Roughness factor, calculation

Roughness factor calculated for a fractal surface, according to the fractal dimension D and probe area a... 

Table 2 Roughness Factor Calculated for a Fractal Surface, According to the Fractal Dimension D and Probe Area a... 

Effective roughness factor calculated by correcting for the increase of contact line density at the... 

The uncertainty in the product, 200 calories, is not simply the sum of the uncertainties in the factors, 0.4°C and 2 grams. Instead, the sum of the percentage uncertainties in the factors determines the uncertainty in a product or a quotient. Fortunately, there is an easy method for estimating it roughly without calculating percentages. This method, based upon the number of figures written, is described in Section 1-2.5. 

Figure 2-41 is a cyclic voltanunogram of an electrochemically platiniaed platinum electrode in 3 M sulfuric add. It is almost the same as that on a smooth platinum electrode. The roughness factor was calculated as ... 

The electrode roughness factor can be determined by using the capacitance measurements and one of the models of the double layer. In the absence of specific adsorption of ions, the inner layer capacitance is independent of the electrolyte concentration, in contrast to the capacitance of the diffuse layer Q, which is concentration dependent. The real surface area can be obtained by measuring the total capacitance C and plotting C against Cj, calculated at pzc from the Gouy-Chapman theory for different electrolyte concentrations. Such plots, called Parsons-Zobel plots, were found to be linear at several charges of the mercury electrode. ... 

Since the factors f are known for only a couple of substances, only more or less rough empirical calculations are possible k To illustrate die concentration dependency of die activity factor f. Table 7.1 lists it for some substances. 

Hints and Help The friction factor, /, calculated from Eq. 24-4 may turn out to be extremely large, which would indicate a very rough riverbed. In fact, in the River Glatt in between the cascades there are small drops every 50 m. Use this fact to explain the rather extreme value of /. ... 

Since the Wenzel roughness factor is an important parameter in many theoretical considerations of wetting phenomena [11-21], it was also calculated as the ratio between the actual surface area to the projected one (Eq. 4). A surface of hexagonally packed hemispheres is considered. In this case, the roughness factor is independent of the particle radii and approximately equal to 1.91 [31,40,41] ... 

The maximum isosteric differential heat of adsorption interpolated from the heat-coverage plots. c The roughness factor is defined as the ratio of the experimental values of the weight of adsorbate required for monolayer coverage to that calculated for the same coverage of a geometrically planar surface. It can be interpreted as the ratio of the real area to the apparent area of the adsorbent. 

Obtain the fnction factor from Figure 8.16 after calculating the Reynolds number and the relative roughness, s/D, for the pipe. From Table 8.4, the roughness factor for steel pipe, s =1.5x10 ft (4.57x10 m). 

Practicing electrochemists who, for years, have worked with dropping or hanging mercury drops never had to face this problem, because the roughness factor for the very smooth surface of the mercury is unity. On the contrary, for solid electrodes, the surface is never perfectly smooth and a roughness factor has to be introduced in calculations. 

Having collected all needed intensity data under the most favorable conditions possible, the crystallographer processes the data, applying absorption corrections and, if necessary, corrections for decomposition of the crystal, and arrives at his data set, consisting of the values of F j / or F / 2, either unsealed or with a rough scale factor calculated by statistical methods. Each datum should be accompanied by a standard deviation o that represents random error (and possible random effects of systematic errors) as derived, for example, with Eq. (13). 

The determination of the real surface area of the electrocatalysts is an important factor for the calculation of the important parameters in the electrochemical reactors. It has been noticed that the real surface area determined by the electrochemical methods depends on the method used and on the experimental conditions. The STM and similar techniques are quite expensive for this single purpose. It is possible to determine the real surface area by means of different electrochemical methods in the aqueous and non-aqueous solutions in the presence of a non-adsorbing electrolyte. The values of the roughness factor using the methods based on the Gouy-Chapman theory are dependent on the diffuse layer thickness via the electrolyte concentration or the solvent dielectric constant. In general, the methods for the determination of the real area are based on either the mass transfer processes under diffusion control, or the adsorption processes at the surface or the measurements of the differential capacitance in the double layer region [56],... 

Line 5 in Fig. 5 is calculated for a surface having slight roughness, according to Eq. 34 and 39. The hydrodynamic roughness factor R is chosen so that this line connects the origin with the experimental point for the highest value of 5. This yielded a value of K = 1.3. 

Fig. 5 Dependence of the parameter AF/pf on the velocity decay length points experimental data, line 1 in both plots indicates an ideally smooth surface, a Influence of strong roughness according to Eq. 44 for different values of -2 69, 3 172, 4 276 nm) and L = 506 nm. b The same for different values of L 2 460, 3 506, 4 690 nm and fn = 172 nm. Line 5 in both plots was calculated for slight roughness (roughness factor R = 1.3, Eqs. 34 and 39). (From [27])...

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