Cross section volume

If the critical separation is determined for a large number of relative geometries of the electron and molecule it is possible to obtain a three-dimensional picture of the probability of ionization as a function of the orientation of the molecule. Effectively, the idea of an ionization cross section, the area the target molecule presents to the electron, is extended to a three-dimensional object defined by the critical distances, with ionization occurring when the electron penetrates the surface enclosing this volume. The volume enclosed by the electron impact ionization surface may be used to obtain an estimate for the cross section (volume averaged cross section) ... 

C solids concentration in the sampler, volume fraction Cb average solids concentration over the pipe cross section, volume fraction... 

Fig.6 SEM graphs of ZrB2-SiC coaling after FPCVD ( a. surface b. polished cross-section ) volume shrinkage accompanied in the PCS pyrolysis. Compared to the surface microstructrures...

Parameters of pressure waves caused by hydrogen + natural gas (NG) deflagra-tion in a 5.21 m non-obstructed volume were measured in [10]. A diagram of the test is given in Fig. 9.16. The square-cross section volume was 2.24 x 2.24 x 1.5 m. The volume was filled with the BE (see compositions in Table 9.2).The combustion processes were triggered by an explosive wire. 

Take an example of estimating gross rock volume, based on seismic data and the results of two wells in a structure (Fig. 7.2). The following cross-section has been generated, and a base case GRV has been calculated. 

Another application areas of microtomography are biology and agriculture. Fig.4a shows an X-ray transmission image through the tulip bulb in wet conditions. Damaged area can be found in the surface of this bulb. Fig.4b shows the reconstructed cross section with information about depth of damaged volume. 

Now integrate the equation (5) taking into account the formulae for pi and pN. As a result we arrive to the specific volume flow rate in a film, referred to the unit of length for cross section ... 

In the case, where all 3 phases are present, the detector measurements reveal the amounts of tracers in each phase and the position of the boundaries between the phases The cross section area of each phase is calculated fi-om the latter. From this the tracer concentrations and hence the volume flows of the 3 phases are calculated. 

A still different approach to multilayer adsorption considers that there is a potential field at the surface of a solid into which adsorbate molecules fall. The adsorbed layer thus resembles the atmosphere of a planet—it is most compressed at the surface of the solid and decreases in density outward. The general idea is quite old, but was first formalized by Polanyi in about 1914—see Brunauer [34]. As illustrated in Fig. XVII-12, one can draw surfaces of equipo-tential that appear as lines in a cross-sectional view of the surface region. The space between each set of equipotential surfaces corresponds to a definite volume, and there will thus be a relationship between potential U and volume 0. 

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 procedures described so far have all required a pore model to be assumed at the outset, usually the cylinder, adopted on the grounds of simplicity rather than correspondence with actuality. Brunauer, Mikhail and Bodor have attempted to eliminate the over-dejjendence on a model by basing their analysis on the hydraulic radius r rather than the Kelvin radius r . The hydraulic radius is defined as the ratio of the cross-sectional area of a tube to its perimeter, so that for a capillary of uniform cross-section r is equal to the ratio of the volume of an element of core to... 

Next we recognize that 6 and X always appear as a ratio in our theory. If we argue that the hole and the polymer chain have comparable cross-sectional areas, we can multiply both the numerator and denominator of the X/6 ratio by this cross section and convert it into the ratio V /V, where is the volume of the flow segment of length X. While we know neither of these volumes directly, there are indications that V /V may be on the order of 10-20 for many linear... 

Equation (9.28) describes the velocity with which a cylindrical shell of liquid moves through a capillary under stationary-state conditions. This velocity times the cross-sectional area of the shell gives the incremental volume of liquid dV which is delivered from the capillary in an interval of time At. The total volume delivered in this interval AV is obtained by integrating this product over all values of r ... 

Until recently most industrial scale, and even bench scale, bioreactors of this type were agitated by a set of Rushton turbines having about one-thind the diameter of the bioreactor (43) (Fig. 3). In this system, the air enters into the lower agitator and is dispersed from the back of the impeller blades by gas-fiUed or ventilated cavities (44). The presence of these cavities causes the power drawn by the agitator, ie, the power requited to drive it through the broth, to fall and this has important consequences for the performance of the bioreactor with respect to aeration (35). k a has been related to the power per unit volume, P/ U, in W/m and to the superficial air velocity, in m/s (20), where is the air flow rate per cross-sectional area of bioreactor. This relationship in water is... 

A steady-state material balance can be carried out on a small section of length and volume (on the basis of unit cross-sectional area) ia the contactor ... 

The actual flotation phenomenon occurs in flotation cells usually arranged in batteries (12) and in industrial plants and individual cells can be any size from a few to 30 m in volume. Column cells have become popular, particularly in the separation of very fine particles in the minerals industry and coUoidal precipitates in environmental appHcations. Such cells can vary from 3 to 9 m in height and have circular or rectangular cross sections of 0.3 to 1.5 m wide. They essentially simulate a number of conventional cells stacked up on top of one another (Fig. 3). Microbubble flotation is a variant of column flotation, where gas bubbles are consistently in the range of 10—50 p.m. 

To illustrate the use of the momentum balance, consider the situation shown in Figure 21c in which the control volume is bounded by the pipe wall and the cross sections 1 and 2. The forces acting on the fluid in the x-direction are the pressure forces acting on cross sections 1 and 2, the shear forces acting along the walls, and the body force arising from gravity. The overall momentum balance is... 

The resistance of a segment of the path described above is proportional to its length, iaversely proportional to its cross-sectional area, and proportional to a specific property of the material of the segment called resistivity or volume resistivity, ie ... 

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