across the porous medium for this example is linearly related to the porosity of the path, which is in turn simply the ratio of the open cross-sectional area to the total cross-sectional area. There are no constriction or tortuosity effects in this example i.e., t = 1 and... 

Figure 15. Quantum (lines) and QCT (points) total cross-sections for the H + H2 1-TS and 2-TS paths.

Table 1.6 Characteristic quantities to be considered for micro-reactor dimensioning and layout. Steps 1, 2, and 3 correspond to the dimensioning of the channel diameter, channel length and channel walls, respectively. Symbols appearing in these expressions not previously defined are the effective axial diffusion coefficient D, the density thermal conductivity specific heat Cp and total cross-sectional area S, of the wall material, the total process gas mass flow m, and the reactant concentration Cg [114].

Current flow in a pore of length I and total cross section S produces an ohmic potential drop in the solution, which is the streaming potential ... 

SiHa is much smaller than the total cross section of charge exchange reactions between and SiHa. 

In one of the more recent continuum models (69), an approach first suggested by Leonardo da Vinci in the fifteenth century, from his observations that the cross-sectional area (CSA) of the main stem of a tree equaled the total cross-sectional area of all the tree branches, was used. The more generalized rule was considered ... 

The top tube sheet is normally aligned with the liquid level in the base of the column Figure 12.58. The outlet pipe should be as short as possible, and have a cross-sectional area at least equal to the total cross-sectional area of the tubes. 

R a Ratio of bundle cross-sectional area in window zone to total cross-sectional ... 

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