Tube of Rectangular Cross-Section

Now let us consider a tube of rectangular cross-section with sides a and b. We assume that the flow region is described by the inequalities 0 X a and 0 Y b. The solution of Eq. (1.5.1) under the no-slip conditions on the tube surface has the form [179] 

By integrating the expression for V, we obtain the volume rate of flow 

For a tube of square section with side a, this formula acquires the form 

Now we suppose that the cross-section of the tube is an equilateral triangle with side b. We place the origin at the center of the cross-section and measure the coordinate X along one of the sides of the triangle. In this case, the solution of Eq. (1.5.1) under the boundary condition (1.5.2) has the form 

The volume rate of flow of this flow is given by the formula 

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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. 

The channel flow cell has been used to study a wide variety of liquid-solid reactions. It consists of a tube of rectangular cross section, typically 4.5 cm long by 0.6 cm wide by 0.1 cm deep (Fig. 5.20). The reactive solid is embedded in the base of the cell and a detector downstream of the reactive solid is used to monitor reactant and product concentrations. 

The Tiselius cell consists of a U-tube of rectangular cross-section, which is divided into a number of sections built up on ground-glass plates so that they can be moved sideways relative to one another. The protein solution is dialysed against buffer (to avoid subsequent disturbance of the boundary by osmotic flow), and then the sections of the cell are filled with buffered protein solution or buffer solution, for example, as shown in Figure 7.8. Large electrode vessels containing reversible electrodes are then attached, and the whole... 

The use of tubes of rectangular cross section provides a maximum amount of wall area and so facilitates the removal of heat to the surroundings, and the maintenance of the apparatus at somewhat below 4 , where the variation of the density of the liquid with temperature is very small, greatly diminishes convection effects. With these improvements, and a device for obtaining initially sharp boundaries, the macroscopic method has proved a valuable means for the study of electrophoresis, and for its utilization to separate particles moving with different speeds. 

A similar idea forms the basis for the operation of the Mintex/RSM slurry analyser based on the work of Holland-Batt the slurry is pumped through a single-turn helical tube of rectangular cross-section and yS-ray attenuation measurements before the helix and at different positions just after the helix (where particle stratification occurs due to centrifugal forces) yield a point on size distribution data. The instrument requires calibration, which can be made at any selected reference size in the range of 10 to 105 pm. 

The measurement of particle velocity in microelectrophoresis is carried out with a type of apparatus shown schematically in Fig. 7.3.1 (Shaw 1969). The apparatus consists basically of a microscope with a calibrated reticule for the observation of the individual particles, a thin flat cell of rectangular cross section, although long cylindrical cells are also used, electrodes across which the potential is applied, and a system of tubing and stopcocks for filling and cleaning the cell and electrode compartments. 

The wheat drying studies were carried out in a spouted bed predryer of rectangular cross section equipped with a draft tube, and also in a cylindrical afterdryer (Tables 15.1 and 15.2). The experimental conditions and the data of the... 

Embedded. Rectangular-cross-section aluminum fin which is wrapped under tension and mechanically embedded in a groove 0.25 0.05 mm (0.010 0.002 in) deep, spirally cut into the outside surface of a tube. 

A novel route for the synthesis of Si02 and Ti02 nanotubes with rectangular cross-section is developed. The high metal content renders these composites attractive materials for nanoelectronics. For probable applications as nanowires the synthesis route must be further optimized to obtain tubes, which are uniform in length and width containing uniformly distributed Pt. 

Numerous fin corrugations have been developed, each with its own special characteristics (Figure 15). Straight fins and straight perforated fins act like parallel tubes with a rectangular cross section. Convective heat exchange occurs due to the friction of the fluid in contact with the surface of the fin. The channels of serrated fins are discontinuous, and the walls of the fins are offset. For air flows,... 

Tube Reactor, Parallel Flow A sketch of this reactor configuration is shown in Figure 17. Here the reactant gas or gas mixture flows axially down a tube (circular or rectangular cross section) over a heated susceptor... 

In axial-flow viscometers, the sample is made to flow through a duct of regular cross-section. Capillary (circular cross-section) and slit (rectangular cross-section) viscometers are controlled stress instruments a known pressure difference (which causes shear stress in the sample) is applied over the duct length, and the resulting volumetric flow rate measured. In the extrusion viscometer, a controlled shear rate instrument, the sample is extruded through a capillary tube by the action of a constant speed piston, acting on the sample in a cylindrical reservoir to which the capillary is attached. The pressure difference between the ends of the capillary is measured. 

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