Mean equivalent diameter

Fig. 38. Ratio of D, ujD as a function of the amount of coke deposited for three HZSM-5 specimens (crystal type, as shown in Fig. 42, with mean equivalent diameters of 8.5 /Am (A), 14 /im ( ), and 28 /iw (v) and an HZSM-5 polycrystalline grain (O cf. Fig. 43) (131-133).

Prego et al., 1998). The embryo that surrounds the perisperm is dicotyledonous and is part of the bran fraction of the seed it is high in proteins and lipids, and contains most of the ash, fiber, and saponins (Mastebroek et al., 2000 Varriano-Marston and DeFrancisco, 1984). The shape of QS is similar to a flattened sphere their mean equivalent diameter varies from 1.4 to 1.6 mm (Chauhan et al., 1992a,b Vilche et al., 2003). As mentioned previously, carbohydrates, proteins, and lipids are the main component of the seeds, and they are mostly responsible for the functional properties that have made them new ingredients in the development of new products. 

Calculate the strength of an agglomerate of particles that may be considered spherical in shape with a mean equivalent diameter of 10.4 mm. The union strength per contact point is 2.4 x 10" kg, and the agglomerate is geometrically arranged in a simple cubic manner. 

For all samples, a peak is observed in the distribution at Df, 0.18mm but the shape of the distribution is different according to the foaming conditions. The Deq distribution is narrow for foam Al. For foam A2, the distribution spreads towards large values, which could result from a lowering of the size of the ultramacropores observed in Al. Finally, the distribution becomes narrow again for samples A3 and A4 (Fig. le). This trend is reflected in the evolution of the mean equivalent diameters and of the standard errors, as presented in Table 1. 

Define the mean equivalent diameter and its standard deviation. 

If the equivalent diameter (EqDiam) of the CFU object is found to be too large or too small, compared with the mean equivalent diameter of all found objects, then this CFU will be rejected (i.e., considered an artifact). IndexOfReject is the index of the matrix element returned by the find statement once the condition is met or fulfilled. StatReject=Stats(IndexOfReject) picks up only the rejected objects. 

These two nomographs provide a convenient means of estimating the equivalent diameter of almost any type of particle Figure 1 of regular particles from their dimensions, and Figure 2 of irregular particles from fractional free volume, specific surface, and shape. 

As mentioned, the data obtained by this method are expressed as cumulative size distribution curves. Since the computations assume Stokes law for spherical particles, the plotted curves give the distribution of spherical particles which would behave like the actual sample with respect to this experiment. For this reason, the sizes on the distribution curves should be labelled Stokes Equivalent Diameter . Because of the underlying assumptions and the above interpretation of the results, it is clear that the repeatability of this method has more meaning than accuracy of comparison with results of other methods... 

For the heat transfer for fluids flowing in non-circular ducts, such as rectangular ventilating ducts, the equations developed for turbulent flow inside a circular pipe may be used if an equivalent diameter, such as the hydraulic mean diameter de discussed previously, is used in place of d. 

If the persistence length Ip is much larger than the mean chain diameter, d, Yamakawa and Fujii gave limiting values for ai = - ln(d/2Ip) and = 0.1382. Freire and Garcia de la Torre [122] have considered further these coefficients. The factor 2Ip appears rather than Ip simply because 2Ip is equivalent to the statistical Kuhn segment length... 

The heat transfer coefficient to the vessel wall can be estimated using the correlations for forced convection in conduits, such as equation 12.11. The fluid velocity and the path length can be calculated from the geometry of the jacket arrangement. The hydraulic mean diameter (equivalent diameter, de) of the channel or half-pipe should be used as the characteristic dimension in the Reynolds and Nusselt numbers see Section 12.8.1. 

The equivalent diameter is used in place of the pipe diameter for non-circular ducts or partially full pipes. For example, it is used to calculate Re as a means of obtaining f. In determining ... 

Here we could be confused with two diameter terms. Remember, however, that d is really a means of expressing area, so Crane14 uses an equivalent diameter of actual flow area that is simply ... 

The calculated parameters X, qf, cp and ri are presented in Tables lb, lib and III. In addition the attachment equivalent diameter 3 was determined from the attachment coefficient 6 = X/Z by means of the attachment theory (Porstendorfer et al., 1979). 

Figure 28a shows the result of SAXS on sample BrlOOO. We used Guinier s formula (see eq. 6) for the small angle scattering intensity, I(k), from randomly located voids with radius of gyration, Rg. Although Guinier s equation assumes a random distribution of pores with a homogeneous pore size, it fits our experimental data well. The slope of the solid line in Fig. 28b gives R - 5.5 A and this value has been used for the calculated curve in Fig. 28a. This suggests a relatively narrow pore-size distribution with an equivalent spherical pore diameter of about 14A. Similar results were found for the other heated resin samples, except that the mean pore diameter changed from about 12 A for samples made at 700°C to about 15 A for samples made at 1100°C.

Equation 2.73 is another way of writing equation 2.13 where, in this case, the pressure drop is expressed in height of fluid instead of in force per unit area. In equation 2.73, de is the equivalent diameter defined as four times the cross-sectional flow area divided by the appropriate flow perimeter,/is the Fanning friction factor for flow in an open channel and u is the mean velocity. Combining equations 2.72 and 2.73, and solving for u gives... 

By size of pore one can mean the diameter of an equivalent cylindrical or the distance between the sides of a slit-shaped pore (i.e., in general a diameter of the largest circle that can be inscribed in a flat cross section of a pore of arbitrary form). The basis of this classification is that each of the size ranges corresponds to characteristic adsorption effect that is manifested in the isotherm of adsorption [53,115], In micropores, the interaction potential is significantly higher than in wider pores, owing to the proximity of the walls. This explains that such pores become totally full with adsorbate at low relative pressures. In mesopores, one will observe formation of mono- and then multilayer molecular film forming over the walls. After formation of a multilayer molecular film,... 

When a silicate solution such as sodium silicate is acidified, a gel of polymeric colloidal silicilic acid is formed as an agglomerate of micro-particles. When the gel is heated, water is expelled leaving a hard, glassy structure with voids between the micro-particles equivalent to a mean pore diameter of about 3 nm and an internal surface of about 500,000 m2/kg. As discussed by Everett and Stone(8) these properties may be varied by controlling the pH of the solution from which the gel is precipitated. 

The Malvern uses light scattering measurements to determine the weight percent of spherical equivalent crystals in each of 16 size classes and the mean size diameter. 

Equivalent radius Hydraulic radius Mean radius/diameter Sedimentation... 

We get particles of different sizes. Each has a mass equivalent diameter," which is the diameter of a sphere with the same mass as the particle. One can characterize the sizes with a cumulative mass distribution such as in the upper part of Figure 14-6. This shows which mass fraction is in the particle with a diameter smaller than a certain value. The frequency distribution underneath is derived from the upper diagram it gives an indication of which diameters are most common. We can try to characterize the drops with a single diameter there are many different ways in which this can be done. They lead to parameters such as the c 32 (Sauter diameter), dso (mean diameter) and dmax (maximum... 

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