Half-value radius

The measured values of the half-value radius, b, of the radial distribution of are shown in Fig. 2.15. The value approaches the following empirical correlation... 

Fig. 2.17 Relation between half-value radius and axial distance...

Concerning the vertical bubbling jets free from the side wall, the half-value radius, bu, of the radial distribution of the axial mean velocity u is approximated by [21] ... 

It is assumed that the merging between two bubbling jets is related to the extent of bubble dispersion region of each bubbling jet. The half-value radius of gas holdup a at a = 50%, designated by ba,so, is approximated by [15,19] ... 

An air-water bubbling jet which is not subjected to the Coanda effect is known to rise straight upward while entraining the surrounding water into it [21]. As a result, the horizontal region in which water moves vertically upward spreads as z increases. The extent of this horizontal region can be represented, for example, by the half-value radius, of the horizontal distribution of the axial mean velocity of water flow, u (see Fig. 3.42). Based on existing experimental study, [21] can be approximated by... 

It has been demonstrated that the half-value radius bu of molten Wood s metal flow induced by He gas injection through a single-hole bottom nozzle can be satisfactorily predicted by (3.14) [32] Accordingly, (3.26) may also be applicable in predicting the interaction between two bubbling jets in a molten metal bath. 

Figure 8.6 shows the vertical distribution of the axial mean velocity u normalized by the centerUne value for the single-phase water jet (gg = OcmVs), m,sw. The vertical distance y is nondimensionalized by the half-value radius for the single-phase... 

The vertical distribution of m can be described if the maximum value m and the half-value radius are known. This section focuses on u and only the maximum value of V is discussed. 

The half-value radius of the vertical distribution of the axial mean velocity component is denoted by b. The measmed values shown in Fig. 8.15 can all be approximated by the solid line of the form ... 

Empirical relations are derived for the maximum values of the axial and vertical velocity components, Tim and Vm, as well as the half-value radius of the axial velocity component, b. The distributions of Mm, Vm, and could be predicted by the empirical relations in (8.20), (8.21), and (8.23) when the velocity ratio r., falls between 4 and 24. When rv is greater than 24, empirical relations originally derived for single-phase jets should be used to predict the three quantities in the water-air two-phase jets. 

Attention should be directed to a notable phenomenon which may occur if capillary condensation is involved in sorption. If a capillary is exposed to vapour of increasing tension, the latter will be first absorbed on its walls. When the pressure has reached a value where condensation can set in, the capillary wall will be covered with a liquid layer, (Fig. 19a) whose radius of curvature is only half the radius of... 

Since the static mixer has a diameter of 0.04 m, the value of Ls is given as 0.01 m, one-half the radius, and is assumed to be constant, although that is a strong approximation. Normalized values of the reactants and products were... 

The physical properties of the Selenium also offer big advantages with respect to radiation shielding and beam collimation. Within the comparison of radiation isodose areas the required area-radius for a survey of 40pSv/h result in a shut off area that is for Selenium only half the size as for iridium. Sources of similar activity and collimators of same absorbtion value (95%) have been used to obtain values as mentioned in Table 3 below. 

The single-bond covalent radius of C can be taken as half the interatomic distance in diamond, i.e. r(C) = 77.2pm. The corresponding values for doubly-bonded and triply-bonded carbon atoms are usually taken to be 66.7 and 60.3 pm respectively though variations occur, depending on details of the bonding and the nature of the attached atom (see also p. 292). Despite these smaller perturbations the underlying trend is clear the covalent radius of the carbon atom becomes smaller the lower the coordination number and the higher the formal bond order. 

Since the expression (41) is deduced for a sphere whose radius is large compared with the molecules of the liquid, it is not known to what extent the behavior of atomic and small molecular ions should be in accordance with (41). It is clear that, if (41) were applicable, the value of the mobility should vary inversely with the viscosity. If for any ion the K on the left-hand side of (41) is set equal to the constant force acting on the ion in a field of unit intensity, the v on the right-hand side of (41) becomes equal to the mobility u. Since K is independent of temperature the product of u and ij should be independent of temperature. From Table 42 it will be seen that at 25°C the viscosity of water is almost exactly half the viscosity at 0°C thus, according to (41) the mobility u of each ion should be double. 

The values in Table VI were obtained in the following way. Values for C, Si, Ge, and Sn are the same as in Table III, for the tetrahedral configuration is the normal one for these atoms. Radii for F, Cl, Br, and I were taken as one-half the band-spectral values for the equilibrium separation in the diatomic molecules of these substances. Inasmuch as these radii for F and Cl are numerically the same as the tetrahedral radii for these atoms, the values for N, 0, P, and S given in Table III were also accepted as normal-valence radii for these atoms. The differences of 0.03 A between the normal-valence radius and the tetrahedral radius for Br and... 

The symmetry axis with maximum strength for each function of set I is 69° 1.35 from the fivefold axis of the pentagonal antiprism, corresponding to the ratio 0.38341 of half height to radius of the antiprism, with the corresponding values for set II of 41° 47.65 and 1.1186. 

The theory has been verified by voltammetric measurements using different hole diameters and by electrochemical simulations [13,15]. The plot of the half-wave potential versus log[(4d/7rr)-I-1] yielded a straight line with a slope of 60 mV (Fig. 3), but the experimental points deviated from the theory for small radii. Equations (3) to (5) show that the half-wave potential depends on the hole radius, the film thickness, the interface position within the hole, and the diffusion coefficient values. When d is rather large or the diffusion coefficient in the organic phase is very low, steady-state diffusion in the organic phase cannot be achieved because of the linear diffusion field within the microcylinder [Fig. 2(c)]. Although no analytical solution has been reported for non-steady-state IT across the microhole, the simulations reported in Ref. 13 showed that the diffusion field is asymmetrical, and concentration profiles are similar to those in micropipettes (see... 

It was shown later that a mass transfer rate sufficiently high to measure the rate constant of potassium transfer [reaction (10a)] under steady-state conditions can be obtained using nanometer-sized pipettes (r < 250 nm) [8a]. Assuming uniform accessibility of the ITIES, the standard rate constant (k°) and transfer coefficient (a) were found by fitting the experimental data to Eq. (7) (Fig. 8). (Alternatively, the kinetic parameters of the interfacial reaction can be evaluated by the three-point method, i.e., the half-wave potential, iii/2, and two quartile potentials, and ii3/4 [8a,27].) A number of voltam-mograms obtained at 5-250 nm pipettes yielded similar values of kinetic parameters, = 1.3 0.6 cm/s, and a = 0.4 0.1. Importantly, no apparent correlation was found between the measured rate constant and the pipette size. The mass transfer coefficient for a 10 nm-radius pipette is > 10 cm/s (assuming D = 10 cm /s). Thus the upper limit for the determinable heterogeneous rate constant is at least 50 cm/s. 

Fig. 4.3.7 The left figure shows the radius of Figure 4.3.6, at the free surface of the Fano the Fano column as a function of the column column (r = Rr), one half radius of the column height (z), which was enlarged towards the (r= 0.5 R) and the center of the column (r= 0). column base. The right figure shows the local The figure clearly shows that there was a large velocity values at three different locations (z) of velocity shear near the fluid entrance, and the the Fano column as a function of the column velocity at the free surface was almost con-height. The three sets of velocity values were stant. measured from the velocity profiles shown in...

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