Apex angle

By feeding the mixture through a converging nozzle, the velocity profile may be made nearly flat or uniform. A Bunsen flame in such a flow has a smaller range of stabiUty but the mechanism is essentially the same and the flame very closely approximates a cone. If the apex angle of the flame is , then S can be obtained from equation 21... 

Seam-to-seam length above the cone Cone apex angle... 

Deep cones having a 70° apex angle are normally used in drill bits to give built-in stability and to obtain greater diamond concentration in the bit-cone apex. 

Experiments were carried out in a conical shape gas fluidized bed (0.1 m-i.d. x 0.6 m-high) that made of a transparent acryl column with an apex angle of 20°. The details of the conical fluidized beds can be found elsewhere [3]. Air velocity (Ug = 0-1.4 m/s) were measured by a flowmeter. The particle used in this study was 1.0 mm glass beads with a density of 2,500... 

The design factor Cc is a function of the half apex angle a ... 

Equation (2-14) provides a way to calculate the liquid temperature in equilibrium with the ready-to-grow bubble if the saturation pressure or temperature, the value of B, and the cavity radius are known (Shai, 1967). Several modified versions of nucleation criteria have since been advanced. An example is the model proposed by Lorenta et al. (1974), which takes into account both the geometric shape of the cavity and the wettability of the surface (in terms of contact angle < >). Consider an idealized conical cavity with apex angle ip, and a liquid with a flat front penetrating into it (Fig. 2.3a). Assume that once the vapor is trapped in by the liquid front, the interface readjusts to form a cap with radius of curvature rn. Conservation of vapor... 

The shape is usually either a sphere (Brinell, and Rockwell B or C) a square pyramid with apex angle = 135° (Vickers) a trigonal pyramid (Berkovich) or an elongated four-sided pyramid (Knoop). (See Figure 1.2). For quality control in manufacturing operations, semi-automatic Rockwell machines, and their various indenters, are also useful. 

As the size of R3P increases so does the value of k. A popular method of assessing the size of R3P is by using Tolman s cone angle. This is the apex angle of the cone centered on P which just encloses the van der Waals radii of the outermost atoms of R3P. The data are shown in Table 2.3 for (2.134) in CO-saturated C2CI4 at 70°C (Ref. 124)... 

It is possible to translate these, in three dimensions, as the motion of a magnet of moment p in an applied magnetic field. The magnet axis becomes inclined to the field, precesses around it, and is defined as the Lamour precession. The half-apex angle of the cone equals 0 and the angular velocity is yBo, so that one finds equation 3.16 now rewritten as equation 3.20 ... 

Figure 12.5 Calculated mean temperature fields in combustors with a set of similar open-edge V-gutter flame holders of height H = 3 cm and apex angle of 60°. The isoterms divide the entire temperature interval from the initial temperature To to combustion temperature Tc into 10 uniform parts and correspond to t = 27.5 ms. The combustor is 1 m long and the distance between the planes of flame holders is 0.05 m. Flame holders are shifted in longitudinal direction by OH (no shift) (a), IH (6), 2H (c), 3H (d), and 5H (e). Combustion of stoichiometric methane-air mixture at the mean inlet velocity Ui = 20 m/s, po = 0.1 MPa, To = 293 K, ko = 0.24 J/kg, /o = 4 mm. The lower and upper boundaries of the computational domain are the symmetry planes...

Table 12.1 Calculated characteristic reaction time tc, residence time tr, and the Mikhelson number Mi for the combustion of the stoichiometric methane-air mixture in a combustor with the open-edge V-gutter flame holder of height H and apex angle 60° at the mean inlet velocity Uin. Also presented is the maximum approach-stream velocity Um- Signs and correspond to stabilized flame and unstable flame, respectively... 

Strohmeier showed that the IR carbonyl frequencies of metal complexes could be used as a measure of the electronic properties of the ligands [8]. Tolman introduced a systematic approach to describe electronic and steric ligand effects [9]. The electronic parameter / is based on the difference in the IR frequencies of Ni(CO)3L and the reference compound Ni(CO)3(P Bu3), similar to the method introduced by Strohmeier. For phosphorus ligands the cone angle 6 is defined as the apex angle of a cylindrical cone, centered at 2.28 A from the center of the P atom, which touches the outermost atoms of the model. 

The diffracted beams make an angle of 26 with the incident beam. Because the crystallites can lie in all directions while still maintaining the Bragg condition, the reflections lie on the surface of cones whose 5emr-apex angles... 

The booster expl may cause an artificially energetic and rapid detonation, called overdrive, in the sample. To correct for overdrive, wedges with apex angles of 1,2,3,4, and 5° are fired, and the resulting failure thicknesses are plotted vs angle. A linear curve is fitted through the data and extrapolated to 0°, and the failure thickness at (T is designated the detonation failure thickness. (Fig 1)... 

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