Cross section, definition

The variable is defined with respect to the axis of the fragmentation jet which is reconstructed from charged particle tracks only. The tracks are clustered by a jet algorithm (TrackJets) and a combined transverse energy of > 1 GeV is required. In order to facilitate the comparison between the measurement and the theory predictions, the TrackJet is not included in the cross section definition. The extrapolation of the measured cross-section amounts to 10%. 

Seismic Anaiysis of Steei-Concrete Composite Buiid-ings Numericai Modeiing, Fig. 20 The cross-sectional definition for the post-elastic range... 

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. 

Permeability, d Arcy, definition, 14-15 for capillary of circular cross-section, 15... 

Microscopic examination of cross sections through the paint layers gives definite information regarding the paint-layer sequence in the area from which the sample was taken (31,66). This information illustrates the artist s use of underlayers and glazes, superposition of compositional elements, and changes in composition. 

Noncircular Channels Calciilation of fric tional pressure drop in noncircular channels depends on whether the flow is laminar or tumu-lent, and on whether the channel is full or open. For turbulent flow in ducts running full, the hydraulic diameter shoiild be substituted for D in the friction factor and Reynolds number definitions, Eqs. (6-32) and (6-33). The hydraiilic diameter is defined as four times the channel cross-sectional area divided by the wetted perimeter. For example, the hydraiilic diameter for a circiilar pipe is = D, for an annulus of inner diameter d and outer diameter D, = D — d, for a rectangiilar duct of sides 7, h, Dij = ah/[2(a + h)].T ie hydraulic radius Rii is defined as one-fourth of the hydraiilic diameter. 

By definition, the resistivity and conductivity of a and cross-sectional area A conductor of length d... 

Let us then consider an arbitrarily selected point in a pipe in winch gas and solid particles are flowing. The flow of the mixture of gas and solid parti cles need not be homogeneous, i.e., the concentration of particles may vary across the cross-section of the pipe. This means that the mixture ratio p. should generally be regarded as a function of position in the pipe, and therefore the definition, Eq. (14.1), should be replaced by... 

Vicat hardness It is a determination of the softening point for TPs that have no definite melting point. The softening point is taken the temperature at which the specimen is usually penetrated to a depth of 1 mm2 (0.0015 in2) circular or square cross section, under a 1,000 g load. 

The connection that has been shown in Section VIII to exist between burn-out in a rod bundle and in an annulus leads to the question of whether or not a link may also exist between, for example, a round tube and an annulus. Now, a round tube has its cross section defined uniquely by one dimension—its diameter therefore if a link exists between a round tube and an annulus section, it must be by way of some suitably defined equivalent diameter. Two possibilities that immediately appear are the hydraulic diameter, dw = d0 — dt, and the heated equivalent diameter, dh = (da2 — rf,2)/ however, there are other possible definitions. To resolve the issue, Barnett (B4) devised a simple test, which is illustrated by Figs. 38 and 39. These show a plot of reliable burn-out data for annulus test sections using water at 1000 psia. Superimposed are the corresponding burn-out lines for round tubes of different diameters based on the correlation given in Section VIII. It is clearly evident that the hydraulic and the heated equivalent diameters are unsuitable, as the discrepancies are far larger than can be explained by any inaccuracies in the data or in the correlation used. 

Such a cross-section is somewhat less than the geometrical one cross-section oj, one can try to determine y via the following relation ... 

Let us note that this definition of y breaks the limits of the Kielson-Storer model and can cause a few contradictions in interpretation of results. If the measured cross-section oj appears to be greater than oo, then, according to (3.45), the sought y does not exist. To be exact, this assertion is valid relative to the cross-section of the rotational energy relaxation oe = (1 — y2)oot since y2 is always positive. As to oj, taking into account the domain of negative values of y, corresponding to the anticorrelated case (see Chapter 2), formula (3.45) fails to define y when oj > 2co. 

Here in Chapter 1 we make the additional assumptions that the fluid has constant density, that the cross-sectional area of the tube is constant, and that the walls of the tube are impenetrable (i.e., no transpiration through the walls), but these assumptions are not required in the general definition of piston flow. In the general case, it is possible for u, temperature, and pressure to vary as a function of z. The axis of the tube need not be straight. Helically coiled tubes sometimes approximate piston flow more closely than straight tubes. Reactors with square or triangular cross sections are occasionally used. However, in most of this book, we will assume that PFRs are circular tubes of length L and constant radius R. 

The double integral in Equation (8.4) is a fairly general definition of the mixing-cup average. It is applicable to arbitrary velocity profiles and noncircular cross sections but does assume straight streamlines of equal length. Treatment of curved streamlines requires a precise and possibly artificial definition of the system boundaries. See Nauman and Buffham. ... 

In the capillary method, the time required for a liquid to flow through a capillary tube is determined. The melt under investigation flows with a constant rate through a tube with a small, definite cross-sectional area, such as a cylindrical capillary. The viscosity can be measured in an absolute way from the pressure drop. This method can yield the most reliable absolute data, the viscosity being given by a modified Hagen-Poiseuille equation ... 

By definition the partial current density ij is the number of charges that in unit time cross the unit cross-sectional area due to the migration of ions j that is,... 

In the above relationship p is an intrinsic property called the specific resistance (or resistivity) of the conductor. The definition of the specific resistance of any given conductor follows from this relationship. It is the resistance in ohms of a specimen of the material, 1 cm long and 1 cm2 in cross-sectional area (units ohm cm-1), the length being in the direction of the current and the cross-section normal to it. In other words, the specific resistance p of a conductor is the resistance of a cube of 1 centimeter edge. If the conductance is denoted by C = 1 /R, then the specific conductance (or conductivity) K, is given by JC= 1/a (units ohm-1 cm-1, mho cm-1, reciprocal ohm cm-1). Therefore, the relationship R = aL/A may be written as R = L/KA (units ohms) and the conductance can be expressed as C = 1/R = KA/l (units reciprocal ohms). 

Using the above definitions and integrating over the channel cross section, with some manipulations, Zuber s kinematic equation results (Hsu and Graham, 1976) ... 

In conclusion, PbB levels of 40-60 pg/dL are considered to be markedly elevated in children, and neuro-behavioral effects are distinct. There are no clear definitions of what constitutes low versus moderate PbB levels, and effects observed at the lower levels (particularly <15 pg/dL), have proven more difficult to separate from socioeconomic and other variables. Many of the cross-sectional studies that showed... 

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