Penetration length

In this paper, we have exposed a solution to improve the resolution in Low Frequency Ultrasonic Tomography. Since the basic principle of ultrasonic reflection tomography prohibits the inspection of objects with strong contrast and large extension, we turn down the frequency of the transducer, in order to increase the penetration length of the wave and the validity of the method. But this is done at the expense of resolution. 

Jet Penetration. At the high gas velocities used in commercial practice, there are jets of gas issuing from distributor holes. It is essential that jets not impinge on any internals, otherwise the internals may be quickly eroded. Figure 14 is a graphical correlation used to determine the jet penetration length as a function of gas velocity and gas density. Jets from horizontal and downflow holes are considerably shorter than those that are pointed upward. 

When relating interface structure to strength, the literature is replete with analyses, which are based on the nail solution [1,58], as shown in Fig. 10. This model is excellent when applied to very weak interfaces (Gic 1 J/m ) where most of the fracture events in the interface occur on a well-defined 2D plane. However, the nail solution is not applicable to strong interfaces (Gic 100-1000 J/m ), where the fracture events occur in a 3D deformation zone, at the crack tip. In Fig. 10, two beams are bonded by E nails per unit area of penetration length L. The fracture energy G c, to pull the beams apart at velocity V is determined by... 

Reproduce penetration length of syringe needle into injector precisely. 

Vertical jet penetration in fluidized beds increases significantly with system pressure as shown in Fig. 18. Vertical jets fluctuate in the vertical direction between a minimum and a maximum value. Most jet penetration correlations are given in terms of the maximum jet penetration length which is designated Lmax (Hirsan et al. 1980). Over a pressure range of 1 to 50 bar with jet nozzles up to 3.8 cm in diameter, Hirsan et al. (1980) developed the following empirical correlation for the maximum jet penetration. 

Overall bed-to-surface heat transfer coefficient = Gas convective heat transfer coefficient = Particle convective heat transfer coefficient = Radiant heat transfer coefficient = Jet penetration length = Width of cyclone inlet = Number of spirals in cyclone = Elasticity modulus for a fluidized bed = Elasticity modulus at minimum bubbling = Richardson-Zaki exponent... 

The jet penetration lengths for upwardly and downwardly directed jets can be calculated from Eq. (1). These equations take into account the effects of pressure and temperature on jet penetration. Knowlton and Hirsan (1980) and Yates et al. found that the jet penetration increases significantly with system pressure. In addition, Sishtla et al. (1989) found that the jet penetration decreases with increasing system temperature. Bed... 

Hirsan, K., Sishtla, C., and Knowlton, T. M., The Effect of Bed and Jet Parameters on Vertical Jet Penetration Length in Gas Fluidized Beds, paper presented at the 73rd Annual AIChE Meeting, Chicago (1980)... 

Grid Jets as a Source of Attrition. Jet attrition affects only a limited bed volume above the distributor, which is defined by the jet length. As soon as the jet is fully submerged its contribution to the particle attrition remains constant with further increasing bed height. Figure 6 shows some respective experimental results by Werther and Xi (1993). The jet penetration length can be estimated by various correlations, e.g., Zenz (1968), Merry (1975), Yates et al. (1986) or Blake et al. (1990). 

In most commercial fluidized bed processes, the bed is much higher than the jet penetration length. There are several parameters that affect attrition in the jetting region, namely the design parameters of the distributor (i.e., orifice diameter, dor, open surface area, Aa, number of orifices, Nor) and the operating parameters (i.e., gas density, pg, volumetric flow rate, vg, superficial gas velocity, t/g, orifice velocity, uor). It holds... 

Ao has the meaning of a penetration length of surface diffusion. We can distinguish two limiting cases ... 

If a reference datum plane (h = 0) is set at the bottom of each of the capillaries shown in the previous Fig. 5.5, the expression for the total driving force, that is the piezometric pressure difference along the penetration length h for a capillary with an upward (I pgh cos a) or a downward (—pgh cos a) orientation, can be represented by following equation (Bouchon and Pyle, 2005b),... 

PE crystal, the penetration length of the mechanical excitation into the lamella was found to be about 5 nm. As a result, if the tie molecule ends in the lamella or continues and ends in an amorphous region, the axial forces it can be exposed to are very small. Such a tie molecule contributes very little to the strength of a semicrystalline solid. 

Quantitative analysis, which is often difficult, requires reducing the size of the diffusing particles and diluting the sample in a matrix such as KCl. KCl is the most often used, in spite of its hygroscopic properties and its affinity for organic matter, because of the considerable penetration length of the beam in this matrix. 

Figure 6.13 shows that for dense canopies (small (CoahC1) the penetration length-scale is a linear function of (CDah) 1. Deviation from linear behavior begins at... 

The incident angle of the reflected beam onto the detector is utilized in a factor often described as correcting for the flatness of a detector. The diffracted beam penetrates into the image plate or fluorescent layer of the detector. The penetration length depends on the angle of incidence and the linear attenuation factor for the utilized wavelength and fluorescent material. 

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