Pure Radial

Line Sink The velocity induced by a line sink is purely radial and is given in cylindrical coordinates by... 

There are indications that the presence of two populations is a common feature of dSph galaxies. Our preliminary analysis of HB stars, Vhei and [Fe/H] measurements in the other galaxies in our sample (Fornax and Sextans dSph Battaglia et al., in prep) also shows very similar characteristics to Scl, especially in the most metal poor component. Pure radial velocity studies [15], [16] have also considered the possibility that kinematically distinct components exist in Ursa Minor, Draco and Sextans dSph galaxies. 

Typically, axial flow pumps are of high flow and low head type and have a high specific speed. On the other hand, purely radial pumps are of high head and low flow rate capabihty and have a low specific speed) Obviously a pump with a moderate flow and head has an average specific speed. 

Note that even for pure radial flow, w = 0, there is still a circumferential dilatation, Fee 7 0. This is because the radial velocity spreads the flow as seen by the dashed differential element in Fig. 2.7. 

As an example, consider a situation for an open tube with purely radial inlet flow. The boundary conditions that describe this situation are, at the inlet boundary r = 1,... 

Fig. 6.22 Nondimensional streamlines and velocity profiles for an isothermal tubular flow with purely radial inlet velocity. The streamlines shown are for a Reynolds number of 1. The nondimensional velocity profiles are shown for Reynolds numbers of 1, 10, and 100.

Now let s adopt the hypothesis on purely radial flow which will hold true if R(t) > q0 (see Fig. 10b). The equation of flow will have the form ... 

Fig. 11a, b. Kinetic identification of the first stage of filling a flat mould through a round (point) runner a flow is purely radial during some limited time interval, flow front is approximately circular b the radius of free boundary becomes equal to half-width of the forming cavity R(t) = B/2... 

Now suppose that the displacement is purely radial in this case, we find... 

Since each gas channel is configured as a channel grid, it does not allow the gas to follow a pure radial direction. Thus, the effect of non-uniform gas distribution needs to be quantified. 

The deviation of the flux from a purely radial configuration can lead to several consequences on the operational conditions of the fuel cell, thus affecting the resultant performance. First of all, if the gas is not well distributed within the cell surface, the reaction rate varies from area to area. This implies the existence of preferred zones for the electrochemical reaction, and, consequently, of local high current density, thus reducing the overall cell voltage. Secondly, different reaction rates throughout the cell causes temperature gradients and, consequently, thermal stresses, which can cause mechanical failure of the cell [2-4], Finally, the existence of (some) preferred zones for the electrochemical reaction implies that part of... 

This equation can be solved by separation of variables, provided the potential is either a constant or a pure radial function, which requires that the Lapla-cian operator be specified in spherical polar coordinates. This transformation and solution of Laplace s equation, V2 / = 0, are well-known mathematical procedures, closely followed in solution of the wave equation. The details will not be repeated here, but serious students of quantum theory should familiarize themselves with the procedures [15]. 

In the previous section, it was recognized that for perfect fluid distribution flow direction has only a second order effect on conversion. In this section, the effects of maldistribution are investigated. In order to eliminate the influence of flow direction, a pseudo-homogeneous plug flow model is used with purely radial flow through the catalyst basket. The governing equation is thus Eqn. (14), which in more convenient form is... 

As far as the theoretical description is concerned, the confined acoustic phonons in an elastic sphere were first theoretically studied by Lamb [29]. He derives two types of confined acoustic modes, spheroidal and torsional modes. The frequencies of these two modes are proportional to the sound velocities in particles and inversely proportional to the particle size. The spheroidal mode is characterized by the quantum number / > 0, while the torsional modes are characterized by / > 1. From the symmetry arguments, Raman-active modes are spheroidal modes with I = 0 and 2. The I = 0 mode is purely radial with spherical symmetry and produces totally polarized spectra, while the Z = 2 mode is quadrapolar and produces partially... 

The waves i ° and 0 can be calculated on the dividing surface without difficulty for any collision energy E, because the inter-fragment potential for i > s is purely radial. The internal eigenfunctions of the BC fragment, (pa i i y) i constitute an orthonormal basis on dS [60,158]. In this representation, the matrices and of the incoming... 

Let us consider now the deformation and stresses of a cylindrical pipe under two different boundary conditions (Fig. 16.2). In both eases the length of the pipe is considered constant according to the requirements for a plane strain problem. The external and internal radii are R2 and R, respectively. If the applied forces and the displacements are also uniform, the deformation is purely radial, and in cylindrical coordinates = u r). According to the Navier equations, rot u = 0. Hence, Vdiv u = 0, which implies... 

The time-dependent fiinction Hit ) is determined by the rate of increase or decrease in the bubble volume. The governing equations and boundary conditions that remain to be satisfied are (1) the radial component of the Navier Stokes equation (2) the kinematic condition, in the form of Eq. (2 129), at the bubble surface and (3) the normal-stress balance, (2 135), at the bubble surface with = 0. Generally, for a gas bubble, the zero-shear-stress condition also must be satisfied at the bubble surface, but xrti = 0, for a purely radial velocity field of the form (4-193), and this condition thus provides no usefirl information for the present problem. 

It is clear from part (a) that the fluid motion cannot be purely radial except, possibly, in the creeping-flow limit, Re -> 0. However, you should be able to demonstrate that the swirl velocity component in the 6 direction is zero. 

Taylor (1953) now made the brilliant assumption that to a first approximation the flow is quasi-steady with respect to axes moving with mean speed U, and that the concentration variation with respect to these axes is purely radial. His solution is therefore an asymptotic one valid for large time, that is, for t > a lD. Actually in his paper he noted that the mean velocity across any plane x is zero, so the transfer of c across such planes depends only on the radial variation of c. He then made essentially the same assumption as above by assuming that in Eq. (4.6.14), if c were independent of x with t large, dddx would be independent of r. Therefore... 

Consider the growth of a small vapor or gas bubble, far from any other body, initially in equilibrium with a large volume of stationary liquid, as a result of a small displacement from equilibrium. The bubble maintains a spherical shape because of surface tension, and the liquid motion is purely radial. Note that this does not imply that the temperature or concentration field is likewise spherically symmetric. The governing equations and boundary... 

Upon integrating the continuity equation for the laminar, purely radial flow of an incompressible fluid, the liquid velocity u is found to be... 

For purely radial modes in a cylindrical cavity the contribution of these losses to the Q factor is given by... 

Moshe 1, Jackel S, Lumer Y, Meir A, Feldman R, Shimony Y (2010) Use of polycrystalline Nd YAG rods to achieve pure radially or azimuthally polarized beams from high-average-power lasers. Opt Lett 35 2511-2513... 

They proposed a pure radial splay model to describe the molecular arrangement aro d the lines of strength S = + 1. In investigations Mackley et al. made on a copolyester prepared from Ho mol % poly(ethylene terephthalate) and 60 mol % p-acetoxybenzoic acid, a number of integer disclinations were also observed. However, according to Viney and Windle who carried out some optical observations of Refects in the same copolyester, if disclinations of strength - 1/2 are not. seen below 3H0°C, they are more numerous than those of strength"1 above this temperature. These observations are at variance with results reported by Mackley et al. but seem to corroborate well with optical observations in polyester I (n = 5) made by Kleman et al.. One of the clearest conclusions of their study is obtained from the predominance of s = 1/2 lines ... 

The turbomachinery configurations are significantly different when implemented using lithography-based microfabrication techniques. The layout is purely radial, with the blade shapes... 

---