Berman velocity profile

Table 14.14 gives the results of calculation of these centrifuge parameters for the Berman-Olander velocity profile (14.214) for UFs at 300 K and peripheral speeds of 400, 500,... 

As this table shows, concentration of counterflow near the outer wall of the centrifuge in the Berman-OIander profile has these principal effects compared with the optimum uniform mass velocity distribution ... 

Because of the transverse velocity component, the velocity profile is a modification of the usual Poiseuille distribution. This problem has been solved by Berman (1953), including the effect of a constant permeation velocity in altering the velocity profile in the x direction and in causing a streamwise variation in the bulk average velocity. However, when the Reynolds number based on the permeation velocity is small, as it generally is, the streamwise component has the same form as for an impermeable wall and the transverse component is proportional to the constant permeation velocity v -, that is,... 

For the far downstream region Dresner used the more accurate approxim-tion to Berman s velocity profile given by Eq. (4.4.6) and showed that, for... 

Finite difference solutions of the full diffusion equation using the more accurate velocity profile of Berman and the boundary condition = -D dd y)iv were obtained by Sherwood et al. (1965). The results are shown in Fig. 4.4.3, where the comparison is seen to be excellent. The curve labeled Analytic (developing) is made up from overlapping the large and small formulas given above. 

Berman has given the exact velocity profiles for the case of a uniform flux of water through the membrane. 

In order to solve (differential) Equation 8.3 under boundary condition Equations 8.4,8.5, and 8.6, the velocity profiles u and v, as a function of the rectangular coordinate (jc, y), have to be known. Berman derived the following equations to describe the velocity profile in a channel between two flat porous plates placed in parallel [277]. 

Berman s treatment of centrifuge hydrodynamics is an attempt to obtain the shape of the axial velocity profile without resorting to the extensive numerical computations employed by Parker (JO). In keeping with the long bowl model, the axial velocity is taken to be a function of radial positions only. The radial and angular components u and v are assumed zero. 

In order to sustain an axial velocity profile by Berman s method, a radial temperature gradient is imposed upon the system. The feed tube at r = ro is taken to be somewhat hotter than the rotor wall at r = rj. Because of this specification, the variation of T with z is neglected. This constitutes a significant departure from Soubbaramayer s approach, in which the axial temperature gradient could not be set equal to zero. 

Ftt . 12. Density-weighted axial velocity profiles. Parker,. 4 25 O Berman, A... 

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