Rectangular channel

Equation (6.27) was obtained for circular channels. Rectangular channels with four or three conductive walls are shown in Eig. 6.10. 

There are only two basic flow channel geometries that are rather easy to analyze the circular flow channel and the slit flow channel (rectangular cross section with W H). Most other geometries are quite difficult to analyze. 

FIGURE 19.1 Scanning electron micrographs of cross-sections of (a) uncoated and (b) coated PDMS channels. Rectangular PDMS channel dimensions are 50 x 35 pm. This fabrication method combines the ease of soft lithography processing with the benefits of a glass surface. (Reprinted from Abate, A. R. et al. 2008. Lab Chip 8 516-518. With permission.)... 

We consider a co-extrusion die consisting of an outer circular distribution channel of rectangular cross-section, connected to an extrusion slot, which is a slowly tapering narrow passage between two flat, non-parallel plates. The polymer melt is fed through an inlet into the distribution channel and flows into... 

Both microwave and millimetre wave radiation can be channelled in any direction by a waveguide made from metal tubing of rectangular cross-section, the dimensions depending on the frequency range. The absorption cell is also made from waveguide tubing. 

In the Davy-Powergas unit (118—120), shown in Figure 13c, the Hquids mn through a draft tube and are pumped by an impeller mnning directly above the draft tube. The dispersion flows out from the top of the mixer and down through a channel into a rectangular settler. Large units of this type are used for copper extraction (7). 

Measurement by Liquid Level. The flow rate of Hquids flowing in open channels is often measured by the use of weirs (see Liquid-LEVEL measurement). The most common type is the rectangular weir shown in Figure 22e. The flow rate across such a weir varies approximately with the quantity. Other shapes of weirs are also employed. Standard civil engineering handbooks describe the precautions necessary for constmcting and interpreting data from weirs. 

A numerical study of the effect of area ratio on the flow distribution in parallel flow manifolds used in a Hquid cooling module for electronic packaging demonstrate the useflilness of such a computational fluid dynamic code. The manifolds have rectangular headers and channels divided with thin baffles, as shown in Figure 12. Because the flow is laminar in small heat exchangers designed for electronic packaging or biochemical process, the inlet Reynolds numbers of 5, 50, and 250 were used for three different area ratio cases, ie, AR = 4, 8, and 16. 

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]). 

For gradual changes in channel cross section and hquid depth, and for slopes less than 10°, the momentum equation for a rectangular channel of width b and liquid depth h may be written as a differential equation in the flow direction x. 

Liquid flow in an open channel may be metered by means of a weir, which consists of a dam over which, or through a notch in which, the liquid flows. The terms rectangular weir, triangular weir, etc., generally refer to the shape of the notch in a notched weir. AU weirs considered here have flat upstream faces that are perpendicular to the bed aud walls of the channel. 

OPTIMISATION OF MICROBAND ELECTRODE SIZES AND LOCATIONS WITHIN A RECTANGULAR MICROFLUIDIC CHANNEL FOR ELECTROCHEMICAL MONITORING OF HYDRODYNAMIC FLOW PROFILES... 

Tables 30.7, 30,8 and 30.9 for rectangular, tubular and channel sections respectively, give the d.c. resistance and...

As a result of the electric field around the conductors the frequency of the system has a very significant bearing on the skin effect. The various curves as established through experiments and, as reproduced in Figures 28.13 (a), (b) and (c) respectively for rectangular, tubular and channel conductors, are thus drawn on the basis. 

Consider channels in a box form for the same requirements and operating conditions as for rectangular sections. 

The rectangular element valve, as the name implies, uses rectangular-shaped sealing elements. These valves are the feather valve, channel valve, and the reed valve. These valves are applied to the industrial air machines for the most part. A channel valve is shown in Figure 3-10. 

Most processing methods involve flow in capillary or rectangular sections, which may be uniform or tapered. Therefore the approach taken here will be to develop first the theory for Newtonian flow in these channels and then when the Non-Newtonian case is considered it may be seen that the steps in the analysis are identical although the mathematics is a little more complex. At the end of the chapter a selection of processing situations are analysed quantitatively to illustrate the use of the theory. It must be stressed however, that even the more complex analysis introduced in this chapter will not give precisely accurate... 

Example 5.13 Derive an expression for the flow length of a power law fluid when it is injected at constant pressure into a rectangular section channel assuming... 

Polyethylene is injected into a mould at a temperature of 170°C and a pressure of 100 MN/m. If the mould cavity has the form of a long channel with a rectangular cross-section 6 mm X 1 mm deep, estimate the length of the flow path after 1 second. The flow may be assumed to be isothermal and over the range of shear rates experienced (10 -10 s ) the material may be considered to be a power law fluid. 

Using the data in Tables 5.1 and 5.2, calculate the flow lengths which would be expected if the following materials were injected at 100 MN/m into a wide rectangular cross-section channel, 1 mm deep. 

The sodium channels are very selective for Na+ over K+, allowing Na+ influx down the electrochemical gradient to generate positive membrane potentials. The sodium channels are also permeable to Li+ and NH4+. The narrowest portion of the channel pore is estimated to be rectangular (3.1 x 5.2 A). 

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