Data sets friction factor

Figure 4.9. Best-fit friction factor y versus experimental time span for 43-bp fragment. The sample is in 0.1 M NaCl, 10 mM cacodylate, 1 mM EDTA, at pH 8.6 and T = 20°C. Twelve data sets were averaged to obtain the best-lit friction factors for each time span. The dashed line is the average of the best-fit values for all four time spans.

The remaining information necessary to derive the heat mass transfer and pressure drop relationships for the regular polygons are the Nusselt Number and Friction Factor (9) for each of these shapes. A set of data for these two shape related quantities is given in Figure 1, where the Friction Factor and average Nusselt Number are plotted against a shape value [l/(l+l/fl)], where n... 

The diffusion coefficient at high cs decreases with increasing molecular weight. This is similar to neutral polymers where the diffusion coefficient is inversely dependent on the friction factor, which is proportional by the power law to polymer molecular weight, i.e., D =/ 1 = M v. The diffusion coefficient at low cs is, on the other hand, independent of polymer molecular weight. This can be also documented by a more detailed data set on molecular weight standards of NaPSS [13] (Figure 8). 

One source of information, hydrodynamic measurements, has recently been reviewed by Squire and Himmel ( ) Their analysis suggests large amounts of water associated with globular proteins, but even their restricted data set shows large variations between the amount of hydration calculated from sedimentation or diffusion results. Because the cube of the friction factor enters into the... 

This equation says that for a given set of cost data the economic velocity is independent of the mass flow handled and dependent on only the. fluid density and the friction factor. More thorough analyses and far more complicated cost equations lead to substantially the same conclusion. For example, for schedule 40 carbon-steel pipe, Boucher and Alves [16] give the data shown in Table 6.4. 

Fig. 11.10 Comparison of the measured storage-modulus spectra of samples A (o and ), B ( and ), C (a and a), and D (o and ) with those calculated (solid lines) using the Rouse theory for both the G1 and GIO components. In calculating the spectra, the frictional factor K is set to be 10 for sample A (line 1) 10 for sample B (line 2) 10 for sample G (line 3) and 10 for sample D (line 4) to avoid overlapping of the lines and the data points. The comparison is made for each sample by shifting the measured spectrum along the frequency axis to match the calculated in the high-frequency bump region.

In this section, experimental data from a friction factor experiment will be considered. This data set consists of four separate runs performed on different pipe diameters collected on different days (often with a large separation in time). 

Table 1.5 Summary statistics for the friction factor data set...

Figure 8. Time-temperature superposition analysis of frictional data collected on thin PMMA. (a) Temperature dependence offriction at four scan velocities (b) same data inverted, i.e. scan-velocity dependence of friction at multiple temperatures (c) master curve of same data sets as in (b), but shifted by variable multiplicative factors af, (d) plot of shift factors ar versus inverse temperature, with linear fit.

To compare the 325 x 2300 LH2, LOX, and GHe FTS test data, all the data sets can be cast into a non-dimensional form in the same way as the historical data in Chapter 3 using equations in Chapter 3 for friction factor and modified LAD screen Re number. FTS data for the exact same 325 x 2300 screen sample are plotted in LH2, LOX, and GHe in Figure 9.15. Data is plotted on a log/log scale as friction factor versus screen Re number. Also plotted for reference is the curve fit using the room temperature fitting parameters for Dutch Twills from Chapter 3. The nominal temperatures for LH2, LOX, and GHe data sets were 24,91, and 296 K, respectively, though the data sets include measurements taken at different LOX and LH2 temperatures. 

Figure 6.1.3 is useful in showing thow the (solids free) gas friction factor in conical- and cylindrical-bodied cyclones varies with cyclone Reynolds number and relative wall roughness, that is fair = f kg/R,Rep). Even so, if we wish to incorporate it into a cyclone computer model, we need to express this functional relationship in equation form. Although the dependency between the variables shown in Fig. 6.1.3 is very nonlinear, and difficult to fit , the authors have developed a set of equations that fit the entire range of fair, kg/R and Rep values shown in Fig. 6.1.3 for both conical- and cylindrical-bodied cyclones. These empirical equations have a maximum error of about 20 to 22% relative to the data points shown in Fig. 6.1.3. This error decreases, of course, with increasing solids loading. The gas phase friction factors computed with the empirical curve fits shown below have proven sufficiently accurate for most design applications.

The search for complete understanding of friction properties led to the methods (17), (18) accounting for the combined effects of the main factors. Prom Ref. (l ) relations are found for the friction coefficient, temperature, wear rate versus sliding velocities and loads. Then by the data obtained, a set of curves is drawn in P — V coordinates, having the same values of the friction coefficient, temperature, and wear rate. It is clear that great difficulties arise in obtaining and using this volume of information. Crease (j ) finds only... 

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