Rectangular averaging

Traversing for Mean Velocity Mean velocity in a duct can be obtained by dividing the cross section into a number of equal areas, finding the local velocity at a representative point in each, and averaging the results. In the case of rectangular passages, the cross section is usually divided into small squares or rectangles and the velocity is found at the center of each. In circular pipes, the cross section is divided into several equal annular areas as shown in Fig. 10-7. Read-... 

The output filter converts the rectified rectangular ac waveform into the dc output. Forward-mode converters have a two-pole L-C filter which produces the dc average of the rectified rectangular waveform. Boost-mode converters have a single-pole, capacitive input filter which produces a dc voltage which is the peak voltage of the rectified waveform. Both are reactive impedance filters and exliibit very little loss. 

A microscopic description characterizes the structure of the pores. The objective of a pore-structure analysis is to provide a description that relates to the macroscopic or bulk flow properties. The major bulk properties that need to be correlated with pore description or characterization are the four basic parameters porosity, permeability, tortuosity and connectivity. In studying different samples of the same medium, it becomes apparent that the number of pore sizes, shapes, orientations and interconnections are enormous. Due to this complexity, pore-structure description is most often a statistical distribution of apparent pore sizes. This distribution is apparent because to convert measurements to pore sizes one must resort to models that provide average or model pore sizes. A common approach to defining a characteristic pore size distribution is to model the porous medium as a bundle of straight cylindrical or rectangular capillaries (refer to Figure 2). The diameters of the model capillaries are defined on the basis of a convenient distribution function. 

Right Fig. 11. Calculated ensemble average of magnetic moment and differential susceptibility for CNTs with rectangular (dotted lines) and triangular (dashed lines) circumference distributions having L , =22 A and L, =942.. 5 A. The solid lines denote experimental results [15],... 

The heat transfer and pressure drop in a rectangular channel with sintered porous inserts, made of stainless steels of different porosity, were investigated. The experimental set-up is shown in Fig. 2.9. Heat fluxes up to 6MW/m were removed by using samples with a porosity of 32% and an average pore diameter of 20 pm. Under these experimental conditions, the temperature difference between the wall and the bulk water did not exceed AT = 55 K at a pressure drop of AP = 4.5 bars (Hetsroni et al. 2006a). 

Fig. 72.—Number and weight average degrees of polymerization prior to gelation and for the sol after gelation vs. the over-all degree of cross-linking (p) for the rectangular distribution. ...

Cumo et al. (1969) reported that the pressure effect on the bubble diameter is linear in a Freon-114 flow, as shown in Figure 5.43. They tested the two-phase Freon-114 flow in a vertical rectangular test section at a mass flux of 100 g/cm2 s (0.737 x 106 lb/ft2 hr). The average bubble diameters at various system pressures were obtained from high-speed photographic recordings. The effect of reduced pressure, p pci, on the average diameter of Freon bubbles is correlated as... 

In 1962 Jottrand and Grunchard (J7) reported on mass transfer to a small rectangular nickel plate immersed in a liquid fluidized bed of sand particles. Mass-transfer rates were five to ten times higher than those measured in an open pipe flow a maximum rate was measured at a bed porosity of 0.58. Le Goff et al. (Lie) later showed that this maximum is directly related to a maximum in the average kinetic energy of the fluidized particles per unit bed volume. 

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