Separation angle

Let us now choose to locate a second equivalent, though not necessarily orthogonal, hybrid orbital h2 in the x-z plane. The axis of h2 will be chosen to make the angle a with the axis of hi. In order for hi and h2 to be equivalent, the values of the angular parts of the hybrids must be identical in their respective directions. This condition is satisfied for any separation angle a by the following expression for h2 ... 

The dimensions of the attached wake are shown in Figs. 5.6, 5.7, and 5.8. The various numerical solutions agree closely with flow visualization results of Taneda (T2), although other workers (K2) report separation slightly closer to the rear. The separation angle, measured in degrees from the front stagnation point, is well approximated by... 

The relative importance of form drag continues to increase in this region with skin friction becoming inferior once Re > 150 (M2), and begins to level out. The separation angle is still given by Eq. (5-10). 

As Re increases further and vortices are shed, the local rate of mass transfer aft of separation should oscillate. Although no measurements have been made for spheres, mass transfer oscillations at the shedding frequency have been observed for cylinders (B9, D6, SI2). At higher Re the forward portion of the sphere approaches boundary layer flow while aft of separation the flow is complex as discussed above. Figure 5.17 shows experimental values of the local Nusselt number Nuj c for heat transfer to air at high Re. The vertical lines on each curve indicate the values of the separation angle. It is clear that the transfer rate at the rear of the sphere increases more rapidly than that at the front and that even at very high Re the minimum Nuj. occurs aft of separation. Also shown in Fig. 5.17 is the thin concentration boundary layer... 

Experimental observations of the flow past a circular cylinder show that separation does indeed occur, with a separation point at 0S — 110 . It should be noted, however, that steady recirculating wakes can be achieved, even with artificial stabilization,24 only up to Re 200, and it is not clear that the separation angle has yet achieved an asymptotic (Re —> oo) value at this large, but finite, Reynolds number. In any case, we should not expect the separation point to be predicted too accurately because it is based on the pressure distribution for an unseparated potential flow, and this becomes increasingly inaccurate as the separation point is approached. The important fact is that the boundary-layer analysis does provide a method to predict whether separation should be expected for a body of specified shape. This is a major accomplishment, as has already been pointed out. 

If Re increases beyond 20 the separation ring moves forward so that the attached re-circulating wake widens and lengthens. The separation angle measured in degrees from the front stagnation point is well approximated by 0 = 180-42.5 (ln(Re/20)) at 20 < Re < 400. The steady wake region appears at 20wake instability corresponds to 130 < Re < 400. 

The purpose of obtaining spectral data on the complex refractive Index of polycarbonate polymer was to permit detailed Interpretations to be made of the IR-RA spectra collected In situ on metal-backed films of this material. Several of the principal methods for obtaining the optical constants n and k of an Isotropic medium have been reviewed by Humphreys-Owen [18]. All of the methods outlined are Insensitive to k when k Is close to zero, which Is the case for frequencies between absorbance bands. For this study, a polarlmetrlc technique (method D In Ref. 18) was chosen to obtain the optical constants of BPA-PC. To apply this method, the ratio of surface reflectances Rp/Rg at two large, but well-separated, angles of Incidence (9 ) was obtained for BPA-PC In the IR. Rp Is defined as the reflectance measured for a sample using radiation polarized parallel to the Incidence plane and R... 

Underflow solids capacity is a function of the spiral diameter and solids density independent of the separation. Angle of inclination 16°. 

While only two cameras are necessary to reconstmct the three-dimensional coordinates of a tracking target in object-space, more than two cameras are recommended to help ensure that a minimum of two cameras see the target every point in time. The cameras should be positioned so that each has a unique perspective of the wortepace. Ideally the cameras should be placed at an angle of 90 with respect to one another. In practice this may not be possible, and every effort should be taken to maintain a minimum separation angle of at least 60 . 

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