Circular sector

CIRCULAR SECTOR r - radius of circle y - angle ncp In degrees Area of Sector ncpo - xh (length of arc nop X r)... 

Figure 7. A78 isomers. The unfolded surface lattice nets at the left are drawn with boundaries along the vectors between nearest neighbour V5s which are marked by the black circular sectors, whereas the boundaries for the nets at the right are along the edges of deltahedral facets. The projected views of the fullerene polyhedra and deltahedra duals in the centre column are all oriented with a corresponding two-fold axis horizontal. For the four mirror-symmetric isomers, there is one mirror plane in the plane of projection and an orthogonal horizontal one. Marking the symmetry elements for each isomer on the deltahedral surface lattice net defines the asymmetric unit.

Before closing this chapter, we feel that it is useful to list in tabular form some isothermal pressure-flow relationships commonly used in die flow simulations. Tables 12.1 and 12.2 deal with flow relationships for the parallel-plate and circular tube channels using Newtonian (N), Power Law (P), and Ellis (E) model fluids. Table 12.3 covers concentric annular channels using Newtonian and Power Law model fluids. Table 12.4 contains volumetric flow rate-pressure drop (die characteristic) relationships only, which are arrived at by numerical solutions, for Newtonian fluid flow in eccentric annular, elliptical, equilateral, isosceles triangular, semicircular, and circular sector and conical channels. In addition, Q versus AP relationships for rectangular and square channels for Newtonian model fluids are given. Finally, Fig. 12.51 presents shape factors for Newtonian fluids flowing in various common shape channels. The shape factor Mq is based on parallel-plate pressure flow, namely,... 

A hemispherical polymer matrix that is coated on all surfaces with an impermeable coating except for an aperture in the center face has been demonstrated to provide near constant rate release profiles ( 18). Another approach consists of a cylinder with impermeable wall and a cavity having a circular sector cross section. 

The center of the circular sector lies outside the cylinder, thereby producing a slit for drug release from the drug containing matrix in the cavity. The release profiles from this system also show a substantial constant rate region (19,20). It is clear that, in both systems, the increase in diffusional distance and consequently the decrease in diffusion rate have been balanced by the increase in area at the diffusion front thereby giving rise to a near constant rate region. 

Further extensions can be made when additional confinements are introduced. Following the example of [10], in which confinement in circular sectors was investigated, the dihedral confinement may be complemented with additional spherical and/or conical, one or two paraboloidal, and spheroidal and/or hyperboloidal boundaries. 

A schematic drawing of a circular sector duct is presented in Fig. 5.54. The fully developed/Re and Nu for circular sector ducts have been obtained by Eckert and Irvine [280], Sparrow and Haji-Sheikh [174], Hu and Chang [265], and Ben-Ali et al. [281]. The results are summarized in Table 5.57. 

TABLE 5.57 Fully Developed/Re, K(oo), and Nu for Laminar Flow in a Circular Sector Duct... 

TABLE 5.58 Flow Parameters for Hydrodynamically Developing Flow in Circular Sector Ducts [282]... 

E. M. Sparrow, and A. Haji-Sheikh, Laminar Heat Transfer and Pressure Drop in Isosceles Triangular, Right Triangular, and Circular Sector Ducts, /. Heat Transfer, (87) 426-427,1965. 

T. M. Ben-Ali, H. M. Soliman, and E. K. Zariffeh, Further Results for Laminar Heat Transfer in Annular Section and Circular Sector Ducts, J. Heal Transfer, (111) 1090-1093,1989. 

Circular Sector (included angle 6) = arc x radius = shindr. (14) Circular Segment=area of sector -area of triangle sin 0 (15)... 

For the circular sector of angle 2a and radius R, the area A is aR the integral needed for x, expressed in polar coordinates, is... 

Fig. 3 shows a storyboard for the animated buttons. Modifying the size of a copy of the button s external circle and the colour of the button s internal circle creates the animation. The copy of the circle was used so the original form of the button was not modified. The copy of the grey external circle s radius is increased from its original size until it touches the circular sector. There is also an increase in the size of the contour and brightness of this circle. The increasing size of the external circle might look like the concentric waves caused by a stone thrown into the water. 

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