Channels shape

Vfjp is the friction velocity and =/pVV2 is the wall stress. The friction velocity is of the order of the root mean square velocity fluctuation perpendicular to the wall in the turbulent core. The dimensionless distance from the wall is y+ = yu p/. . The universal velocity profile is vahd in the wall region for any cross-sectional channel shape. For incompressible flow in constant diameter circular pipes, = AP/4L where AP is the pressure drop in length L. In circular pipes, Eq. (6-44) gives a surprisingly good fit to experimental results over the entire cross section of the pipe, even though it is based on assumptions which are vahd only near the pipe wall. 

The critical Reynolds number for transition from laminar to turbulent flow in noncirciilar channels varies with channel shape. In rectangular ducts, 1,900 < Re < 2,800 (Hanks and Ruo, Ind. Eng. Chem. Fundam., 5, 558-561 [1966]). In triangular ducts, 1,600 < Re < 1,800 (Cope and Hanks, Ind. Eng. Chem. Fundam., II, 106-117 [1972] Bandopadhayay and Hinwood, j. Fluid Mech., 59, 775-783 [1973]). 

Whipstock A long wedge and channel-shaped piece of steel with a collar at its top through which the subs and drillstring may pass. The face of the whipstock sets an angle to deflect the bit. 

Author Micro-channel Shape 4i [mm] Fluid Re P exp/POtheor Poiseuille number Dependence on Re Relative roughness % fe/rol RCcr... 

All available experimental data (except the data by Peng and Peterson 1996 Peng and Wang 1998) show that the friction factor is inversely proportional to the Reynolds number, i.e., A = const/Re. The constant depends on the micro-channel shape only and agrees fairly well with the result of a dimensional analysis carried... 

Flow is typically laminar in microchannel devices, although not always rigorously so. Correlations for fully developed laminar flow in perfectly rectangular microchannels have been validated in the literature [33-35]. Transition and turbulent flows in a microchannel have no such consistent treatise, and are highly dependent upon channel shape, aspect ratio, and surface characteristics [36, 37]. 

Besides channels with different cross-sections, channels with specific periodic shapes were considered by several authors, mostly in the framework of 2-D simulations. Three different channel shapes having been studied are shown in... 

Figure 2.18 Different channel shapes for which flow distributions have been computed, a zigzag (upper left), a sinusoidally curved (upper right) and a converging-diverging channel (bottom).

Also deoxycholic acid (6) crystallizes in an inclusion lattice with channel-shaped cavities 13). Figure 3 shows that they are formed by facing molecules of deoxycholic acid, 4). This characteristic structural unit is a double layer of head-to-tail linked deoxycholic acid molecules at which specific H-bridges between hydroxy and carboxy groups are the decisive fact. The channels as such (e.g. in case of the orthorhombic crystal, see Fig. 3) are lined with lipophilic groups. Thus only van der Waals contacts are kept between the included guest molecules (also for polar molecules like acetone, Fig. 3) and the molecules of the channel wall. 

These performance expressions were first developed by Bosworth (1948) for zero order, by Denbigh (1951) for second order, and by Cleland and Wilhelm (1956) for first order reactions. For other kinetics, channel shapes, or types of fluids insert the proper terms in the general performance expression and integrate. 

Recently, a set of correlations including the effect of channel shape has been proposed by Ramanathan et al. (2003) on the basis of solution of the Navier-Stokes equations in the channel, with different solutions derived for ignited-reaction and extinct-reaction regimes. The comparison of various empirical and theoretical correlations with experimentally evaluated mass transfer coefficients is given by West et al. (2003). The correlations by Ramanathan et al. (2003) or Tronconi and Forzatti (1992) have been used in most simulations presented in this chapter. 

Keulegan (Kl3), 1938 Extension of Prandtl-von KdrmSn turbulent flow theories to turbulent flow in open channels. Effects of wall roughness, channel shape, and free surface on velocity distribution are considered. 

The channel shape is properly cut into a spacer foil of low thermal conductive material which is inserted between the metal blocks. The material of the foil must be resistant to the solvents used within the range of operating tempera-... 

It is no surprise that monoliths are applied in many morphologies (cell sizes, wall thicknesses, channel shapes, materials of construction, microstructures (texture of the coating)) and overall dimensions. Monoliths are flexible to operate. They are well suited to optimal semi-batch, batch, continuous, and transient processing. Catalytic conversion can be... 

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